From 4db8cce170edfe702f967c86670649139d8e28c3 Mon Sep 17 00:00:00 2001
From: JunkaiWang-TheoPhy <1181100960@qq.com>
Date: Thu, 30 Jul 2026 20:03:02 +0800
Subject: [PATCH 1/3] Submit Wander Issue 276 quantum geometry

Add the self-contained Quantum Harness capsule for non-Abelian projector geometry as a chaos probe in an exactly degenerate Laughlin manifold. Include source, tests, seven figures, the 17-page article, technical report, release manifest, artwork, bilingual caption, and Wander team metadata.

Scope: Changes are confined to tracks/mps/solutions/Wander-276 and preserve the public research release at commit d0a03ae.

Tested: bash tracks/mps/solutions/Wander-276/verify.sh; 17/17 release checks; 38/38 focused tests

Co-authored-by: OmX <omx@oh-my-codex.dev>
---
 tracks/mps/solutions/Wander-276/PR_BODY.md    |   78 +
 tracks/mps/solutions/Wander-276/README.md     |   66 +
 .../research/00_main/main_dashboard.md        |   48 +
 .../research/01_task_folder/task_05/README.md |  138 ++
 .../task_05/script/lgeth/__init__.py          |  117 ++
 .../task_05/script/lgeth/bundle_geometry.py   |  422 ++++++
 .../task_05/script/lgeth/channels.py          |  230 +++
 .../task_05/script/lgeth/combinatorics.py     |  223 +++
 .../task_05/script/lgeth/controls.py          |  341 +++++
 .../task_05/script/lgeth/form_factors.py      |  272 ++++
 .../task_05/script/lgeth/grassmann.py         |  350 +++++
 .../task_05/script/lgeth/holonomy.py          |  267 ++++
 .../task_05/script/lgeth/jacobi.py            |  312 ++++
 .../task_05/script/lgeth/lattice.py           |  489 +++++++
 .../task_05/script/lgeth/manybody_response.py |  459 ++++++
 .../task_05/script/lgeth/root_operators.py    |  142 ++
 .../task_05/script/lgeth/statistics.py        |  570 ++++++++
 .../task_05/script/lgeth/twist_bundle.py      |  332 +++++
 .../task_05/script/lgeth/wick_channels.py     |  442 ++++++
 .../make_geometric_eth_topology_assets_v3.py  |  272 ++++
 .../script/make_large_scale_figures_v1.py     |  811 +++++++++++
 ..._matrix_element_geometric_eth_figure_v3.py |  334 +++++
 .../script/make_release_manifest_v1.py        |  232 +++
 .../make_spectral_silence_figures_v2.py       | 1088 ++++++++++++++
 .../make_topological_holonomy_figure_v3.py    |  454 ++++++
 .../script/output/citation_audit_v1.json      | 1266 +++++++++++++++++
 .../script/output/covariance_model_v1.json    |  108 ++
 .../output/figure_1_physical_law_v1.pdf       |  Bin 0 -> 62269 bytes
 .../output/figure_1_physical_law_v1.png       |  Bin 0 -> 233772 bytes
 .../output/figure_1_spectral_silence_v2.pdf   |  Bin 0 -> 53192 bytes
 .../output/figure_1_spectral_silence_v2.png   |  Bin 0 -> 318452 bytes
 .../figure_2_falsification_triangle_v2.pdf    |  Bin 0 -> 46270 bytes
 .../figure_2_falsification_triangle_v2.png    |  Bin 0 -> 201455 bytes
 .../output/figure_2_scale_hierarchy_v1.pdf    |  Bin 0 -> 43540 bytes
 .../output/figure_2_scale_hierarchy_v1.png    |  Bin 0 -> 287229 bytes
 .../output/figure_3_atom_crossover_v1.pdf     |  Bin 0 -> 79606 bytes
 .../output/figure_3_atom_crossover_v1.png     |  Bin 0 -> 251936 bytes
 .../figure_3_independent_channels_v2.pdf      |  Bin 0 -> 43648 bytes
 .../figure_3_independent_channels_v2.png      |  Bin 0 -> 217515 bytes
 .../script/output/figure_4_finite_size_v1.pdf |  Bin 0 -> 32470 bytes
 .../script/output/figure_4_finite_size_v1.png |  Bin 0 -> 102729 bytes
 .../figure_4_geometric_hierarchy_v2.pdf       |  Bin 0 -> 50266 bytes
 .../figure_4_geometric_hierarchy_v2.png       |  Bin 0 -> 256963 bytes
 .../figure_5_covariance_mechanism_v1.pdf      |  Bin 0 -> 36785 bytes
 .../figure_5_covariance_mechanism_v1.png      |  Bin 0 -> 251139 bytes
 .../output/figure_5_jacobi_atoms_v2.pdf       |  Bin 0 -> 43197 bytes
 .../output/figure_5_jacobi_atoms_v2.png       |  Bin 0 -> 332956 bytes
 .../output/figure_6_wick_factorization_v3.pdf |  Bin 0 -> 26905 bytes
 .../output/figure_6_wick_factorization_v3.png |  Bin 0 -> 346911 bytes
 .../figure_7_topological_holonomy_v3.pdf      |  Bin 0 -> 29598 bytes
 .../figure_7_topological_holonomy_v3.png      |  Bin 0 -> 289213 bytes
 .../script/output/figure_manifest_v1.json     |   67 +
 .../script/output/figure_manifest_v2.json     |   77 +
 .../script/output/figure_manifest_v3.json     |   42 +
 ..._local_repulsion_to_global_geometry_v1.pdf |  Bin 0 -> 513246 bytes
 .../script/output/generated_numbers_v1.tex    |   30 +
 .../script/output/generated_numbers_v2.tex    |   22 +
 .../script/output/generated_numbers_v3.tex    |   30 +
 .../script/output/generated_tables_v1.tex     |   13 +
 .../script/output/generated_tables_v2.tex     |   13 +
 .../script/output/generated_tables_v3.tex     |   10 +
 .../geometric_eth_topology_assets_v3.json     |   24 +
 ...metric_eth_topology_delivery_audit_v3.json |  191 +++
 .../output/large_scale_delivery_audit_v1.json |  111 ++
 .../matrix_element_delivery_audit_v3.json     |   59 +
 .../matrix_element_geometric_eth_v3.json      |  260 ++++
 .../matrix_element_geometric_eth_v3.npz       |  Bin 0 -> 53248 bytes
 .../matrix_element_topology_theory_v3.json    |   30 +
 .../script/output/physical_ensemble_v1.json   |   49 +
 .../task_05/script/output/pytest_v1.txt       |    2 +
 .../task_05/script/output/pytest_v2.txt       |    2 +
 .../script/output/rank_scaling_v1.json        |  256 ++++
 .../script/output/release_manifest_v1.json    |  334 +++++
 ...pectral_silence_and_geometric_chaos_v2.pdf |  Bin 0 -> 550522 bytes
 ...pectral_silence_and_geometric_chaos_v3.pdf |  Bin 0 -> 672204 bytes
 .../spectral_silence_delivery_audit_v2.json   |  147 ++
 .../spectral_silence_statistics_v2.json       |  141 ++
 .../output/spectral_silence_statistics_v2.npz |  Bin 0 -> 86073 bytes
 .../script/output/spectral_silence_v2.json    |  103 ++
 .../output/statistical_analysis_v1.json       |  399 ++++++
 .../script/output/statistical_analysis_v1.npz |  Bin 0 -> 63060 bytes
 ...opological_holonomy_delivery_audit_v3.json |   72 +
 ...ogical_holonomy_mesh12_alias_audit_v3.json |  309 ++++
 .../output/topological_holonomy_v3.json       |  332 +++++
 .../script/output/topological_holonomy_v3.npz |  Bin 0 -> 3785530 bytes
 .../task_05/script/requirements.txt           |    7 +
 .../task_05/script/run_covariance_model_v1.py |  458 ++++++
 .../task_05/script/run_full_recompute_v1.sh   |   11 +
 .../run_geometric_eth_topology_article_v3.sh  |   41 +
 .../script/run_large_scale_article_v1.sh      |   38 +
 .../run_matrix_element_geometric_eth_v3.py    |  575 ++++++++
 .../script/run_physical_ensemble_v1.py        |  235 +++
 .../task_05/script/run_quick_verify_v1.sh     |   15 +
 .../task_05/script/run_rank_scaling_v1.py     |  472 ++++++
 .../script/run_spectral_silence_article_v2.sh |   23 +
 .../run_spectral_silence_statistics_v2.py     |  721 ++++++++++
 .../task_05/script/run_spectral_silence_v2.py |  684 +++++++++
 .../script/run_statistical_analysis_v1.py     |  597 ++++++++
 .../script/run_topological_holonomy_v3.py     |  877 ++++++++++++
 .../script/tests/test_bundle_geometry_v3.py   |  144 ++
 .../task_05/script/tests/test_controls_v2.py  |  109 ++
 .../tests/test_covariance_model_runner.py     |   41 +
 .../script/tests/test_form_factors_v2.py      |  152 ++
 .../test_geometric_eth_topology_article_v3.py |   34 +
 .../test_geometric_eth_topology_assets_v3.py  |   73 +
 .../task_05/script/tests/test_holonomy_v3.py  |  132 ++
 .../script/tests/test_independent_core.py     |   65 +
 .../script/tests/test_large_scale_delivery.py |   34 +
 .../script/tests/test_large_scale_figures.py  |   35 +
 .../tests/test_large_scale_statistics.py      |   59 +
 .../script/tests/test_manybody_response_v3.py |  136 ++
 ...atrix_element_geometric_eth_delivery_v3.py |   40 +
 ..._matrix_element_geometric_eth_figure_v3.py |   47 +
 ..._matrix_element_geometric_eth_runner_v3.py |   91 ++
 .../test_matrix_element_topology_theory_v3.py |   27 +
 .../tests/test_physical_ensemble_runner.py    |   38 +
 .../script/tests/test_rank_scaling_runner.py  |   59 +
 .../script/tests/test_release_contract_v1.py  |   73 +
 .../test_spectral_silence_delivery_v2.py      |   55 +
 .../tests/test_spectral_silence_figures_v2.py |   72 +
 .../tests/test_spectral_silence_runner_v2.py  |   51 +
 .../test_spectral_silence_statistics_v2.py    |   87 ++
 .../test_topological_holonomy_delivery_v3.py  |   69 +
 .../test_topological_holonomy_runner_v3.py    |   82 ++
 .../script/tests/test_twist_bundle_v3.py      |   74 +
 .../script/tests/test_wick_channels_v3.py     |  190 +++
 .../task_05/script/validate_citations_v1.py   |  685 +++++++++
 ...erify_geometric_eth_topology_article_v3.py |  282 ++++
 .../script/verify_large_scale_article_v1.py   |  360 +++++
 .../verify_matrix_element_geometric_eth_v3.py |  203 +++
 ...erify_matrix_element_topology_theory_v3.py |  220 +++
 .../script/verify_release_contract_v1.py      |  218 +++
 .../verify_spectral_silence_article_v2.py     |  474 ++++++
 .../script/verify_topological_holonomy_v3.py  |  272 ++++
 .../task_05/task_05_dashboard.md              |  407 ++++++
 .../Wander-276/research/CITATION.cff          |   29 +
 .../mps/solutions/Wander-276/research/LICENSE |  674 +++++++++
 .../solutions/Wander-276/research/README.md   |   69 +
 ...uantum-geometry-harness-challenge-draft.md |   94 ++
 .../docs/2026-07-30-task05-pr-body.md         |   90 ++
 .../2026-07-30-task05-pr-review-comment.md    |   25 +
 ...6-07-30-task05-public-release-checklist.md |   59 +
 .../docs/2026-07-30-task05-release-notes.md   |   39 +
 .../2026-07-30-task05-technical-report.md     |  148 ++
 .../geometric_eth_large_scale/.gitignore      |    8 +
 .../appendices/matrix-element-topology-v3.tex |  128 ++
 .../appendices/numerical-methods.tex          |  246 ++++
 .../figures/figure_1_physical_law_v1.pdf      |  Bin 0 -> 62269 bytes
 .../figures/figure_1_spectral_silence_v2.pdf  |  Bin 0 -> 53192 bytes
 .../figure_2_falsification_triangle_v2.pdf    |  Bin 0 -> 46270 bytes
 .../figures/figure_2_scale_hierarchy_v1.pdf   |  Bin 0 -> 43540 bytes
 .../figures/figure_3_atom_crossover_v1.pdf    |  Bin 0 -> 79606 bytes
 .../figure_3_independent_channels_v2.pdf      |  Bin 0 -> 43648 bytes
 .../figures/figure_4_finite_size_v1.pdf       |  Bin 0 -> 32470 bytes
 .../figure_4_geometric_hierarchy_v2.pdf       |  Bin 0 -> 50266 bytes
 .../figure_5_covariance_mechanism_v1.pdf      |  Bin 0 -> 36785 bytes
 .../figures/figure_5_jacobi_atoms_v2.pdf      |  Bin 0 -> 43197 bytes
 .../figure_6_wick_factorization_v3.pdf        |  Bin 0 -> 26905 bytes
 .../figure_7_topological_holonomy_v3.pdf      |  Bin 0 -> 29598 bytes
 .../generated/generated_numbers_v1.tex        |   30 +
 .../generated/generated_numbers_v2.tex        |   22 +
 .../generated/generated_numbers_v3.tex        |   30 +
 .../generated/generated_tables_v1.tex         |   13 +
 .../generated/generated_tables_v2.tex         |   13 +
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 .../geometric_eth_large_scale/main.pdf        |  Bin 0 -> 672204 bytes
 .../geometric_eth_large_scale/main.tex        |   68 +
 .../geometric_eth_large_scale/references.bib  |  355 +++++
 .../sections/01-introduction.tex              |  139 ++
 .../sections/02-ensembles.tex                 |  181 +++
 .../sections/03-physical-law.tex              |  157 ++
 .../sections/04-covariance-eth.tex            |  117 ++
 .../sections/05-rank-crossover.tex            |   79 +
 .../sections/06-thouless-hierarchy.tex        |   87 ++
 .../sections/07-conclusion.tex                |   75 +
 .../sections/08-matrix-elements-topology.tex  |   53 +
 tracks/mps/solutions/Wander-276/verify.sh     |    6 +
 177 files changed, 25976 insertions(+)
 create mode 100644 tracks/mps/solutions/Wander-276/PR_BODY.md
 create mode 100644 tracks/mps/solutions/Wander-276/README.md
 create mode 100644 tracks/mps/solutions/Wander-276/research/00_main/main_dashboard.md
 create mode 100644 tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/README.md
 create mode 100644 tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/lgeth/__init__.py
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 create mode 100644 tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/lgeth/combinatorics.py
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diff --git a/tracks/mps/solutions/Wander-276/PR_BODY.md b/tracks/mps/solutions/Wander-276/PR_BODY.md
new file mode 100644
index 000000000..726a39e40
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/PR_BODY.md
@@ -0,0 +1,78 @@
+<!-- wander-artwork -->
+![Wander — Issue #276](https://raw.githubusercontent.com/JunkaiWang-TheoPhy/quantum.harness/664506886413b68cdbc5a362a6075c78fd5d2c46/docs/showcase/ranger-archive/assets/missions-v2/07-quantum-geometry-curved-state-space-v2.png)
+
+> **EN** The world seemed flat only because no one had lifted the tablecloth.
+>
+> **中文** 世界之所以显得平坦，只因从未有人掀起那块桌布。
+<!-- /wander-artwork -->
+
+<!-- wander-team -->
+## Team
+
+| Field | Value |
+|---|---|
+| **Team name** | Wander |
+| **Members** | Chenxi Wan, Yedi Shen, Junkai Wang |
+| **Contact email** | WangTheoPhys@outlook.com |
+<!-- /wander-team -->
+
+## Challenge
+
+Addresses #276: **What is the probe of quantum chaos for a degenerate eigenstate subspace?**
+
+This PR gives an executable answer: the probe is the **non-Abelian quantum geometry of the degenerate projector over coupling space**. Exact degeneracy turns the connected energy spectral form factor into an exact baseline, while Berry curvature, a gauge-invariant four-channel response tensor, and Wilson holonomy resolve the internal complexity of the manifold.
+
+## Scientific Advance
+
+| Layer | New capability | Registered result |
+|---|---|---|
+| Exact spectrum | Exact spectral-flatness reference | \(K_{E,c}=0\) identically |
+| Local geometry | Parameter-free finite-\(D\) Jacobi kernel and SFF | Physical curvature tracks the registered Jacobi ramp |
+| Matrix elements | Covariance-whitened four-channel tensor | `deformed_geometric_eth` |
+| Global topology | Isospectral, fixed-Chern Wilson control | `fixed_chern_deformed_holonomy` |
+
+## Four Innovations
+
+1. **Metric-normalized signature compression** maps the many-body projector response to an exact finite-rank complex-Jacobi process.
+2. **Boundary-atom form-factor theory** treats exact \(\lambda=\pm1\) modes algebraically and reaches \(D=800\).
+3. **Matrix-element Geometric ETH** measures a gauge-invariant connected four-channel component on the genuine \(N=3,4,5\) sequence.
+4. **Fixed-Chern holonomy engineering** tunes relative Wilson transport while preserving every energy, the external gap, and \(C_1\).
+
+These capabilities create a condensed-matter bridge from the Berry-curvature chaos program for degenerate BPS microstates to a local frustration-free bosonic Laughlin parent Hamiltonian.
+
+## Quantitative Evidence
+
+- 20,000 physical tangent pairs with a frozen `12000/4000/4000` train/validation/test split.
+- At \(\tau=0.5\), physical \(K_{F,c}=0.502\) and finite-Jacobi \(K_{J,c}=0.501\).
+- Four-channel connected excess \(0.15385\to0.10078\to0.08183\) across \(N=3,4,5\).
+- Fixed Chern numbers \(C_1=6,10\) with reproducibly shifted Wilson statistics.
+- Exact rank sequence through \(D=800\), including 120 atoms at each boundary and connected plateau `0.7`.
+- Seven synchronized publication figures and an audited 17-page article.
+
+## Deliverables
+
+- [Harness solution overview](https://github.com/JunkaiWang-TheoPhy/quantum.harness/blob/codex/issue-276-quantum-geometry/tracks/mps/solutions/Wander-276/README.md)
+- [Innovation-first research guide](https://github.com/JunkaiWang-TheoPhy/quantum.harness/blob/codex/issue-276-quantum-geometry/tracks/mps/solutions/Wander-276/research/README.md)
+- [Markdown technical report](https://github.com/JunkaiWang-TheoPhy/quantum.harness/blob/codex/issue-276-quantum-geometry/tracks/mps/solutions/Wander-276/research/docs/2026-07-30-task05-technical-report.md)
+- [17-page article](https://github.com/JunkaiWang-TheoPhy/quantum.harness/blob/codex/issue-276-quantum-geometry/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/spectral_silence_and_geometric_chaos_v3.pdf)
+- [Release manifest](https://github.com/JunkaiWang-TheoPhy/quantum.harness/blob/codex/issue-276-quantum-geometry/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/release_manifest_v1.json)
+- [Public research repository](https://github.com/JunkaiWang-TheoPhy/Chaos-of-Quantum-Geometry/tree/codex/task-05-geometric-chaos-baseline)
+
+## Verification
+
+```bash
+cd tracks/mps/solutions/Wander-276
+bash verify.sh
+```
+
+- Release contract: 17/17 checks.
+- Quick path: 38/38 tests.
+- Complete compact suite: 86 passing tests plus six manifest-activated production tests.
+- Article delivery: 25/25 checks across 17 pages and seven figures.
+- Article SHA-256: `a75377f76acd78eb3354e186a57933abdf11abbbe5e9a8abd43482ca8c4e05ad`.
+
+## MPS Track Continuation
+
+The exact-kernel calculation supplies the calibration layer for an MPS extension of Issue #276: reproduce the projector response and four-channel invariant at ED-accessible sizes, then scale the same gauge-invariant observables with a tensor-network representation of the degenerate manifold. The next registered targets are \(N=6\), a second exact-degeneracy mechanism, and a locality-based derivation of the connected channel law.
+
+@OkongOyangO, please review the projector-geometry interpretation, the four-channel law, and the fixed-Chern holonomy construction as Wander's ready submission for #276.
diff --git a/tracks/mps/solutions/Wander-276/README.md b/tracks/mps/solutions/Wander-276/README.md
new file mode 100644
index 000000000..61ea74529
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/README.md
@@ -0,0 +1,66 @@
+# Wander — Issue #276: Non-Abelian Quantum Geometry as a Chaos Probe
+
+![Quantum geometry over an exactly degenerate manifold](https://raw.githubusercontent.com/JunkaiWang-TheoPhy/quantum.harness/664506886413b68cdbc5a362a6075c78fd5d2c46/docs/showcase/ranger-archive/assets/missions-v2/07-quantum-geometry-curved-state-space-v2.png)
+
+> **EN** The world seemed flat only because no one had lifted the tablecloth.
+>
+> **中文** 世界之所以显得平坦，只因从未有人掀起那块桌布。
+
+## Team
+
+| Field | Value |
+|---|---|
+| **Team name** | Wander |
+| **Members** | Chenxi Wan, Yedi Shen, Junkai Wang |
+| **Contact email** | WangTheoPhys@outlook.com |
+
+## Challenge
+
+This submission addresses [QuantumBFS/quantum.harness#276](https://github.com/QuantumBFS/quantum.harness/issues/276): **What is the probe of quantum chaos for a degenerate eigenstate subspace?**
+
+The executable answer is the **non-Abelian quantum geometry of the degenerate projector over coupling space**. Exact degeneracy makes the connected energy spectral form factor silent, while Berry curvature, the gauge-invariant four-channel response tensor, and Wilson holonomy remain informative.
+
+## Headline Result
+
+The benchmark uses a bosonic Laughlin zero-mode manifold of a Kapit–Mueller parent Hamiltonian. It combines four advances:
+
+1. **Metric-normalized signature compression** maps the many-body projector response to an exact finite-rank complex-Jacobi process.
+2. **Boundary-atom form-factor theory** treats exact \(\lambda=\pm1\) modes algebraically and reaches rank \(D=800\).
+3. **Matrix-element Geometric ETH** measures a gauge-invariant connected four-channel component on the genuine \(N=3,4,5\) sequence.
+4. **Fixed-Chern holonomy engineering** tunes relative Wilson transport while preserving the full spectrum, the gap, and the Chern class.
+
+At \(\tau=0.5\), the physical curvature form factor is \(K_{F,c}=0.502\), compared with the finite-Jacobi value \(K_{J,c}=0.501\). The connected four-channel excess decreases as \(0.15385\to0.10078\to0.08183\). The registered result branches are `deformed_geometric_eth` and `fixed_chern_deformed_holonomy`.
+
+## Deliverables
+
+- [Innovation-first project guide](research/README.md)
+- [Task-level reproduction guide](research/01_task_folder/task_05/README.md)
+- [Markdown technical report](research/docs/2026-07-30-task05-technical-report.md)
+- [17-page article](research/01_task_folder/task_05/script/output/spectral_silence_and_geometric_chaos_v3.pdf)
+- [Machine-readable release manifest](research/01_task_folder/task_05/script/output/release_manifest_v1.json)
+- [Seven publication figures](research/01_task_folder/task_05/script/output/)
+- [Full REVTeX manuscript](research/overleaf_sync/geometric_eth_large_scale/)
+- [Public research repository](https://github.com/JunkaiWang-TheoPhy/Chaos-of-Quantum-Geometry/tree/codex/task-05-geometric-chaos-baseline)
+
+## Verification
+
+```bash
+cd tracks/mps/solutions/Wander-276
+bash verify.sh
+```
+
+Verified release state:
+
+- 17/17 public-release contract checks;
+- 38/38 focused quick-path tests;
+- 86 passing compact-checkout tests plus six production-data tests activated by the manifest-listed arrays;
+- 25/25 article-delivery checks across 17 rendered pages and seven synchronized figures;
+- article SHA-256 `a75377f76acd78eb3354e186a57933abdf11abbbe5e9a8abd43482ca8c4e05ad`.
+
+## MPS Growth Path
+
+Issue #276 is registered on the MPS track. This exact-kernel package supplies the finite-size calibration layer for a tensor-network extension: reproduce the projector response and four-channel invariants at the ED-accessible sizes, then scale the same gauge-invariant observables with an MPS representation of the degenerate manifold. The preregistered next targets are \(N=6\), a second exact-degeneracy mechanism, and a locality-based derivation of the connected channel law.
+
+## Provenance
+
+The capsule is synchronized from public commit `d0a03ae` of `JunkaiWang-TheoPhy/Chaos-of-Quantum-Geometry`. Compact artifacts are stored in Git; 25 production arrays totaling 447,704,793 bytes are recorded by SHA-256, byte size, and producer command in the release manifest.
diff --git a/tracks/mps/solutions/Wander-276/research/00_main/main_dashboard.md b/tracks/mps/solutions/Wander-276/research/00_main/main_dashboard.md
new file mode 100644
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+++ b/tracks/mps/solutions/Wander-276/research/00_main/main_dashboard.md
@@ -0,0 +1,48 @@
+# Main Dashboard
+
+Global ledger for *Chaos of Quantum Geometry*. Read this first every session, then open the active task's `task_X_dashboard.md`.
+
+## Global Conventions
+- **No mid-paragraph line breaks.** Keep each paragraph on one continuous physical line (no manual newlines inside a paragraph); do not hard-wrap prose at ~70/80 columns. Paragraphs stay separated by a blank line. Exceptions: list items, table rows, code, and the interior lines of multi-line math environments. Canonical rule lives in `CLAUDE.md` §9.1.
+- **LaTeX cross-references.** Never use the `§`/`\S` form or hardcoded numbers to cite a section; always use `\label`/`\ref` — `Appendix~\ref{...}`, `Sec.~\ref{...}`, `Eq.~\eqref{...}`, `Fig.~\ref{...}` (non-breaking `~`). Canonical rule lives in `CLAUDE.md` §9.2.
+- **Statuses:** ⚪ Start · 🟡 Ongoing · 🟢 Finished · 🔴 Blocked · ❌ Failed. The status here must match the status inside each `task_X_dashboard.md`.
+
+## Task Ledger
+
+| Task | Objective | Status | Last Updated |
+|---|---|---|---|
+| task_01 | Initialize the task-centric workspace (00_main / 01_task_folder / 02_recycle), sync the prompt family, and adopt the PRL workspace conventions | 🟢 Finished | 2026-06-18 [Claude] |
+| task_02 | Read the seed paper (arXiv:2604.23287) end-to-end and expand `docs/paper-summary.md` per section; pin down the non-Abelian Berry curvature + quantum metric definitions | 🟡 Ongoing | 2026-07-27 [Codex] |
+| task_03 | Build an FCI / correlated flat-band feasibility map for many-body non-Abelian quantum geometry as a chaos diagnostic | 🟡 Ongoing | 2026-07-27 [Codex] |
+| task_05 | Deliver spectral silence, Geometric ETH channel memory, and fixed-Chern holonomy as an audited public paper/code release | 🟡 Ongoing | 2026-07-30 [Codex] |
+
+## Session Log
+- 2026-06-18 [Claude]: **task_01 — workspace restructured to mirror PRL_Nonreciprocal.** Created `00_main/` (this dashboard + `system_prompt.md` + `history/`), `01_task_folder/` (task_01 init + task_02 seed-paper), and `02_recycle/`. Synced the prompt family (`system_prompt.md` ≡ `AGENTS.md` ≡ `.cursorrules`; `CLAUDE.md` superset). Renamed `literature/` → `lib/` and `overleaf-sync/` → `overleaf_sync/` to match PRL; removed the old flat `task/` folder (roadmap now lives in this ledger). Updated all READMEs + `.gitignore` cross-references. 🟢 task_01 Finished.
+- 2026-06-18 [Claude]: **task_02 created** — read the seed paper end-to-end and expand the per-section summary; this is the first live research task. 🟡 Ongoing.
+- 2026-07-13 09:15 [Codex]: **task_02 discussion triage** — reviewed the repo plus the Junkai/Desperado planning chat. The sharp next move is to finish the seed-paper definitions while opening the first concrete condensed-matter feasibility lane around FCI / correlated flat-band many-body quantum geometry, rather than expanding the manuscript title before a calculable model exists. 🟡 Ongoing.
+- 2026-07-13 10:56 [Codex]: **task_03 created** - saved the Junkai/Desperado conversation triage as `docs/2026-07-13-junkai-desperado-research-triage.md` and opened the FCI / correlated flat-band feasibility lane as the first condensed-matter execution task. 🟡 Ongoing.
+- 2026-07-27 14:10 [Codex]: **task_02 repo and literature reading** — read the active repo state against the full seed paper, verified Yiming Chen's recent `BPS Chaos` → `Fortuity in SYK Models` → Berry-curvature research chain, and added a clickable Chinese guide at `docs/2026-07-27-repo-and-yiming-chen-berry-geometry-guide.md`. The task stays 🟡 Ongoing because the per-section technical summary and numerical reproduction remain open.
+- 2026-07-27 14:27 [Codex]: **task_03 candidate-system prioritization** — ranked condensed-matter targets and saved a clickable literature-backed note at `docs/2026-07-27-priority-condensed-matter-systems.md`. Recommended continuum FQH calibration → minimal lattice FCI → controlled chaos-axis tuning, with SUSY lattice fermions as a high-risk BPS analog and moiré/Josephson systems deferred. 🟡 Ongoing.
+- 2026-07-27 14:31 [Codex]: **task_03 A0/A1 design discussion** — proposed a matched bosonic $\nu=1/2$ implementation: Kapit-Mueller lattice-Laughlin calibration plus continuum-LLL cross-check for A0, and a full-real-space checkerboard hard-core-boson FCI for A1, both using a shared gauge-covariant projector/link/Wilson-loop/QGT engine. No implementation started pending human approval. 🟡 Ongoing.
+- 2026-07-27 15:15 [Codex]: **task_03 A0/A1 numerical delivery** — completed and reproduced the matched bosonic $\nu=1/2$ A0/A1 benchmarks. A0 combines a Kapit-Mueller lattice-Laughlin parent with a direct-coordinate continuum torus Laughlin overlap audit; A1 validates the flat-band checkerboard FCI through $N_b=4,5,6$. Both $8\times8$ twist bundles have $C_1=1$, unit Wilson determinant winding, an open external gap, nonsingular overlaps, resolved principal-log branches, and random local $U(2)$ gauge invariance. The complete runner passes 11 tests and a checksummed artifact audit. task_03 stays 🟡 Ongoing because the growing-rank quasihole chaos test is not part of A0/A1.
+- 2026-07-27 15:54 [Codex]: **task_03 conclusion boundary** — recorded the safe interpretation of A0/A1: local non-Abelian curvature and quantum metric distinguish the continuum-like Laughlin parent from the matched checkerboard FCI despite identical integrated $C_1=1$, but the rank-two bundle cannot establish random-matrix chaos. The next decisive stage is a growing-rank quasihole zero-mode bundle plus a controlled perturbation and comparison to conventional chaos diagnostics. 🟡 Ongoing.
+- 2026-07-27 16:24 [Codex]: **task_03 flagship-program discussion** — the human selected a two-plus-year, high-risk condensed-matter program. Compared large-rank FQH/FCI quasihole bundles, local exact-zero-mode constrained matter, and non-Abelian anyon holonomy; recommended Geometric ETH / random Hilbert-bundle universality as the main spine and saved the clickable literature-backed comparison at `docs/2026-07-27-yiming-level-condensed-matter-program-options.md`. No implementation or design approval is assumed. 🟡 Ongoing.
+- 2026-07-27 16:39 [Codex]: **task_03 standard-model alternative discussion** — accepted the human's proposal to test Berry phase as a chaos diagnostic in familiar condensed-matter models as a useful low-risk calibration. Recommended a twisted $J_1$-$J_2$ XXZ/spinless-fermion model using local curvature, QGT, and small-loop phase statistics, with symmetry-resolved level statistics and dynamics as controls; saved the clickable scope review at `docs/2026-07-27-common-model-berry-phase-chaos-scope.md`. 🟡 Ongoing.
+- 2026-07-27 17:03 [Codex]: **task_03 flagship architecture discussion** — developed the first concrete design section for “Geometric ETH in a fractional topological manifold”: a growing-rank Laughlin quasihole kernel as the structured bundle, off-bundle virtual mixing as the mechanism for changing projector geometry, and a finite-rank block-Wishart law for the joint non-Abelian QGT as the analytic target. Awaiting human approval before formal design documentation or implementation. 🟡 Ongoing.
+- 2026-07-27 17:18 [Codex]: **task_03 flagship narrative revision** — accepted the human's criticism that the first architecture lacked a memorable paradox. Reframed the recommended story as “hidden chaos inside one fractional topological phase”: the protected $U(1)$ curvature keeps the same Chern/Hall data while the traceless $SU(D)$ quantum geometry changes from structured to random; Geometric ETH remains the explanatory engine rather than the headline. 🟡 Ongoing.
+- 2026-07-27 17:32 [Codex]: **task_03 flagship writing architecture** — developed a result-dependent target abstract, six-paragraph introduction logic, argument-first section order, main-figure sequence, and explicit claim ladder for *Hidden Chaos Within a Topological Phase*. The manuscript is designed around the same-phase paradox; the Geometric-ETH mechanism appears after the phenomenon rather than leading the story. 🟡 Ongoing.
+- 2026-07-27 16:52 [Codex]: **task_03 local-zero-mode second-paper discussion** — reviewed local SUSY/cohomology models and the July 2026 East–West-chain competition. Reframed the second paper around “the index counts zero modes, not their complexity,” with a finite-range random three-fermion supercharge as the proposed main model, Fendley–Schoutens zero modes as the structured control, and random-kernel Berry geometry as the analytic target. Saved the clickable review at `docs/2026-07-27-local-exact-zero-mode-geometric-chaos-options.md`. 🟡 Ongoing.
+- 2026-07-27 17:58 [Codex]: **task_03 first-paper approval** — the human selected *Hidden Chaos Within a Topological Phase* for completion. Saved the approved research design at `docs/plans/2026-07-27-hidden-chaos-topological-phase-design.md`, requiring a growing-rank soft-core/projected Laughlin quasihole parent, a fixed-Hilbert gapped path, explicit central/traceless curvature separation, finite-\(D\) block-Wishart theory, cross-model controls, conventional chaos comparisons, and a complete reproducible manuscript. An exploratory audit demoted the existing hard-core underfilled A0 backend from a quasihole-parent candidate because it does not reproduce the continuum admissible count. 🟡 Ongoing.
+- 2026-07-27 18:16 [Codex]: **task_03 first-paper implementation plan** — saved the twelve-task, test-driven implementation plan at `docs/plans/2026-07-27-hidden-chaos-topological-phase-implementation-plan.md`. It specifies exact file interfaces, growing-rank and same-phase gates, block-Wishart and conventional-chaos tests, generated figure/table/macro contracts, manuscript sections, and a one-command completion audit. Inline execution starts with the soft-core Laughlin parent and exact quasihole counting. 🟡 Ongoing.
+- 2026-07-27 18:34 [Codex]: **task_03 A2 foundation** — implemented cyclic \((1,2)\)-admissible quasihole counting and a full soft-core boson Hamiltonian with correct occupation factors, contact interaction, density/on-site terms, and boundary twists. The pre-registered algebraic ranks are \(D=9,16,25\); the complete suite passes 19 tests. Spectral realization of those ranks is deliberately deferred to the next go/no-go runner. 🟡 Ongoing.
+- 2026-07-27 18:58 [Codex]: **task_03 A2 parent gate passed** — added a rigorous projected-contact backend and degeneracy-safe QR/Rayleigh–Ritz eigensolver. The generated feasibility artifact verifies exact \(D=25,36,50\) Laughlin kernels at four twists, minimum external gaps \(0.0946952,0.0936047,0.0977652\), sub-\(1.1\times10^{-15}\) internal bandwidth, and 27 passing tests. Dense re-audit corrected the earlier sparse-solver error: legacy hard-core \(N_b=3\) has the correct 16 states; \(N_b=2\) has 21 rather than 20. 🟡 Ongoing.
+- 2026-07-27 19:24 [Codex]: **task_03 arbitrary-rank physical bundle** — implemented the symmetric-boson Fock lift for twist-dependent band bases and overlap-only non-Abelian QGT geometry. The \(D=25\), \(5\times5\) parent bundle passes with \(C_1=10\), external gap \(0.0952460\), overlap singular value \(0.796310\), and \(U(25)\) gauge errors below \(4\times10^{-15}\). A retained \(3\times3\) failure shows determinant central-phase aliasing despite safe individual Wilson eigenphases; the new lift-mismatch diagnostic rejects it. The suite passes 31 tests. 🟡 Ongoing.
+- 2026-07-27 19:51 [Codex]: **task_03 same-phase path passed** — screened four deterministic fixed-site-Hilbert endpoints and selected `generic_mid` by a frozen gap-times-projector-response score. The full \(D=25\), \(6\times6\), five-point path preserves \(C_1=10\), keeps the external gap above \(0.0396120\), limits bandwidth/gap to \(0.0574195\), and moves the physical projector to mean distance \(0.424107\). All branch, overlap, and \(U(25)\) gauge checks pass; the suite passes 37 tests. 🟡 Ongoing.
+- 2026-07-27 17:57 [Codex]: **task_03 finite-rank RMT baseline** — derived exact finite-\(D\) block-Wishart second, fourth, and sixth moments by Wick-permutation sums and validated them against 4,000 samples for each \(M=4,\ldots,128\). The \(D=25\) same-phase path moves monotonically closer to the \(M=128\) eigenvalue law, but its endpoint moment and gap-ratio statistics remain nonuniversal; this is recorded as a quantitative onset rather than a plateau. Generalized finite-range density interactions were added as a negative mechanism control, and the suite passes 46 tests. 🟡 Ongoing.
+- 2026-07-27 18:21 [Codex]: **task_03 growing-rank hidden-chaos and independent FCI control** — defined a gauge-covariant curvature increment by cross-bundle polar transport back to the Laughlin parent. Its endpoint gap ratio approaches the generated block-Wishart reference \(0.597503\): \(0.566145\) at \(D=25\) and \(0.592594\) at \(D=50\), with open gaps and fixed Chern data. A separately constructed disordered checkerboard FCI passes the same gates and gives \(0.540028,0.580106\). The total curvature retains a structured background, so the supported universality is local spectral repulsion of the transported increment. A fixed-quasihole \(D=36\) size control remains open. 🟡 Ongoing.
+- 2026-07-27 18:52 [Codex]: **task_03 fixed-two-quasihole size control** — completed the \(D=25,36\) branch-resolved endpoint calculation at fixed \(N_\phi=2N_b+2\). The transported-increment gap ratio moves \(0.549255\to0.576366\) toward the block-Wishart \(0.597503\), with open endpoint gaps and fixed Chern data. The strict pre-registered gate remains false solely because the \(D=36\) bandwidth/gap \(0.517923\) exceeds the \(0.5\) ceiling; every other check passes and no threshold was relaxed. The result is retained as qualified finite-size evidence. 🟡 Ongoing.
+- 2026-07-27 18:57 [Codex]: **task_03 conventional-chaos controls** — generated matched Poisson/GUE references, quasihole energy gap ratios, and twist-ensemble spectral form factors. On the Kapit–Mueller path, energy correlations enter the RMT window at \(g=0.25\), before the transported geometry at \(g=1.0\) (\(D=25\)) and \(g=0.75\) (\(D=50\)); the checkerboard \(D=50\) control reverses the sampled ordering. The conventional-control gate and 58 tests pass, establishing that geometric and spectral chaos scales are not redundant. 🟡 Ongoing.
+- 2026-07-27 19:04 [Codex]: **task_03 manuscript figure package** — generated five argument-ordered paper figures, vector/raster manuscript assets, provenance JSON, an endpoint table, and script-derived LaTeX numerical macros. The production script enforces all positive scientific gates and preserves the fixed-two-quasihole strict-gate failure as an explicit manuscript limitation. The suite remains at 58 passing tests. 🟡 Ongoing.
+- 2026-07-27 19:17 [Codex]: **task_03 first-paper delivery** — completed the 17-page preprint *Hidden Chaos Within a Topological Phase* with five generated main figures, full formalism/results/Geometric-ETH narrative, methods and limitations appendices, and an audited primary-source bibliography. The final delivery gate verifies warning-free compilation, figure hashes, extracted PDF content, all scientific gates, the retained fixed-quasihole strict failure, and 61 passing tests. The paper deliverable is complete; task_03 remains 🟡 Ongoing for larger-size scaling, external review, and subsequent research branches.
+- 2026-07-30 19:30 [Codex]: **task_05 public-release preparation** — assembled the innovation-first repository entry points, 17-page paper, Markdown technical report, release notes, citation metadata, challenge draft, PR body, collaborator review comment, and public checklist. The compact release passes 17/17 contract checks, 38/38 quick tests, 86 tests with six production-data activations in the complete suite, and 25/25 article gates across seven synchronized figures. The prepared branch is ready for the human's Issue-first PR sequence; task_05 remains 🟡 Ongoing through review.
+- 2026-07-30 19:50 [Codex]: **task_05 Issue-linked PR handoff** — linked the public release to `QuantumBFS/quantum.harness#276`, aligned the PR opening statement with the challenge question, and synchronized the prepared collaborator review comment and submission checklist. The release proceeds as a draft PR from `codex/task-05-geometric-chaos-baseline` into `main`. 🟡 Ongoing through scientific review.
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/README.md b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/README.md
new file mode 100644
index 000000000..413a6b74a
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/README.md
@@ -0,0 +1,138 @@
+# Spectral Silence and Geometric Chaos
+
+> **One exactly flat energy band. Three geometric correlation scales. A reproducible route to Geometric ETH.**
+
+![Spectral flatness and geometric ramp](script/output/figure_1_spectral_silence_v2.png)
+
+This task provides a self-contained analytic and numerical baseline for chaos diagnostics inside an exactly degenerate bosonic Laughlin zero-mode manifold. It resolves the spectrum, local non-Abelian curvature, invariant response tensors, and closed-surface holonomy as complementary layers of one quantum-geometric structure.
+
+## Result at a Glance
+
+| Question | Evidence | Advance |
+|---|---|---|
+| What replaces internal level statistics under exact degeneracy? | \(K_{E,\mathrm{raw}}=D\) and \(K_{E,c}=0\) identically | An exact spectral-flatness reference |
+| Does geometry develop universal correlations? | Physical curvature follows the finite-\(D\) Jacobi ramp over the registered window | Local geometric chaos |
+| How does the full response tensor behave? | Median \(R_4\) evolves \(0.37093\to0.24715\to0.20906\) across \(N=3,4,5\) | `deformed_geometric_eth` |
+| Can topology and relative transport move independently? | \(C_1=6,10\) and the complete spectrum stay fixed while Wilson statistics change significantly | `fixed_chern_deformed_holonomy` |
+| What global structure survives? | Wilson gap-ratio and form-factor data define a structured universality class distinct from CUE | Measurable microscopic memory |
+
+The central article is [*Spectral Silence and Geometric Chaos in an Exactly Degenerate Topological Manifold*](script/output/spectral_silence_and_geometric_chaos_v3.pdf). Its final SHA-256, page count, figures, and source artifacts are recorded by the release manifest and delivery audit.
+
+## Scientific Flow
+
+```mermaid
+flowchart TD
+    A["Kapit–Mueller bosonic Laughlin parent"] --> B["Exact zero-mode projector P"]
+    B --> C["Internal channel PHP"]
+    B --> D["External response P(dH)Q"]
+    C --> E["Controlled Poisson-to-GUE interpolation at fixed P"]
+    D --> F["Metric-normalized Berry curvature"]
+    F --> G["Finite-Jacobi local statistics and ramp"]
+    D --> H["Gauge-invariant four-channel tensor"]
+    H --> I["Resolved connected response cumulant"]
+    B --> J["Closed twist-torus bundle"]
+    J --> K["Fixed C1 with deformable Wilson holonomy"]
+```
+
+## Why the Kapit–Mueller Parent Is Essential
+
+The Kapit–Mueller lattice realizes an exactly flat Chern band whose projected contact interaction supports bosonic Laughlin zero modes. This gives the calculation four rare ingredients simultaneously:
+
+1. an exactly known degenerate kernel;
+2. a finite external excitation gap;
+3. boundary twists that form a closed parameter torus;
+4. local tangent operators whose response maps can be computed and compared at fixed topology.
+
+The parent Hamiltonian is positive semidefinite and frustration free: the target manifold is its exact kernel. This algebraic structure makes spectral flatness exact while allowing the projector to rotate through Hilbert space, which is precisely the regime where quantum geometry becomes the informative observable.
+
+## Algorithmic Innovations
+
+### 1. Metric-normalized signature compression
+
+Projector-to-complement response maps are assembled into a channel matrix and whitened by the quantum metric. The curvature reduces to a compression of a fixed signature matrix by a Stiefel row space. A Haar row space therefore produces an exact finite-dimensional complex-Jacobi point process. This converts a many-body geometric response into a parameter-free random-matrix benchmark at the actual finite rank.
+
+### 2. Exact finite-Jacobi form factor with boundary atoms
+
+The implementation evaluates the determinantal kernel directly by Gauss–Jacobi quadrature. When \(D>M\), exact eigenvalues at \(\lambda=\pm1\) are separated algebraically, yielding the plateau law
+
+$$K_{J,c}^{\mathrm{full}}=\frac{k}{D}K_{J,c}^{(k)},\qquad k=2M-D.$$
+
+This preserves the continuous Jacobi ramp and accounts exactly for deterministic geometric modes.
+
+### 3. Gauge-invariant matrix-element Geometric ETH
+
+For response maps \(X_\mu\), the release whitens the channel covariance and evaluates
+
+$$T_{\mu\nu\rho\sigma}=\frac{1}{D}\operatorname{Tr}(\widetilde X_\mu\widetilde X_\nu^\dagger\widetilde X_\rho\widetilde X_\sigma^\dagger).$$
+
+The finite-size reference uses independently generated covariance-matched complex-Gaussian samples. The residual therefore measures a genuine connected operator-channel component while remaining invariant under independent frame rotations in the zero-mode and complementary subspaces.
+
+### 4. Fixed-Chern holonomy engineering
+
+A smooth periodic ambient unitary \(\mathcal U_g:T^2\to U(\mathcal H)\) produces an exactly isospectral family \(H_g=\mathcal U_gH_0\mathcal U_g^\dagger\). The bundle isomorphism preserves \(C_1\), while the projected connection acquires a tunable one-form. This creates a controlled laboratory for separating determinant topology from relative non-Abelian transport.
+
+## Reproduction Tiers
+
+### Tier 0: inspect the frozen evidence
+
+- [Combined article audit](script/output/geometric_eth_topology_delivery_audit_v3.json)
+- [Matrix-element result](script/output/matrix_element_geometric_eth_v3.json)
+- [Topology result](script/output/topological_holonomy_v3.json)
+- [Release manifest](script/output/release_manifest_v1.json)
+- [Technical report](../../docs/2026-07-30-task05-technical-report.md)
+
+### Tier 1: quick verification
+
+```bash
+cd 01_task_folder/task_05/script
+python -m venv .venv
+source .venv/bin/activate
+python -m pip install -r requirements.txt
+bash run_quick_verify_v1.sh
+```
+
+This read-only path verifies result labels, paper and figure hashes, task isolation, tracked-file size policy, exact Jacobi/form-factor identities, holonomy algebra, Wick contractions, and 38 focused tests.
+
+### Tier 2: rebuild the article
+
+```bash
+cd 01_task_folder/task_05/script
+bash run_geometric_eth_topology_article_v3.sh
+```
+
+The article build uses compact published artifacts and performs a full PDF delivery audit. System tools: `latexmk` and `pdftoppm`.
+
+### Tier 3: full numerical recomputation
+
+```bash
+cd 01_task_folder/task_05/script
+bash run_full_recompute_v1.sh
+```
+
+This production path rebuilds the large-scale, spectral-flatness, matrix-element, topology, figure, and paper layers with resumable checkpoints.
+
+## Artifact Contract
+
+Git contains every source file, test, compact result table, figure, manuscript input, and final verdict required for review. The release manifest records 25 production arrays totaling 447704793 bytes with exact paths, byte sizes, SHA-256 hashes, storage classes, and producing commands. These arrays can be regenerated by Tier 3 and are ready for a future DOI-backed archive.
+
+In a compact checkout, the complete test command reports 86 passing tests and 6 data-dependent tests marked as skipped. Restoring the listed production arrays activates those six tests automatically.
+
+## Figure Guide
+
+| Figure | Scientific role |
+|---|---|
+| [Figure 1](script/output/figure_1_spectral_silence_v2.png) | Exact spectral flatness beside the geometric ramp |
+| [Figure 2](script/output/figure_2_falsification_triangle_v2.png) | Structured, physical, and finite-Jacobi comparison triangle |
+| [Figure 3](script/output/figure_3_independent_channels_v2.png) | Independently tunable spectral and projector-geometric axes |
+| [Figure 4](script/output/figure_4_geometric_hierarchy_v2.png) | Local-to-ramp-to-long-range correlation hierarchy |
+| [Figure 5](script/output/figure_5_jacobi_atoms_v2.png) | Finite-Jacobi boundary atoms and plateau law |
+| [Figure 6](script/output/figure_6_wick_factorization_v3.png) | Gauge-invariant four-channel residual along \(N=3,4,5\) |
+| [Figure 7](script/output/figure_7_topological_holonomy_v3.png) | Fixed Chern numbers with deformable Wilson holonomy |
+
+## Established Scope and Growth Path
+
+This release establishes exact spectral flatness, finite-rank Jacobi-like local curvature correlations, causal independence of \(PHP\) and \(P(\partial H)Q\), a shrinking connected four-channel component, and changing relative holonomy at fixed complete spectrum and fixed first Chern number.
+
+The next research horizon extends the matrix-element sequence through \(N=6\), derives its scaling from locality, realizes the same invariant law in a second exact-degeneracy mechanism, and connects the geometric hierarchy to real-time dynamics.
+
+The issue-ready handoff is [the Quantum Harness challenge draft](../../docs/2026-07-30-quantum-geometry-harness-challenge-draft.md).
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/lgeth/__init__.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/lgeth/__init__.py
new file mode 100644
index 000000000..cba872e98
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/lgeth/__init__.py
@@ -0,0 +1,117 @@
+"""Independent numerical core for the large-scale Geometric-ETH companion."""
+
+from .channels import (
+    PhysicalChannelCache,
+    build_physical_channel_cache,
+    cached_channel,
+    normalized_potential,
+    root_response_partition,
+)
+from .grassmann import covariance_deformed_rows
+from .form_factors import (
+    FormFactorParts,
+    JacobiFormFactor,
+    atom_raw_decomposition,
+    degenerate_energy_form_factor,
+    finite_jacobi_form_factor,
+    form_factor_parts,
+)
+from .controls import (
+    FixedProjectorControl,
+    FourierTangentPair,
+    fixed_projector_spectral_ensemble,
+    fourier_tangent_pairs,
+    gram_normalize,
+    scrambled_tangent_pair,
+)
+from .jacobi import (
+    NormalizedCurvature,
+    jacobi_parameters,
+    normalized_curvature,
+    sample_jacobi_interior,
+)
+from .manybody_response import (
+    KernelFrame,
+    ManyBodyCase,
+    SiteResponseCache,
+    build_site_response_cache,
+    registered_fixed_two_qh_cases,
+    solve_kernel_frame,
+)
+from .wick_channels import (
+    WickResult,
+    assemble_channels,
+    covariance_matched_wick,
+    fourier_density_panel,
+    gaussian_r4_reference,
+    local_density_panels,
+)
+from .bundle_geometry import (
+    BundleGeometry,
+    analyze_ambient_frame_mesh,
+    analyze_frame_bundle,
+    manybody_frame_overlap,
+)
+from .twist_bundle import (
+    TwistBundle,
+    build_twist_bundle,
+    load_twist_bundle,
+    save_twist_bundle,
+)
+from .holonomy import (
+    ambient_unitary,
+    cue_wilson_reference,
+    deform_orbital_mesh,
+    local_generator_pair,
+    wilson_statistics,
+)
+
+__all__ = [
+    "FormFactorParts",
+    "BundleGeometry",
+    "FixedProjectorControl",
+    "FourierTangentPair",
+    "JacobiFormFactor",
+    "KernelFrame",
+    "ManyBodyCase",
+    "NormalizedCurvature",
+    "PhysicalChannelCache",
+    "SiteResponseCache",
+    "TwistBundle",
+    "WickResult",
+    "atom_raw_decomposition",
+    "analyze_ambient_frame_mesh",
+    "analyze_frame_bundle",
+    "ambient_unitary",
+    "assemble_channels",
+    "build_physical_channel_cache",
+    "build_site_response_cache",
+    "build_twist_bundle",
+    "cached_channel",
+    "covariance_deformed_rows",
+    "covariance_matched_wick",
+    "cue_wilson_reference",
+    "degenerate_energy_form_factor",
+    "deform_orbital_mesh",
+    "finite_jacobi_form_factor",
+    "fixed_projector_spectral_ensemble",
+    "form_factor_parts",
+    "fourier_tangent_pairs",
+    "fourier_density_panel",
+    "gaussian_r4_reference",
+    "gram_normalize",
+    "jacobi_parameters",
+    "local_density_panels",
+    "local_generator_pair",
+    "load_twist_bundle",
+    "manybody_frame_overlap",
+    "normalized_curvature",
+    "normalized_potential",
+    "registered_fixed_two_qh_cases",
+    "root_response_partition",
+    "sample_jacobi_interior",
+    "save_twist_bundle",
+    "scrambled_tangent_pair",
+    "solve_kernel_frame",
+    "wilson_statistics",
+]
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/lgeth/bundle_geometry.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/lgeth/bundle_geometry.py
new file mode 100644
index 000000000..75ae0bb4b
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/lgeth/bundle_geometry.py
@@ -0,0 +1,422 @@
+"""Gauge-covariant geometry of a degenerate bundle over a periodic mesh."""
+
+from __future__ import annotations
+
+from dataclasses import dataclass
+from functools import lru_cache
+from math import factorial, prod, sqrt
+
+import numpy as np
+from scipy.linalg import schur
+
+from .lattice import BosonBasis
+
+
+@dataclass(frozen=True)
+class BundleGeometry:
+    """Discrete links, curvature, topology, and noncontractible holonomy."""
+
+    link_x: np.ndarray
+    link_y: np.ndarray
+    plaquette: np.ndarray
+    plaquette_curvature: np.ndarray
+    wilson_x: np.ndarray
+    wilson_y: np.ndarray
+    wilson_x_phases: np.ndarray
+    wilson_y_phases: np.ndarray
+    chern_determinant: float
+    chern_trace_log: float
+    determinant_branch_margin: float
+    minimum_overlap_singular_value: float
+    maximum_link_unitarity_error: float
+    maximum_plaquette_unitarity_error: float
+
+
+def polar_unitary(matrix: np.ndarray) -> tuple[np.ndarray, np.ndarray]:
+    """Return the polar unitary and singular values of a square overlap."""
+
+    values = np.asarray(matrix, dtype=complex)
+    if values.ndim != 2 or values.shape[0] != values.shape[1]:
+        raise ValueError("overlap matrix must be square")
+    left, singular_values, right_h = np.linalg.svd(
+        values,
+        full_matrices=False,
+    )
+    return left @ right_h, singular_values
+
+
+@lru_cache(maxsize=None)
+def _ordered_particle_indices(
+    state: tuple[int, ...],
+) -> tuple[tuple[int, ...], ...]:
+    particles = sum(state)
+    if particles == 0:
+        return ((),)
+    occupations = list(state)
+    result: list[tuple[int, ...]] = []
+
+    def visit(prefix: tuple[int, ...]) -> None:
+        if len(prefix) == particles:
+            result.append(prefix)
+            return
+        for orbital, population in enumerate(occupations):
+            if population == 0:
+                continue
+            occupations[orbital] -= 1
+            visit((*prefix, orbital))
+            occupations[orbital] += 1
+
+    visit(())
+    return tuple(result)
+
+
+def _occupation_tensor_amplitude(state: tuple[int, ...]) -> float:
+    return sqrt(
+        prod(factorial(population) for population in state)
+        / factorial(sum(state))
+    )
+
+
+def apply_bosonic_fock_lift(
+    basis: BosonBasis,
+    single_particle_overlap: np.ndarray,
+    frames: np.ndarray,
+) -> np.ndarray:
+    """Apply the symmetric bosonic lift of a one-particle overlap."""
+
+    overlap = np.asarray(single_particle_overlap, dtype=complex)
+    if overlap.shape != (basis.n_orbitals, basis.n_orbitals):
+        raise ValueError("single-particle overlap has the wrong shape")
+    coefficient_frames = np.asarray(frames, dtype=complex)
+    if coefficient_frames.ndim == 1:
+        coefficient_frames = coefficient_frames[:, None]
+    if (
+        coefficient_frames.ndim != 2
+        or coefficient_frames.shape[0] != basis.dimension
+    ):
+        raise ValueError("coefficient frames have the wrong shape")
+    particles = basis.n_particles
+    vectors = coefficient_frames.shape[1]
+    if particles == 0:
+        return coefficient_frames.copy()
+    tensor = np.zeros(
+        (basis.n_orbitals,) * particles + (vectors,),
+        dtype=complex,
+    )
+    for state_index, state in enumerate(basis.states):
+        ordered = _ordered_particle_indices(state)
+        indices = tuple(
+            np.asarray(
+                [entry[axis] for entry in ordered],
+                dtype=int,
+            )
+            for axis in range(particles)
+        )
+        tensor[indices + (slice(None),)] = (
+            _occupation_tensor_amplitude(state)
+            * coefficient_frames[state_index]
+        )
+    transformed = tensor
+    for axis in range(particles):
+        transformed = np.tensordot(
+            overlap,
+            transformed,
+            axes=(1, axis),
+        )
+        transformed = np.moveaxis(transformed, 0, axis)
+    result = np.empty(
+        (basis.dimension, vectors),
+        dtype=complex,
+    )
+    for state_index, state in enumerate(basis.states):
+        ordered = _ordered_particle_indices(state)
+        indices = tuple(
+            np.asarray(
+                [entry[axis] for entry in ordered],
+                dtype=int,
+            )
+            for axis in range(particles)
+        )
+        result[state_index] = (
+            _occupation_tensor_amplitude(state)
+            * np.sum(
+                transformed[indices + (slice(None),)],
+                axis=0,
+            )
+        )
+    return result
+
+
+def manybody_frame_overlap(
+    basis: BosonBasis,
+    left_frame: np.ndarray,
+    right_frame: np.ndarray,
+    left_orbitals: np.ndarray,
+    right_orbitals: np.ndarray,
+) -> np.ndarray:
+    """Return the physical overlap of two projected many-body frames."""
+
+    left_orbitals = np.asarray(left_orbitals, dtype=complex)
+    right_orbitals = np.asarray(right_orbitals, dtype=complex)
+    if left_orbitals.shape != right_orbitals.shape:
+        raise ValueError("orbital frames must have equal shape")
+    single_overlap = left_orbitals.conj().T @ right_orbitals
+    lifted_right = apply_bosonic_fock_lift(
+        basis,
+        single_overlap,
+        right_frame,
+    )
+    return np.asarray(left_frame, dtype=complex).conj().T @ lifted_right
+
+
+def _orthonormal_frame(frame: np.ndarray) -> np.ndarray:
+    values = np.asarray(frame, dtype=complex)
+    if values.ndim != 2 or values.shape[0] < values.shape[1]:
+        raise ValueError("frame must be a tall two-dimensional matrix")
+    orthonormal, _ = np.linalg.qr(values)
+    return orthonormal
+
+
+def _curvature_from_unitary(
+    unitary: np.ndarray,
+    area: float,
+) -> tuple[np.ndarray, np.ndarray]:
+    triangular, vectors = schur(unitary, output="complex")
+    phases = np.angle(np.diag(triangular))
+    curvature = (
+        vectors
+        @ np.diag(phases / area)
+        @ vectors.conj().T
+    )
+    return 0.5 * (curvature + curvature.conj().T), phases
+
+
+def _analyze_overlap_links(
+    overlaps_x: np.ndarray,
+    overlaps_y: np.ndarray,
+    delta_x: float,
+    delta_y: float,
+) -> BundleGeometry:
+    if (
+        overlaps_x.ndim != 4
+        or overlaps_x.shape != overlaps_y.shape
+        or overlaps_x.shape[-1] != overlaps_x.shape[-2]
+    ):
+        raise ValueError("overlap arrays must have shape (nx, ny, D, D)")
+    nx, ny, rank, _ = overlaps_x.shape
+    link_x = np.empty_like(overlaps_x, dtype=complex)
+    link_y = np.empty_like(overlaps_y, dtype=complex)
+    minimum_singular = np.inf
+    maximum_link_error = 0.0
+    identity = np.eye(rank, dtype=complex)
+    for ix in range(nx):
+        for iy in range(ny):
+            link_x[ix, iy], singular_x = polar_unitary(
+                overlaps_x[ix, iy]
+            )
+            link_y[ix, iy], singular_y = polar_unitary(
+                overlaps_y[ix, iy]
+            )
+            minimum_singular = min(
+                minimum_singular,
+                float(np.min(singular_x)),
+                float(np.min(singular_y)),
+            )
+            maximum_link_error = max(
+                maximum_link_error,
+                float(
+                    np.linalg.norm(
+                        link_x[ix, iy].conj().T
+                        @ link_x[ix, iy]
+                        - identity
+                    )
+                ),
+                float(
+                    np.linalg.norm(
+                        link_y[ix, iy].conj().T
+                        @ link_y[ix, iy]
+                        - identity
+                    )
+                ),
+            )
+    plaquette = np.empty_like(link_x)
+    curvature = np.empty_like(link_x)
+    determinant_flux = 0.0
+    trace_log_flux = 0.0
+    maximum_plaquette_error = 0.0
+    maximum_trace_phase = 0.0
+    area = float(delta_x * delta_y)
+    for ix in range(nx):
+        for iy in range(ny):
+            loop = (
+                link_x[ix, iy]
+                @ link_y[(ix + 1) % nx, iy]
+                @ link_x[ix, (iy + 1) % ny].conj().T
+                @ link_y[ix, iy].conj().T
+            )
+            loop, _ = polar_unitary(loop)
+            plaquette[ix, iy] = loop
+            maximum_plaquette_error = max(
+                maximum_plaquette_error,
+                float(
+                    np.linalg.norm(
+                        loop.conj().T @ loop - identity
+                    )
+                ),
+            )
+            curvature[ix, iy], phases = _curvature_from_unitary(
+                loop,
+                area,
+            )
+            trace_phase = float(np.sum(phases))
+            determinant_phase = float(
+                np.angle(np.exp(1j * trace_phase))
+            )
+            determinant_flux += determinant_phase
+            trace_log_flux += trace_phase
+            maximum_trace_phase = max(
+                maximum_trace_phase,
+                abs(trace_phase),
+            )
+    wilson_x = np.empty((ny, rank, rank), dtype=complex)
+    wilson_y = np.empty((nx, rank, rank), dtype=complex)
+    wilson_x_phases = np.empty((ny, rank), dtype=float)
+    wilson_y_phases = np.empty((nx, rank), dtype=float)
+    for iy in range(ny):
+        loop = identity.copy()
+        for ix in range(nx):
+            loop = loop @ link_x[ix, iy]
+        loop, _ = polar_unitary(loop)
+        wilson_x[iy] = loop
+        wilson_x_phases[iy] = np.sort(np.angle(np.linalg.eigvals(loop)))
+    for ix in range(nx):
+        loop = identity.copy()
+        for iy in range(ny):
+            loop = loop @ link_y[ix, iy]
+        loop, _ = polar_unitary(loop)
+        wilson_y[ix] = loop
+        wilson_y_phases[ix] = np.sort(np.angle(np.linalg.eigvals(loop)))
+    return BundleGeometry(
+        link_x=link_x,
+        link_y=link_y,
+        plaquette=plaquette,
+        plaquette_curvature=curvature,
+        wilson_x=wilson_x,
+        wilson_y=wilson_y,
+        wilson_x_phases=wilson_x_phases,
+        wilson_y_phases=wilson_y_phases,
+        chern_determinant=determinant_flux / (2.0 * np.pi),
+        chern_trace_log=trace_log_flux / (2.0 * np.pi),
+        determinant_branch_margin=float(np.pi - maximum_trace_phase),
+        minimum_overlap_singular_value=float(minimum_singular),
+        maximum_link_unitarity_error=maximum_link_error,
+        maximum_plaquette_unitarity_error=maximum_plaquette_error,
+    )
+
+
+def analyze_ambient_frame_mesh(
+    frames: np.ndarray,
+) -> BundleGeometry:
+    """Analyze a periodic ambient-frame mesh."""
+
+    values = np.asarray(frames, dtype=complex)
+    if values.ndim != 4:
+        raise ValueError("frames must have shape (nx, ny, ambient, rank)")
+    nx, ny, _, rank = values.shape
+    normalized = np.empty_like(values)
+    for ix in range(nx):
+        for iy in range(ny):
+            normalized[ix, iy] = _orthonormal_frame(values[ix, iy])
+    overlaps_x = np.empty((nx, ny, rank, rank), dtype=complex)
+    overlaps_y = np.empty_like(overlaps_x)
+    for ix in range(nx):
+        for iy in range(ny):
+            frame = normalized[ix, iy]
+            overlaps_x[ix, iy] = (
+                frame.conj().T @ normalized[(ix + 1) % nx, iy]
+            )
+            overlaps_y[ix, iy] = (
+                frame.conj().T @ normalized[ix, (iy + 1) % ny]
+            )
+    return _analyze_overlap_links(
+        overlaps_x,
+        overlaps_y,
+        2.0 * np.pi / nx,
+        2.0 * np.pi / ny,
+    )
+
+
+def analyze_frame_bundle(
+    coefficient_frames: np.ndarray,
+    orbital_frames: np.ndarray,
+    basis: BosonBasis,
+) -> BundleGeometry:
+    """Analyze physical many-body frames whose orbital bases vary on a mesh."""
+
+    coefficients = np.asarray(coefficient_frames, dtype=complex)
+    orbitals = np.asarray(orbital_frames, dtype=complex)
+    if (
+        coefficients.ndim != 4
+        or orbitals.ndim != 4
+        or coefficients.shape[:2] != orbitals.shape[:2]
+        or coefficients.shape[2] != basis.dimension
+        or orbitals.shape[-1] != basis.n_orbitals
+    ):
+        raise ValueError("coefficient/orbital frame meshes are incompatible")
+    nx, ny, _, rank = coefficients.shape
+    overlaps_x = np.empty((nx, ny, rank, rank), dtype=complex)
+    overlaps_y = np.empty_like(overlaps_x)
+    for ix in range(nx):
+        for iy in range(ny):
+            overlaps_x[ix, iy] = manybody_frame_overlap(
+                basis,
+                coefficients[ix, iy],
+                coefficients[(ix + 1) % nx, iy],
+                orbitals[ix, iy],
+                orbitals[(ix + 1) % nx, iy],
+            )
+            overlaps_y[ix, iy] = manybody_frame_overlap(
+                basis,
+                coefficients[ix, iy],
+                coefficients[ix, (iy + 1) % ny],
+                orbitals[ix, iy],
+                orbitals[ix, (iy + 1) % ny],
+            )
+    return _analyze_overlap_links(
+        overlaps_x,
+        overlaps_y,
+        2.0 * np.pi / nx,
+        2.0 * np.pi / ny,
+    )
+
+
+def random_local_gauge(
+    frames: np.ndarray,
+    seed: int,
+) -> np.ndarray:
+    """Apply independent local frame gauges on a periodic mesh."""
+
+    values = np.asarray(frames, dtype=complex)
+    if values.ndim != 4:
+        raise ValueError("frames must have shape (nx, ny, ambient, rank)")
+    rng = np.random.default_rng(int(seed))
+    result = np.empty_like(values)
+    rank = values.shape[-1]
+    for ix in range(values.shape[0]):
+        for iy in range(values.shape[1]):
+            matrix = rng.normal(size=(rank, rank))
+            matrix = matrix + 1j * rng.normal(size=matrix.shape)
+            unitary, _ = np.linalg.qr(matrix)
+            result[ix, iy] = values[ix, iy] @ unitary
+    return result
+
+
+def sorted_wilson_eigenphases(
+    geometry: BundleGeometry,
+) -> np.ndarray:
+    """Return both noncontractible Wilson-loop phase spectra."""
+
+    return np.concatenate(
+        [geometry.wilson_x_phases, geometry.wilson_y_phases],
+        axis=0,
+    )
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/lgeth/channels.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/lgeth/channels.py
new file mode 100644
index 000000000..2708f6c0d
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/lgeth/channels.py
@@ -0,0 +1,230 @@
+"""Model-independent channel geometry and exact nullity accounting."""
+
+from __future__ import annotations
+
+from dataclasses import dataclass
+from typing import Any
+
+import numpy as np
+
+from .combinatorics import laughlin_zero_mode_count, root_descendant_partition
+from .lattice import (
+    build_kapit_laughlin_parent,
+    channel_matrix,
+    manybody_one_body_operator,
+    projected_site_potential,
+)
+
+
+@dataclass(frozen=True)
+class NullityDecomposition:
+    """Accessibility and pulled-back-form contributions to curvature nullity."""
+
+    target_dimension: int
+    active_rank: int
+    curvature_rank: int
+    total: int
+    accessibility: int
+    form: int
+    active_cutoff: float
+    curvature_cutoff: float
+
+
+@dataclass(frozen=True)
+class PhysicalChannelCache:
+    """Task-local factorization of the physical tangent-to-channel map."""
+
+    N: int
+    n_flux: int
+    rank: int
+    external_dimension: int
+    energies: np.ndarray
+    tangent_basis: np.ndarray
+    channel_basis: np.ndarray
+    tangent_gram: np.ndarray
+    external_gap: float
+    kernel_bandwidth: float
+    metadata: dict[str, Any]
+
+
+def build_physical_channel_cache(
+    n_particles: int = 3,
+    n_flux: int = 10,
+    theta_x: float = 0.17,
+    theta_y: float = 0.29,
+) -> PhysicalChannelCache:
+    """Build the fixed Kapit--Mueller tangent-channel cache independently."""
+
+    N = int(n_particles)
+    n = int(n_flux)
+    system = build_kapit_laughlin_parent(N, n, theta_x, theta_y)
+    parent = system.parent.toarray()
+    energies, vectors = np.linalg.eigh(0.5 * (parent + parent.conj().T))
+    rank = laughlin_zero_mode_count(N, n)
+    energies_p = energies[:rank]
+    energies_q = energies[rank:]
+    vectors_p = vectors[:, :rank]
+    vectors_q = vectors[:, rank:]
+    physical_sites = system.orbitals.shape[0]
+    tangent_basis = np.empty(
+        (physical_sites, system.basis.dimension, system.basis.dimension),
+        dtype=complex,
+    )
+    channel_basis = np.empty(
+        (physical_sites, rank, system.basis.dimension - rank),
+        dtype=complex,
+    )
+    for site in range(physical_sites):
+        potential = np.zeros(physical_sites, dtype=float)
+        potential[site] = 1.0
+        projected = projected_site_potential(system.orbitals, potential)
+        tangent = manybody_one_body_operator(system.basis, projected)
+        tangent_basis[site] = tangent.toarray()
+        channel_basis[site] = channel_matrix(
+            energies_p,
+            vectors_p,
+            energies_q,
+            vectors_q,
+            tangent,
+        )
+    tangent_gram = np.einsum(
+        "iab,jab->ij",
+        tangent_basis.conj(),
+        tangent_basis,
+        optimize=True,
+    ).real
+    return PhysicalChannelCache(
+        N=N,
+        n_flux=n,
+        rank=rank,
+        external_dimension=system.basis.dimension - rank,
+        energies=energies,
+        tangent_basis=tangent_basis,
+        channel_basis=channel_basis,
+        tangent_gram=tangent_gram,
+        external_gap=float(energies_q[0] - energies_p[-1]),
+        kernel_bandwidth=float(np.ptp(energies_p)),
+        metadata={
+            "theta_x": float(theta_x),
+            "theta_y": float(theta_y),
+            "basis_dimension": int(system.basis.dimension),
+            "physical_sites": int(physical_sites),
+        },
+    )
+
+
+def normalized_potential(
+    rng: np.random.Generator,
+    sites: int,
+) -> np.ndarray:
+    """Draw a mean-zero unit vector of local-potential coefficients."""
+
+    values = rng.normal(size=int(sites))
+    values -= np.mean(values)
+    norm = float(np.linalg.norm(values))
+    if norm <= 0.0:
+        raise RuntimeError("local potential has zero norm")
+    return values / norm
+
+
+def cached_channel(
+    coefficients: np.ndarray,
+    cache: PhysicalChannelCache,
+) -> np.ndarray:
+    """Evaluate and Hilbert--Schmidt normalize a cached physical channel."""
+
+    vector = np.asarray(coefficients, dtype=float)
+    norm_squared = float(vector @ cache.tangent_gram @ vector)
+    if norm_squared <= 0.0:
+        raise RuntimeError("many-body tangent has zero norm")
+    return (
+        np.tensordot(vector, cache.channel_basis, axes=(0, 0))
+        / np.sqrt(norm_squared)
+    )
+
+
+def root_response_partition(N: int, n: int):
+    """Return the exact first-descendant root partition."""
+
+    return root_descendant_partition(int(N), int(n), q=1, k=1, r=2)
+
+
+def _validated_channel_pair(
+    channel_v: np.ndarray,
+    channel_w: np.ndarray,
+) -> tuple[np.ndarray, np.ndarray]:
+    x = np.asarray(channel_v, dtype=complex)
+    y = np.asarray(channel_w, dtype=complex)
+    if x.ndim != 2 or y.ndim != 2:
+        raise ValueError("channels must be two-dimensional")
+    if x.shape != y.shape:
+        raise ValueError("channels must have equal shape")
+    if x.shape[0] == 0 or x.shape[1] == 0:
+        raise ValueError("channels must be nonempty")
+    return x, y
+
+
+def curvature_from_channels(
+    channel_v: np.ndarray,
+    channel_w: np.ndarray,
+) -> np.ndarray:
+    """Return the Hermitian non-Abelian curvature channel form."""
+
+    x, y = _validated_channel_pair(channel_v, channel_w)
+    curvature = 1j * (x @ y.conj().T - y @ x.conj().T)
+    return 0.5 * (curvature + curvature.conj().T)
+
+
+def _rank_with_cutoff(
+    matrix: np.ndarray,
+    rtol: float,
+    atol: float,
+) -> tuple[int, float]:
+    if rtol < 0.0 or atol < 0.0:
+        raise ValueError("rank tolerances must be nonnegative")
+    singular_values = np.linalg.svd(
+        np.asarray(matrix, dtype=complex),
+        compute_uv=False,
+    )
+    if singular_values.size == 0:
+        return 0, float(atol)
+    cutoff = max(float(atol), float(rtol) * float(singular_values[0]))
+    return int(np.count_nonzero(singular_values > cutoff)), cutoff
+
+
+def nullity_decomposition(
+    channel_v: np.ndarray,
+    channel_w: np.ndarray,
+    rtol: float = 1e-12,
+    atol: float = 0.0,
+) -> NullityDecomposition:
+    """Return the exact rank-nullity split at a specified numerical tolerance."""
+
+    x, y = _validated_channel_pair(channel_v, channel_w)
+    stacked = np.concatenate([x, y], axis=1)
+    active_rank, active_cutoff = _rank_with_cutoff(
+        stacked,
+        rtol=rtol,
+        atol=atol,
+    )
+    curvature = curvature_from_channels(x, y)
+    curvature_rank, curvature_cutoff = _rank_with_cutoff(
+        curvature,
+        rtol=rtol,
+        atol=atol,
+    )
+    target_dimension = x.shape[0]
+    accessibility = target_dimension - active_rank
+    form = active_rank - curvature_rank
+    if accessibility < 0 or form < 0:
+        raise RuntimeError("rank accounting produced a negative nullity")
+    return NullityDecomposition(
+        target_dimension=target_dimension,
+        active_rank=active_rank,
+        curvature_rank=curvature_rank,
+        total=target_dimension - curvature_rank,
+        accessibility=accessibility,
+        form=form,
+        active_cutoff=active_cutoff,
+        curvature_cutoff=curvature_cutoff,
+    )
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/lgeth/combinatorics.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/lgeth/combinatorics.py
new file mode 100644
index 000000000..7f35e3aee
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/lgeth/combinatorics.py
@@ -0,0 +1,223 @@
+"""Exact root combinatorics for geometric-accessibility filtrations."""
+
+from __future__ import annotations
+
+from dataclasses import dataclass
+from functools import lru_cache
+from math import comb
+from typing import Iterator
+
+
+Occupation = tuple[int, ...]
+
+
+@dataclass(frozen=True)
+class RootPartition:
+    """Partition a fixed-particle root space by deletion accessibility."""
+
+    n_particles: int
+    n_flux: int
+    q: int
+    k: int
+    r: int
+    states: tuple[Occupation, ...]
+    zero_modes: tuple[int, ...]
+    descendants: tuple[int, ...]
+    descendant_external: tuple[int, ...]
+    primitive: tuple[int, ...]
+
+
+def occupation_states(
+    n_particles: int,
+    n_orbitals: int,
+) -> Iterator[Occupation]:
+    """Yield weak compositions in deterministic lexicographic order."""
+
+    particles = int(n_particles)
+    orbitals = int(n_orbitals)
+    if particles < 0:
+        raise ValueError("n_particles must be nonnegative")
+    if orbitals <= 0:
+        raise ValueError("n_orbitals must be positive")
+
+    def recurse(remaining: int, length: int) -> Iterator[Occupation]:
+        if length == 1:
+            yield (remaining,)
+            return
+        for population in range(remaining + 1):
+            for suffix in recurse(remaining - population, length - 1):
+                yield (population,) + suffix
+
+    yield from recurse(particles, orbitals)
+
+
+def cyclic_kr_admissible(
+    state: Occupation,
+    k: int,
+    r: int,
+) -> bool:
+    """Return whether every cyclic window of length ``r`` contains at most ``k``."""
+
+    if not state:
+        raise ValueError("state must be nonempty")
+    cluster = int(k)
+    window = int(r)
+    if cluster < 0:
+        raise ValueError("k must be nonnegative")
+    if window <= 0 or window > len(state):
+        raise ValueError("r must lie between one and the orbital count")
+    return all(
+        sum(
+            state[(start + offset) % len(state)]
+            for offset in range(window)
+        )
+        <= cluster
+        for start in range(len(state))
+    )
+
+
+def _validate_laughlin_domain(
+    n_particles: int,
+    n_flux: int,
+) -> tuple[int, int]:
+    particles = int(n_particles)
+    flux = int(n_flux)
+    if particles <= 0:
+        raise ValueError("n_particles must be positive")
+    if flux < 2 * particles:
+        raise ValueError("n_flux must be at least 2*n_particles")
+    return particles, flux
+
+
+def laughlin_zero_mode_count(
+    n_particles: int,
+    n_flux: int,
+) -> int:
+    """Return the cyclic bosonic Laughlin ``(1,2)`` root count."""
+
+    particles, flux = _validate_laughlin_domain(
+        n_particles,
+        n_flux,
+    )
+    return (
+        flux
+        * comb(flux - particles, particles)
+        // (flux - particles)
+    )
+
+
+def laughlin_onebody_capacity(
+    n_particles: int,
+    n_flux: int,
+) -> int:
+    """Return ``dim(W_N^(1)/P_N)`` for cyclic Laughlin roots."""
+
+    particles, flux = _validate_laughlin_domain(
+        n_particles,
+        n_flux,
+    )
+    if particles == 1:
+        return 0
+    return 2 * flux * comb(flux - particles, particles - 2)
+
+
+def _bounded_removals(
+    state: Occupation,
+    total: int,
+) -> Iterator[Occupation]:
+    """Yield occupation removals bounded componentwise by ``state``."""
+
+    target = int(total)
+
+    def recurse(
+        orbital: int,
+        remaining: int,
+        prefix: Occupation,
+    ) -> Iterator[Occupation]:
+        if orbital == len(state):
+            if remaining == 0:
+                yield prefix
+            return
+        maximum = min(state[orbital], remaining)
+        for removed in range(maximum + 1):
+            yield from recurse(
+                orbital + 1,
+                remaining - removed,
+                prefix + (removed,),
+            )
+
+    yield from recurse(0, target, ())
+
+
+@lru_cache(maxsize=None)
+def _deletion_accessible(
+    state: Occupation,
+    q: int,
+    k: int,
+    r: int,
+) -> bool:
+    for removal in _bounded_removals(state, q):
+        reduced = tuple(
+            population - removed
+            for population, removed in zip(state, removal, strict=True)
+        )
+        if cyclic_kr_admissible(reduced, k=k, r=r):
+            return True
+    return False
+
+
+def root_descendant_partition(
+    n_particles: int,
+    n_flux: int,
+    q: int,
+    k: int = 1,
+    r: int = 2,
+) -> RootPartition:
+    """Partition roots by whether deleting ``q`` particles leaves an admissible root."""
+
+    particles = int(n_particles)
+    flux = int(n_flux)
+    body_order = int(q)
+    if particles <= 0:
+        raise ValueError("n_particles must be positive")
+    if flux <= 0:
+        raise ValueError("n_flux must be positive")
+    if body_order < 0 or body_order > particles:
+        raise ValueError("q must lie between zero and n_particles")
+    if r > flux:
+        raise ValueError("r cannot exceed n_flux")
+
+    states = tuple(occupation_states(particles, flux))
+    zero_modes = tuple(
+        index
+        for index, state in enumerate(states)
+        if cyclic_kr_admissible(state, k=k, r=r)
+    )
+    descendants = tuple(
+        index
+        for index, state in enumerate(states)
+        if _deletion_accessible(
+            state,
+            q=body_order,
+            k=int(k),
+            r=int(r),
+        )
+    )
+    zero_set = set(zero_modes)
+    descendant_set = set(descendants)
+    descendant_external = tuple(sorted(descendant_set - zero_set))
+    primitive = tuple(
+        sorted(set(range(len(states))) - descendant_set)
+    )
+    return RootPartition(
+        n_particles=particles,
+        n_flux=flux,
+        q=body_order,
+        k=int(k),
+        r=int(r),
+        states=states,
+        zero_modes=zero_modes,
+        descendants=descendants,
+        descendant_external=descendant_external,
+        primitive=primitive,
+    )
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/lgeth/controls.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/lgeth/controls.py
new file mode 100644
index 000000000..bbfe6ce60
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/lgeth/controls.py
@@ -0,0 +1,341 @@
+"""Independent interventions for spectral and projector-geometric chaos."""
+
+from __future__ import annotations
+
+from dataclasses import dataclass
+
+import numpy as np
+
+from .form_factors import form_factor_parts
+from .statistics import bulk_gap_ratio_per_spectrum
+
+
+@dataclass(frozen=True)
+class FourierTangentPair:
+    """Momentum-resolved real quadratures on a square physical lattice."""
+
+    length: int
+    kx: int
+    ky: int
+    orbit_key: tuple[int, int]
+    v: np.ndarray
+    w: np.ndarray
+
+
+@dataclass(frozen=True)
+class FixedProjectorControl:
+    """Energy statistics varied inside one exactly fixed target projector."""
+
+    alphas: np.ndarray
+    times: np.ndarray
+    energy_spectra: np.ndarray
+    mean_gap_ratio: np.ndarray
+    energy_raw: np.ndarray
+    energy_disconnected: np.ndarray
+    energy_connected: np.ndarray
+    projector_distance: np.ndarray
+    curvature_spectrum_error: np.ndarray
+    seed: int
+
+
+def fourier_tangent_pairs(length: int) -> list[FourierTangentPair]:
+    """Return every nonzero momentum cosine/sine pair exactly once."""
+
+    linear_size = int(length)
+    if linear_size < 3 or linear_size % 2 == 0:
+        raise ValueError("length must be an odd integer at least three")
+    coordinates = np.asarray(
+        [
+            (x, y)
+            for y in range(linear_size)
+            for x in range(linear_size)
+        ],
+        dtype=float,
+    )
+    pairs: list[FourierTangentPair] = []
+    for ky in range(linear_size):
+        for kx in range(linear_size):
+            if (kx, ky) == (0, 0):
+                continue
+            phase = (
+                2.0
+                * np.pi
+                * (
+                    kx * coordinates[:, 0]
+                    + ky * coordinates[:, 1]
+                )
+                / linear_size
+            )
+            v = np.cos(phase)
+            w = np.sin(phase)
+            v -= np.mean(v)
+            w -= np.mean(w)
+            norm_v = float(np.linalg.norm(v))
+            norm_w = float(np.linalg.norm(w))
+            if norm_v <= 1e-14 or norm_w <= 1e-14:
+                raise RuntimeError("nonzero momentum has a null real quadrature")
+            v /= norm_v
+            w /= norm_w
+            inverse = (
+                (-kx) % linear_size,
+                (-ky) % linear_size,
+            )
+            orbit_key = min((kx, ky), inverse)
+            pairs.append(
+                FourierTangentPair(
+                    length=linear_size,
+                    kx=kx,
+                    ky=ky,
+                    orbit_key=orbit_key,
+                    v=v,
+                    w=w,
+                )
+            )
+    return pairs
+
+
+def _validated_tangent_gram(
+    tangent_gram: np.ndarray,
+    dimension: int,
+) -> np.ndarray:
+    gram = np.asarray(tangent_gram, dtype=float)
+    if gram.shape != (dimension, dimension):
+        raise ValueError("tangent_gram has the wrong shape")
+    if np.any(~np.isfinite(gram)):
+        raise ValueError("tangent_gram must be finite")
+    gram = 0.5 * (gram + gram.T)
+    eigenvalues = np.linalg.eigvalsh(gram)
+    if float(eigenvalues[0]) < -1e-10 * max(
+        float(eigenvalues[-1]),
+        1.0,
+    ):
+        raise ValueError("tangent_gram must be positive semidefinite")
+    return gram
+
+
+def gram_normalize(
+    values: np.ndarray,
+    tangent_gram: np.ndarray,
+) -> np.ndarray:
+    """Mean-center and normalize a coefficient vector in the tangent Gram."""
+
+    vector = np.asarray(values, dtype=float)
+    if vector.ndim != 1 or vector.size < 2 or np.any(~np.isfinite(vector)):
+        raise ValueError("tangent coefficients must be a finite vector")
+    gram = _validated_tangent_gram(tangent_gram, vector.size)
+    centered = vector - np.mean(vector)
+    norm_squared = float(centered @ gram @ centered)
+    if norm_squared <= 1e-24:
+        raise ValueError("tangent coefficients have zero Gram norm")
+    return centered / np.sqrt(norm_squared)
+
+
+def scrambled_tangent_pair(
+    pair: FourierTangentPair,
+    random_v: np.ndarray,
+    random_w: np.ndarray,
+    g: float,
+    tangent_gram: np.ndarray,
+) -> tuple[np.ndarray, np.ndarray]:
+    """Interpolate from a structured momentum pair to random local tangents."""
+
+    coupling = float(g)
+    if not 0.0 <= coupling <= 1.0:
+        raise ValueError("g must lie in [0,1]")
+    if pair.v.shape != pair.w.shape:
+        raise ValueError("Fourier tangent pair has inconsistent shapes")
+    gram = _validated_tangent_gram(tangent_gram, pair.v.size)
+    structured_v = gram_normalize(pair.v, gram)
+    structured_w = gram_normalize(pair.w, gram)
+    residual_v = gram_normalize(random_v, gram)
+    residual_w = gram_normalize(random_w, gram)
+    mixed_v = (
+        np.sqrt(1.0 - coupling) * structured_v
+        + np.sqrt(coupling) * residual_v
+    )
+    mixed_w = (
+        np.sqrt(1.0 - coupling) * structured_w
+        + np.sqrt(coupling) * residual_w
+    )
+    return (
+        gram_normalize(mixed_v, gram),
+        gram_normalize(mixed_w, gram),
+    )
+
+
+def _center_and_normalize_hermitian(matrix: np.ndarray) -> np.ndarray:
+    values = np.asarray(matrix, dtype=complex)
+    if values.ndim != 2 or values.shape[0] != values.shape[1]:
+        raise ValueError("matrix must be square")
+    values = 0.5 * (values + values.conj().T)
+    values -= np.trace(values) / values.shape[0] * np.eye(
+        values.shape[0],
+        dtype=complex,
+    )
+    norm = float(np.linalg.norm(values))
+    if norm <= 1e-14:
+        raise RuntimeError("Hermitian control has zero norm")
+    return values / norm
+
+
+def _numerical_projector_distance(
+    target_block: np.ndarray,
+) -> float:
+    dimension = int(target_block.shape[0])
+    full = np.zeros((2 * dimension, 2 * dimension), dtype=complex)
+    full[:dimension, :dimension] = 0.1 * target_block
+    full[dimension:, dimension:] = np.diag(
+        np.linspace(2.0, 3.0, dimension)
+    )
+    eigenvalues, eigenvectors = np.linalg.eigh(full)
+    if float(eigenvalues[dimension - 1]) >= float(eigenvalues[dimension]):
+        raise RuntimeError("fixed-projector control closed its external gap")
+    observed = (
+        eigenvectors[:, :dimension]
+        @ eigenvectors[:, :dimension].conj().T
+    )
+    expected = np.zeros_like(full)
+    expected[:dimension, :dimension] = np.eye(dimension)
+    return float(np.linalg.norm(observed - expected))
+
+
+def projector_curvature_invariance(
+    reference_spectrum: np.ndarray,
+    repeated_spectra: np.ndarray,
+) -> dict[str, float]:
+    """Return maximum absolute and relative errors of repeated curvature data."""
+
+    reference = np.asarray(reference_spectrum, dtype=float)
+    repeated = np.asarray(repeated_spectra, dtype=float)
+    if reference.ndim != 1 or repeated.ndim != 2:
+        raise ValueError("reference must be 1D and repeated_spectra must be 2D")
+    if repeated.shape[1] != reference.size:
+        raise ValueError("curvature spectra have incompatible dimensions")
+    difference = repeated - reference[None, :]
+    absolute = float(np.max(np.abs(difference)))
+    scale = max(float(np.max(np.abs(reference))), 1e-15)
+    return {
+        "maximum_absolute_error": absolute,
+        "maximum_relative_error": absolute / scale,
+    }
+
+
+def fixed_projector_spectral_ensemble(
+    dimension: int,
+    samples: int,
+    alphas: np.ndarray,
+    seed: int,
+    reference_curvature_spectrum: np.ndarray | None = None,
+    times: np.ndarray | None = None,
+) -> FixedProjectorControl:
+    """Generate a Poisson-to-GUE interpolation inside one fixed projector."""
+
+    rank = int(dimension)
+    count = int(samples)
+    alpha_grid = np.asarray(alphas, dtype=float)
+    time_grid = (
+        np.linspace(0.0, 3.0, 61)
+        if times is None
+        else np.asarray(times, dtype=float)
+    )
+    if rank < 4 or count < 2:
+        raise ValueError("require dimension>=4 and samples>=2")
+    if (
+        alpha_grid.ndim != 1
+        or alpha_grid.size < 1
+        or np.any(~np.isfinite(alpha_grid))
+        or np.any((alpha_grid < 0.0) | (alpha_grid > 1.0))
+    ):
+        raise ValueError("alphas must be a finite one-dimensional grid in [0,1]")
+    if (
+        time_grid.ndim != 1
+        or time_grid.size < 1
+        or np.any(~np.isfinite(time_grid))
+    ):
+        raise ValueError("times must be a finite one-dimensional grid")
+    if reference_curvature_spectrum is None:
+        reference = np.linspace(-1.0, 1.0, rank)
+    else:
+        reference = np.asarray(
+            reference_curvature_spectrum,
+            dtype=float,
+        )
+    if reference.shape != (rank,) or np.any(~np.isfinite(reference)):
+        raise ValueError("reference_curvature_spectrum must match dimension")
+    rng = np.random.default_rng(int(seed))
+    spectra = np.empty(
+        (alpha_grid.size, count, rank),
+        dtype=np.float32,
+    )
+    first_matrices = np.empty(
+        (alpha_grid.size, rank, rank),
+        dtype=complex,
+    )
+    for sample in range(count):
+        spacings = rng.exponential(size=rank)
+        levels = np.cumsum(spacings)
+        poisson_matrix = _center_and_normalize_hermitian(
+            np.diag(levels)
+        )
+        gaussian = (
+            rng.normal(size=(rank, rank))
+            + 1j * rng.normal(size=(rank, rank))
+        )
+        gue_matrix = _center_and_normalize_hermitian(
+            gaussian + gaussian.conj().T
+        )
+        for index, alpha in enumerate(alpha_grid):
+            matrix = (
+                np.sqrt(1.0 - alpha * alpha) * poisson_matrix
+                + alpha * gue_matrix
+            )
+            spectra[index, sample] = np.linalg.eigvalsh(matrix)
+            if sample == 0:
+                first_matrices[index] = matrix
+    mean_gap_ratio = np.empty(alpha_grid.size, dtype=float)
+    raw = np.empty((alpha_grid.size, time_grid.size), dtype=float)
+    disconnected = np.empty_like(raw)
+    connected = np.empty_like(raw)
+    projector_distance = np.empty(alpha_grid.size, dtype=float)
+    repeated_curvature = np.repeat(
+        reference[None, :],
+        alpha_grid.size,
+        axis=0,
+    )
+    for index, alpha in enumerate(alpha_grid):
+        mean_gap_ratio[index] = float(
+            np.mean(
+                bulk_gap_ratio_per_spectrum(
+                    spectra[index],
+                    bulk_fraction=0.7,
+                )
+            )
+        )
+        parts = form_factor_parts(spectra[index], time_grid)
+        raw[index] = parts.raw
+        disconnected[index] = parts.disconnected
+        connected[index] = parts.connected
+        projector_distance[index] = _numerical_projector_distance(
+            first_matrices[index]
+        )
+    invariance = projector_curvature_invariance(
+        reference,
+        repeated_curvature,
+    )
+    curvature_error = np.full(
+        alpha_grid.size,
+        invariance["maximum_absolute_error"],
+        dtype=float,
+    )
+    return FixedProjectorControl(
+        alphas=alpha_grid,
+        times=time_grid,
+        energy_spectra=spectra,
+        mean_gap_ratio=mean_gap_ratio,
+        energy_raw=raw,
+        energy_disconnected=disconnected,
+        energy_connected=connected,
+        projector_distance=projector_distance,
+        curvature_spectrum_error=curvature_error,
+        seed=int(seed),
+    )
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/lgeth/form_factors.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/lgeth/form_factors.py
new file mode 100644
index 000000000..91af82f21
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/lgeth/form_factors.py
@@ -0,0 +1,272 @@
+"""Exact and empirical form factors for degenerate quantum geometry."""
+
+from __future__ import annotations
+
+from dataclasses import dataclass
+
+import numpy as np
+from scipy.special import eval_jacobi, gammaln, roots_jacobi
+
+from .jacobi import jacobi_parameters
+
+
+@dataclass(frozen=True)
+class FormFactorParts:
+    """Raw, disconnected, and connected form-factor components."""
+
+    raw: np.ndarray
+    disconnected: np.ndarray
+    connected: np.ndarray
+    normalization: int
+
+
+@dataclass(frozen=True)
+class JacobiFormFactor:
+    """Finite-dimensional connected Jacobi form factor."""
+
+    times: np.ndarray
+    connected_continuous: np.ndarray
+    connected_full: np.ndarray
+    plateau_full: float
+    unfolded_nodes: np.ndarray
+    quadrature_order: int
+    interior_dimension: int
+    atom_count_each: int
+    rank: int
+    channels: int
+    exponent: int
+    mass_error: float
+    orthogonality_error: float
+
+
+def _validated_spectra_times(
+    spectra: np.ndarray,
+    times: np.ndarray,
+) -> tuple[np.ndarray, np.ndarray]:
+    values = np.asarray(spectra, dtype=float)
+    grid = np.asarray(times, dtype=float)
+    if (
+        values.ndim != 2
+        or values.shape[0] < 1
+        or values.shape[1] < 1
+        or np.any(~np.isfinite(values))
+    ):
+        raise ValueError("spectra must be a finite nonempty two-dimensional array")
+    if grid.ndim != 1 or grid.size < 1 or np.any(~np.isfinite(grid)):
+        raise ValueError("times must be a finite nonempty one-dimensional array")
+    return values, grid
+
+
+def form_factor_parts(
+    spectra: np.ndarray,
+    times: np.ndarray,
+    phase_scale: float = 2.0 * np.pi,
+) -> FormFactorParts:
+    """Return one consistently normalized form-factor decomposition."""
+
+    values, grid = _validated_spectra_times(spectra, times)
+    scale = float(phase_scale)
+    if not np.isfinite(scale):
+        raise ValueError("phase_scale must be finite")
+    levels = int(values.shape[1])
+    partition = np.empty((values.shape[0], grid.size), dtype=np.complex128)
+    for start in range(0, values.shape[0], 512):
+        stop = min(start + 512, values.shape[0])
+        phases = np.exp(
+            -1j
+            * scale
+            * values[start:stop, :, None]
+            * grid[None, None, :]
+        )
+        partition[start:stop] = np.sum(phases, axis=1)
+    raw = np.mean(np.abs(partition) ** 2, axis=0) / levels
+    disconnected = np.abs(np.mean(partition, axis=0)) ** 2 / levels
+    connected = raw - disconnected
+    connected[np.abs(connected) < 5e-15] = 0.0
+    return FormFactorParts(
+        raw=raw,
+        disconnected=disconnected,
+        connected=connected,
+        normalization=levels,
+    )
+
+
+def degenerate_energy_form_factor(
+    dimension: int,
+    times: np.ndarray,
+) -> FormFactorParts:
+    """Return the exact centered SFF of a rank-``dimension`` flat band."""
+
+    rank = int(dimension)
+    if rank < 1:
+        raise ValueError("dimension must be positive")
+    spectra = np.zeros((2, rank), dtype=float)
+    return form_factor_parts(spectra, times, phase_scale=1.0)
+
+
+def _log_jacobi_norm(order: int, exponent: int) -> float:
+    degree = int(order)
+    alpha = int(exponent)
+    return float(
+        (2 * alpha + 1) * np.log(2.0)
+        - np.log(2 * degree + 2 * alpha + 1)
+        + 2 * gammaln(degree + alpha + 1)
+        - gammaln(degree + 1)
+        - gammaln(degree + 2 * alpha + 1)
+    )
+
+
+def _weighted_jacobi_projector(
+    interior_dimension: int,
+    exponent: int,
+    quadrature_order: int,
+) -> tuple[np.ndarray, np.ndarray, float, float]:
+    k = int(interior_dimension)
+    alpha = int(exponent)
+    order = int(quadrature_order)
+    if k < 1:
+        raise ValueError("interior_dimension must be positive")
+    if alpha < 0:
+        raise ValueError("exponent must be nonnegative")
+    if order < max(32, k):
+        raise ValueError("quadrature_order must be at least max(32,k)")
+    nodes, weights = roots_jacobi(order, alpha, alpha)
+    basis = np.empty((order, k), dtype=float)
+    square_root_weights = np.sqrt(weights)
+    for degree in range(k):
+        polynomial = eval_jacobi(degree, alpha, alpha, nodes)
+        basis[:, degree] = (
+            square_root_weights
+            * polynomial
+            * np.exp(-0.5 * _log_jacobi_norm(degree, alpha))
+        )
+    if np.any(~np.isfinite(basis)):
+        raise RuntimeError("nonfinite orthonormal Jacobi basis")
+    gram = basis.T @ basis
+    orthogonality_error = float(
+        np.max(np.abs(gram - np.eye(k, dtype=float)))
+    )
+    if orthogonality_error > 2e-8:
+        raise RuntimeError(
+            "Gauss--Jacobi basis failed orthogonality: "
+            f"{orthogonality_error:.3e}"
+        )
+    projector = basis @ basis.T
+    density_mass = np.diag(projector)
+    mass_error = float(abs(np.sum(density_mass) - k))
+    if mass_error > 2e-8:
+        raise RuntimeError(
+            f"Jacobi quadrature mass failed: {mass_error:.3e}"
+        )
+    unfolded_nodes = np.cumsum(density_mass) - 0.5 * density_mass
+    return projector, unfolded_nodes, mass_error, orthogonality_error
+
+
+def finite_jacobi_form_factor(
+    r: int,
+    M: int,
+    times: np.ndarray,
+    quadrature_order: int = 512,
+) -> JacobiFormFactor:
+    """Return the exact finite-rank unfolded complex-Jacobi connected SFF."""
+
+    parameters = jacobi_parameters(r, M)
+    grid = np.asarray(times, dtype=float)
+    if (
+        grid.ndim != 1
+        or grid.size < 1
+        or np.any(~np.isfinite(grid))
+        or np.any(grid < 0.0)
+    ):
+        raise ValueError("times must be a finite nonnegative one-dimensional grid")
+    k = int(parameters.interior_dimension)
+    if k < 1:
+        raise ValueError("the continuous Jacobi sector is empty")
+    projector, unfolded, mass_error, orthogonality_error = (
+        _weighted_jacobi_projector(
+            k,
+            parameters.exponent,
+            quadrature_order,
+        )
+    )
+    cluster_kernel = np.abs(projector) ** 2
+    continuous = np.empty(grid.size, dtype=float)
+    for index, time in enumerate(grid):
+        phase = np.exp(-2j * np.pi * float(time) * unfolded)
+        cluster = float(
+            np.real(np.vdot(phase, cluster_kernel @ phase))
+        )
+        value = 1.0 - cluster / k
+        if -5e-11 < value < 0.0:
+            value = 0.0
+        continuous[index] = value
+    atom_count = int(parameters.plus_atoms)
+    full = (k / parameters.r) * continuous
+    return JacobiFormFactor(
+        times=grid,
+        connected_continuous=continuous,
+        connected_full=full,
+        plateau_full=float(k / parameters.r),
+        unfolded_nodes=unfolded,
+        quadrature_order=int(quadrature_order),
+        interior_dimension=k,
+        atom_count_each=atom_count,
+        rank=int(parameters.r),
+        channels=int(parameters.M),
+        exponent=int(parameters.exponent),
+        mass_error=mass_error,
+        orthogonality_error=orthogonality_error,
+    )
+
+
+def atom_raw_decomposition(
+    interior_spectra: np.ndarray,
+    minus_atoms: int,
+    plus_atoms: int,
+    times: np.ndarray,
+    phase_scale: float = 2.0 * np.pi,
+) -> dict[str, np.ndarray]:
+    """Decompose a full raw SFF into exact atom and continuum terms."""
+
+    interior, grid = _validated_spectra_times(interior_spectra, times)
+    negative = int(minus_atoms)
+    positive = int(plus_atoms)
+    if negative < 0 or positive < 0:
+        raise ValueError("atom counts must be nonnegative")
+    total = int(interior.shape[1] + negative + positive)
+    if total < 1:
+        raise ValueError("the full spectrum must be nonempty")
+    scale = float(phase_scale)
+    continuum_partition = np.sum(
+        np.exp(
+            -1j
+            * scale
+            * interior[:, :, None]
+            * grid[None, None, :]
+        ),
+        axis=1,
+    )
+    atom_partition = (
+        negative * np.exp(1j * scale * grid)
+        + positive * np.exp(-1j * scale * grid)
+    )
+    atom_atom = np.abs(atom_partition) ** 2 / total
+    atom_continuum = (
+        2.0
+        * np.real(
+            atom_partition.conj()
+            * np.mean(continuum_partition, axis=0)
+        )
+        / total
+    )
+    continuum_continuum = (
+        np.mean(np.abs(continuum_partition) ** 2, axis=0) / total
+    )
+    full = atom_atom + atom_continuum + continuum_continuum
+    return {
+        "full": full,
+        "atom_atom": atom_atom,
+        "atom_continuum": atom_continuum,
+        "continuum_continuum": continuum_continuum,
+        "normalization": np.asarray(total, dtype=int),
+    }
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/lgeth/grassmann.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/lgeth/grassmann.py
new file mode 100644
index 000000000..c83c9c644
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/lgeth/grassmann.py
@@ -0,0 +1,350 @@
+"""Grassmannian diagnostics and covariance-deformed Geometric-ETH models."""
+
+from __future__ import annotations
+
+from collections.abc import Iterable
+from typing import Any
+
+import numpy as np
+from scipy.linalg import solve_sylvester
+
+
+def _validated_row_isometry(
+    rows: np.ndarray,
+    tolerance: float = 1e-9,
+) -> np.ndarray:
+    matrix = np.asarray(rows, dtype=complex)
+    if matrix.ndim != 2 or matrix.shape[0] < 1:
+        raise ValueError("rows must be a nonempty two-dimensional matrix")
+    if matrix.shape[0] > matrix.shape[1]:
+        raise ValueError("a row isometry cannot have more rows than columns")
+    residual = np.linalg.norm(
+        matrix @ matrix.conj().T - np.eye(matrix.shape[0])
+    )
+    if residual > float(tolerance):
+        raise ValueError("rows do not form an isometry")
+    return matrix
+
+
+def row_projector(rows: np.ndarray) -> np.ndarray:
+    """Return the ambient projector onto a whitened channel row space."""
+
+    matrix = _validated_row_isometry(rows)
+    projector = matrix.conj().T @ matrix
+    return 0.5 * (projector + projector.conj().T)
+
+
+def mean_projector_anisotropy(
+    row_isometries: Iterable[np.ndarray],
+) -> dict[str, Any]:
+    """Measure the departure of the ensemble mean projector from Haar."""
+
+    matrices = [_validated_row_isometry(rows) for rows in row_isometries]
+    if not matrices:
+        raise ValueError("at least one row isometry is required")
+    shape = matrices[0].shape
+    if any(matrix.shape != shape for matrix in matrices):
+        raise ValueError("all row isometries must have equal shape")
+    rank, dimension = shape
+    mean_projector = np.mean(
+        [row_projector(matrix) for matrix in matrices],
+        axis=0,
+    )
+    isotropic = (rank / dimension) * np.eye(dimension)
+    difference = mean_projector - isotropic
+    eigenvalues = np.linalg.eigvalsh(mean_projector)
+    return {
+        "rank": rank,
+        "ambient_dimension": dimension,
+        "samples": len(matrices),
+        "trace": float(np.trace(mean_projector).real),
+        "relative_frobenius": float(
+            np.linalg.norm(difference) / np.linalg.norm(isotropic)
+        ),
+        "spectral_spread": float(eigenvalues[-1] - eigenvalues[0]),
+        "minimum_eigenvalue": float(eigenvalues[0]),
+        "maximum_eigenvalue": float(eigenvalues[-1]),
+        "mean_projector": mean_projector,
+    }
+
+
+def coordinate_participation(rows: np.ndarray) -> dict[str, float]:
+    """Return the effective number of ambient coordinates used by a row space."""
+
+    projector = row_projector(rows)
+    weights = np.diag(projector).real
+    rank = float(np.sum(weights))
+    denominator = float(np.sum(weights * weights))
+    if denominator <= 0.0:
+        raise RuntimeError("projector diagonal has zero quadratic weight")
+    effective = rank * rank / denominator
+    return {
+        "effective_coordinates": effective,
+        "fraction": effective / projector.shape[0],
+    }
+
+
+def polarization_imbalance(rows: np.ndarray) -> float:
+    """Return normalized weight imbalance between the two channel halves."""
+
+    projector = row_projector(rows)
+    dimension = projector.shape[0]
+    if dimension % 2:
+        raise ValueError("polarization requires an even ambient dimension")
+    half = dimension // 2
+    plus = float(np.trace(projector[:half, :half]).real)
+    minus = float(np.trace(projector[half:, half:]).real)
+    rank = plus + minus
+    return (plus - minus) / rank
+
+
+def frame_overlap(first: np.ndarray, second: np.ndarray) -> float:
+    """Return ``Tr(P_first P_second)`` without forming ambient projectors."""
+
+    left = _validated_row_isometry(first)
+    right = _validated_row_isometry(second)
+    if left.shape != right.shape:
+        raise ValueError("row isometries must have equal shape")
+    overlap = left @ right.conj().T
+    return float(np.linalg.norm(overlap) ** 2)
+
+
+def haar_frame_overlap_mean(rank: int, dimension: int) -> float:
+    """Return the exact mean frame overlap of independent Haar projectors."""
+
+    rows = int(rank)
+    columns = int(dimension)
+    if rows < 1 or columns < rows:
+        raise ValueError("require 1 <= rank <= dimension")
+    return rows * rows / columns
+
+
+def principal_angles(first: np.ndarray, second: np.ndarray) -> np.ndarray:
+    """Return principal angles between two equal-dimensional row spaces."""
+
+    left = _validated_row_isometry(first)
+    right = _validated_row_isometry(second)
+    if left.shape != right.shape:
+        raise ValueError("row isometries must have equal shape")
+    singular_values = np.linalg.svd(
+        left @ right.conj().T,
+        compute_uv=False,
+    )
+    return np.arccos(np.clip(singular_values, 0.0, 1.0))
+
+
+def entry_fourth_ratio(row_isometries: Iterable[np.ndarray]) -> float:
+    """Return ``E|Y_ia|^4 / E|Y_ia|^2^2`` over an isometry ensemble."""
+
+    matrices = [_validated_row_isometry(rows) for rows in row_isometries]
+    if not matrices:
+        raise ValueError("at least one row isometry is required")
+    squared = np.concatenate(
+        [np.abs(matrix).ravel() ** 2 for matrix in matrices]
+    )
+    second = float(np.mean(squared))
+    fourth = float(np.mean(squared * squared))
+    return fourth / (second * second)
+
+
+def regularize_covariance(
+    covariance: np.ndarray,
+    floor_fraction: float = 1e-3,
+) -> np.ndarray:
+    """Return a positive covariance with a scale-relative eigenvalue floor."""
+
+    matrix = np.asarray(covariance, dtype=complex)
+    if matrix.ndim != 2 or matrix.shape[0] != matrix.shape[1]:
+        raise ValueError("covariance must be square")
+    hermitian = 0.5 * (matrix + matrix.conj().T)
+    values, vectors = np.linalg.eigh(hermitian)
+    scale = float(values[-1])
+    if scale <= 0.0 or values[0] < -1e-10 * scale:
+        raise ValueError("covariance must be positive semidefinite")
+    fraction = float(floor_fraction)
+    if not 0.0 < fraction <= 1.0:
+        raise ValueError("floor_fraction must lie in (0,1]")
+    floored = np.maximum(values, fraction * scale)
+    regularized = (vectors * floored[None, :]) @ vectors.conj().T
+    trace = float(np.trace(regularized).real)
+    return regularized * (matrix.shape[0] / trace)
+
+
+def covariance_deformed_row_isometry(
+    rank: int,
+    covariance: np.ndarray,
+    rng: np.random.Generator,
+    floor_fraction: float = 1e-3,
+) -> np.ndarray:
+    """Sample an elliptical Gaussian row space and whiten its left metric."""
+
+    regularized = regularize_covariance(
+        covariance,
+        floor_fraction=floor_fraction,
+    )
+    dimension = regularized.shape[0]
+    rows = int(rank)
+    if rows < 1 or rows > dimension:
+        raise ValueError("require 1 <= rank <= covariance dimension")
+    values, vectors = np.linalg.eigh(regularized)
+    gaussian = (
+        rng.normal(size=(rows, dimension))
+        + 1j * rng.normal(size=(rows, dimension))
+    ) / np.sqrt(2.0)
+    channels = (
+        gaussian * np.sqrt(values)[None, :]
+    ) @ vectors.conj().T
+    gram = channels @ channels.conj().T
+    gram_values, gram_vectors = np.linalg.eigh(
+        0.5 * (gram + gram.conj().T)
+    )
+    if gram_values[0] <= 0.0:
+        raise RuntimeError("elliptical channel Gram matrix is singular")
+    inverse_sqrt = (
+        gram_vectors * (gram_values ** -0.5)[None, :]
+    ) @ gram_vectors.conj().T
+    row_isometry = inverse_sqrt @ channels
+    _validated_row_isometry(row_isometry, tolerance=1e-8)
+    return row_isometry
+
+
+def covariance_deformed_row_isometries(
+    rank: int,
+    covariance: np.ndarray,
+    samples: int,
+    rng: np.random.Generator,
+    floor_fraction: float = 1e-3,
+) -> list[np.ndarray]:
+    """Sample several elliptical row spaces with one covariance factorization."""
+
+    regularized = regularize_covariance(
+        covariance,
+        floor_fraction=floor_fraction,
+    )
+    dimension = regularized.shape[0]
+    rows = int(rank)
+    count = int(samples)
+    if rows < 1 or rows > dimension or count < 1:
+        raise ValueError("require 1 <= rank <= dimension and samples >= 1")
+    values, vectors = np.linalg.eigh(regularized)
+    square_root_right = np.sqrt(values)[:, None] * vectors.conj().T
+    result: list[np.ndarray] = []
+    for _ in range(count):
+        gaussian = (
+            rng.normal(size=(rows, dimension))
+            + 1j * rng.normal(size=(rows, dimension))
+        ) / np.sqrt(2.0)
+        channels = gaussian @ square_root_right
+        gram = channels @ channels.conj().T
+        gram_values, gram_vectors = np.linalg.eigh(
+            0.5 * (gram + gram.conj().T)
+        )
+        if gram_values[0] <= 0.0:
+            raise RuntimeError("elliptical channel Gram matrix is singular")
+        inverse_sqrt = (
+            gram_vectors * (gram_values ** -0.5)[None, :]
+        ) @ gram_vectors.conj().T
+        row_isometry = inverse_sqrt @ channels
+        _validated_row_isometry(row_isometry, tolerance=1e-8)
+        result.append(row_isometry)
+    return result
+
+
+def covariance_deformed_rows(
+    rank: int,
+    covariance: np.ndarray,
+    samples: int,
+    rng: np.random.Generator,
+    floor_fraction: float = 1e-3,
+):
+    """Yield covariance-deformed row isometries without retaining the ensemble."""
+
+    regularized = regularize_covariance(
+        covariance,
+        floor_fraction=floor_fraction,
+    )
+    dimension = regularized.shape[0]
+    rows = int(rank)
+    count = int(samples)
+    if rows < 1 or rows > dimension or count < 1:
+        raise ValueError("require 1 <= rank <= dimension and samples >= 1")
+    values, vectors = np.linalg.eigh(regularized)
+    square_root_right = np.sqrt(values)[:, None] * vectors.conj().T
+    for _ in range(count):
+        gaussian = (
+            rng.normal(size=(rows, dimension))
+            + 1j * rng.normal(size=(rows, dimension))
+        ) / np.sqrt(2.0)
+        channels = gaussian @ square_root_right
+        gram = channels @ channels.conj().T
+        gram_values, gram_vectors = np.linalg.eigh(
+            0.5 * (gram + gram.conj().T)
+        )
+        if gram_values[0] <= 0.0:
+            raise RuntimeError("elliptical channel Gram matrix is singular")
+        inverse_sqrt = (
+            gram_vectors * (gram_values ** -0.5)[None, :]
+        ) @ gram_vectors.conj().T
+        row_isometry = inverse_sqrt @ channels
+        _validated_row_isometry(row_isometry, tolerance=1e-8)
+        yield row_isometry
+
+
+def covariance_first_order_variation(
+    gaussian: np.ndarray,
+    perturbation: np.ndarray,
+    channel_form: np.ndarray,
+) -> dict[str, np.ndarray]:
+    """Return the exact first variation at ``C=I+epsilon*K``.
+
+    The derivative of the inverse square root is fixed by its Sylvester
+    equation, so no commutativity between ``G G^dagger`` and
+    ``G K G^dagger`` is assumed.
+    """
+
+    G = np.asarray(gaussian, dtype=complex)
+    K = np.asarray(perturbation, dtype=complex)
+    J = np.asarray(channel_form, dtype=complex)
+    if G.ndim != 2 or G.shape[0] > G.shape[1]:
+        raise ValueError("gaussian must have shape rank x dimension")
+    dimension = G.shape[1]
+    if K.shape != (dimension, dimension):
+        raise ValueError("perturbation shape disagrees with gaussian")
+    if J.shape != (dimension, dimension):
+        raise ValueError("channel form shape disagrees with gaussian")
+    K = 0.5 * (K + K.conj().T)
+    A = G @ G.conj().T
+    values, vectors = np.linalg.eigh(0.5 * (A + A.conj().T))
+    if values[0] <= 0.0:
+        raise ValueError("gaussian matrix must have full row rank")
+    square_root = (
+        vectors * np.sqrt(values)[None, :]
+    ) @ vectors.conj().T
+    inverse_sqrt = (
+        vectors * (values ** -0.5)[None, :]
+    ) @ vectors.conj().T
+    B = G @ K @ G.conj().T
+    sylvester_source = -inverse_sqrt @ B @ inverse_sqrt
+    delta_inverse_sqrt = solve_sylvester(
+        square_root,
+        square_root,
+        sylvester_source,
+    )
+    Y = inverse_sqrt @ G
+    delta_Y = (
+        delta_inverse_sqrt @ G
+        + 0.5 * inverse_sqrt @ G @ K
+    )
+    omega = Y @ J @ Y.conj().T
+    delta_omega = (
+        delta_Y @ J @ Y.conj().T
+        + Y @ J @ delta_Y.conj().T
+    )
+    return {
+        "Y": Y,
+        "delta_Y": delta_Y,
+        "omega": 0.5 * (omega + omega.conj().T),
+        "delta_omega": 0.5
+        * (delta_omega + delta_omega.conj().T),
+        "delta_inverse_sqrt": delta_inverse_sqrt,
+    }
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/lgeth/holonomy.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/lgeth/holonomy.py
new file mode 100644
index 000000000..acb7a9e16
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/lgeth/holonomy.py
@@ -0,0 +1,267 @@
+"""Periodic isospectral unitary orbits and Wilson-loop chaos statistics."""
+
+from __future__ import annotations
+
+import numpy as np
+from scipy.linalg import expm
+
+from .bundle_geometry import BundleGeometry
+
+
+def _normalize_hermitian(matrix: np.ndarray) -> np.ndarray:
+    values = np.asarray(matrix, dtype=complex)
+    values = 0.5 * (values + values.conj().T)
+    values -= np.trace(values) / values.shape[0] * np.eye(
+        values.shape[0],
+        dtype=complex,
+    )
+    norm = float(np.linalg.norm(values, 2))
+    if norm <= 1e-12:
+        raise RuntimeError("local generator has zero spectral norm")
+    return values / norm
+
+
+def _local_hopping_generator(
+    length: int,
+    rng: np.random.Generator,
+) -> np.ndarray:
+    sites = length * length
+    matrix = np.zeros((sites, sites), dtype=complex)
+    for y in range(length):
+        for x in range(length):
+            source = y * length + x
+            for nx, ny in (
+                ((x + 1) % length, y),
+                (x, (y + 1) % length),
+            ):
+                destination = ny * length + nx
+                amplitude = (
+                    rng.normal() + 1j * rng.normal()
+                ) / np.sqrt(2.0)
+                matrix[destination, source] += amplitude
+                matrix[source, destination] += np.conjugate(amplitude)
+    return _normalize_hermitian(matrix)
+
+
+def local_generator_pair(
+    length: int,
+    seed: int,
+    commuting: bool,
+) -> tuple[np.ndarray, np.ndarray]:
+    """Return deterministic local Hermitian generators on a square torus."""
+
+    linear = int(length)
+    if linear < 2:
+        raise ValueError("generator lattice length must be at least two")
+    rng = np.random.default_rng(int(seed))
+    sites = linear * linear
+    if commuting:
+        first = np.diag(rng.normal(size=sites))
+        second = np.diag(rng.normal(size=sites))
+        return (
+            _normalize_hermitian(first),
+            _normalize_hermitian(second),
+        )
+    first = _local_hopping_generator(linear, rng)
+    second = _local_hopping_generator(linear, rng)
+    if float(np.linalg.norm(first @ second - second @ first)) <= 1e-3:
+        raise RuntimeError("noncommuting generator seed is accidentally singular")
+    return first, second
+
+
+def ambient_unitary(
+    theta_x: float,
+    theta_y: float,
+    g: float,
+    generators: tuple[np.ndarray, np.ndarray],
+) -> np.ndarray:
+    """Return a smooth periodic physical-site unitary."""
+
+    coupling = float(g)
+    if coupling < 0.0 or not np.isfinite(coupling):
+        raise ValueError("g must be finite and nonnegative")
+    first, second = (
+        np.asarray(generators[0], dtype=complex),
+        np.asarray(generators[1], dtype=complex),
+    )
+    if (
+        first.ndim != 2
+        or first.shape[0] != first.shape[1]
+        or second.shape != first.shape
+    ):
+        raise ValueError("ambient generators must be equal square matrices")
+    return expm(
+        1j * coupling * np.sin(float(theta_x)) * first
+    ) @ expm(
+        1j * coupling * np.sin(float(theta_y)) * second
+    )
+
+
+def deform_orbital_mesh(
+    orbital_frames: np.ndarray,
+    g: float,
+    seed: int,
+    commuting: bool,
+) -> np.ndarray:
+    """Apply the periodic ambient unitary orbit to physical orbital frames."""
+
+    frames = np.asarray(orbital_frames, dtype=complex)
+    if frames.ndim != 4 or frames.shape[0] != frames.shape[1]:
+        raise ValueError(
+            "orbital frames must have shape (mesh, mesh, sites, orbitals)"
+        )
+    sites = frames.shape[2]
+    length = int(round(np.sqrt(sites)))
+    if length * length != sites:
+        raise ValueError("physical sites do not form a square lattice")
+    generators = local_generator_pair(
+        length,
+        seed=int(seed),
+        commuting=bool(commuting),
+    )
+    mesh = frames.shape[0]
+    twists = 2.0 * np.pi * np.arange(mesh) / mesh
+    result = np.empty_like(frames)
+    for ix, theta_x in enumerate(twists):
+        for iy, theta_y in enumerate(twists):
+            result[ix, iy] = (
+                ambient_unitary(
+                    theta_x,
+                    theta_y,
+                    g,
+                    generators,
+                )
+                @ frames[ix, iy]
+            )
+    return result
+
+
+def _circular_gap_ratio(phases: np.ndarray) -> float:
+    angles = np.sort(np.mod(np.asarray(phases, dtype=float), 2.0 * np.pi))
+    if angles.size < 3:
+        raise ValueError("circular gap ratio requires at least three phases")
+    spacings = np.diff(np.concatenate([angles, angles[:1] + 2.0 * np.pi]))
+    next_spacings = np.roll(spacings, -1)
+    maximum = np.maximum(spacings, next_spacings)
+    valid = maximum > 1e-14
+    if not np.any(valid):
+        return 0.0
+    ratios = np.minimum(spacings[valid], next_spacings[valid]) / maximum[valid]
+    return float(np.mean(ratios))
+
+
+def _loop_statistics(
+    loops: np.ndarray,
+    k_values: np.ndarray,
+) -> tuple[np.ndarray, np.ndarray, np.ndarray, np.ndarray]:
+    values = np.asarray(loops, dtype=complex)
+    count, rank, second = values.shape
+    if rank != second:
+        raise ValueError("Wilson loops must be square")
+    phases = np.empty((count, rank), dtype=float)
+    gap_ratio = np.empty(count, dtype=float)
+    form_factor = np.empty((count, k_values.size), dtype=float)
+    determinant_phase = np.empty(count, dtype=float)
+    for index, loop in enumerate(values):
+        eigenphases = np.sort(np.angle(np.linalg.eigvals(loop)))
+        phases[index] = eigenphases
+        gap_ratio[index] = _circular_gap_ratio(eigenphases)
+        determinant_phase[index] = float(
+            np.angle(np.exp(1j * np.sum(eigenphases)))
+        )
+        form_factor[index] = [
+            abs(np.sum(np.exp(1j * k * eigenphases))) ** 2 / rank
+            for k in k_values
+        ]
+    return phases, gap_ratio, form_factor, determinant_phase
+
+
+def wilson_statistics(
+    geometry: BundleGeometry,
+    wilson_x: np.ndarray | None = None,
+    wilson_y: np.ndarray | None = None,
+    k_values: np.ndarray | None = None,
+) -> dict[str, np.ndarray | float]:
+    """Return common-phase-invariant Wilson spectral statistics."""
+
+    loops_x = geometry.wilson_x if wilson_x is None else wilson_x
+    loops_y = geometry.wilson_y if wilson_y is None else wilson_y
+    rank = loops_x.shape[-1]
+    if loops_x.shape[-2:] != (rank, rank) or loops_y.shape[-2:] != (
+        rank,
+        rank,
+    ):
+        raise ValueError("Wilson loop dimensions disagree")
+    ks = (
+        np.arange(1, rank + 1, dtype=int)
+        if k_values is None
+        else np.asarray(k_values, dtype=int)
+    )
+    if ks.ndim != 1 or ks.size == 0 or np.any(ks < 1):
+        raise ValueError("Wilson powers must be positive integers")
+    phases_x, gaps_x, form_x, determinant_x = _loop_statistics(
+        loops_x,
+        ks,
+    )
+    phases_y, gaps_y, form_y, determinant_y = _loop_statistics(
+        loops_y,
+        ks,
+    )
+    return {
+        "k_values": ks,
+        "phases": np.concatenate([phases_x, phases_y], axis=0),
+        "gap_ratio": np.concatenate([gaps_x, gaps_y]),
+        "form_factor": np.concatenate([form_x, form_y], axis=0),
+        "determinant_phase_x": determinant_x,
+        "determinant_phase_y": determinant_y,
+        "mean_gap_ratio": float(np.mean(np.concatenate([gaps_x, gaps_y]))),
+        "mean_form_factor": np.mean(
+            np.concatenate([form_x, form_y], axis=0),
+            axis=0,
+        ),
+    }
+
+
+def _haar_unitary(
+    dimension: int,
+    rng: np.random.Generator,
+) -> np.ndarray:
+    gaussian = (
+        rng.normal(size=(dimension, dimension))
+        + 1j * rng.normal(size=(dimension, dimension))
+    ) / np.sqrt(2.0)
+    q, r = np.linalg.qr(gaussian)
+    phases = np.diag(r)
+    phases = phases / np.abs(phases)
+    return q * phases.conj()[None, :]
+
+
+def cue_wilson_reference(
+    D: int,
+    samples: int,
+    k_values: np.ndarray,
+    seed: int,
+) -> dict[str, np.ndarray]:
+    """Return independent circular-unitary Wilson statistics."""
+
+    rank = int(D)
+    count = int(samples)
+    ks = np.asarray(k_values, dtype=int)
+    if rank < 3 or count < 1 or ks.ndim != 1 or np.any(ks < 1):
+        raise ValueError("invalid CUE reference dimensions")
+    rng = np.random.default_rng(int(seed))
+    gaps = np.empty(count, dtype=float)
+    form_factor = np.empty((count, ks.size), dtype=float)
+    for sample in range(count):
+        unitary = _haar_unitary(rank, rng)
+        phases = np.angle(np.linalg.eigvals(unitary))
+        gaps[sample] = _circular_gap_ratio(phases)
+        form_factor[sample] = [
+            abs(np.sum(np.exp(1j * k * phases))) ** 2 / rank
+            for k in ks
+        ]
+    return {
+        "k_values": ks,
+        "gap_ratio": gaps,
+        "form_factor": form_factor,
+    }
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/lgeth/jacobi.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/lgeth/jacobi.py
new file mode 100644
index 000000000..f1bc36330
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/lgeth/jacobi.py
@@ -0,0 +1,312 @@
+"""Metric-normalized curvature and finite Jacobi compression theory."""
+
+from __future__ import annotations
+
+from dataclasses import dataclass
+
+import numpy as np
+from scipy import linalg
+from scipy.special import eval_jacobi, gammaln
+
+from .channels import _validated_channel_pair
+
+
+@dataclass(frozen=True)
+class NormalizedCurvature:
+    """Curvature whitened by the channel Gram matrix on its support."""
+
+    rank: int
+    kernel_dimension: int
+    cutoff: float
+    active_basis: np.ndarray
+    gamma_eigenvalues: np.ndarray
+    Y: np.ndarray
+    J: np.ndarray
+    omega: np.ndarray
+
+
+@dataclass(frozen=True)
+class JacobiParameters:
+    """Finite-dimensional parameters of a Haar signature compression."""
+
+    r: int
+    M: int
+    interior_dimension: int
+    exponent: int
+    plus_atoms: int
+    minus_atoms: int
+
+
+def canonical_channel_form(M: int) -> np.ndarray:
+    """Return the Hermitian channel form for ``[X_v,X_w]``."""
+
+    channels = int(M)
+    if channels < 1:
+        raise ValueError("M must be positive")
+    identity = np.eye(channels, dtype=complex)
+    zero = np.zeros_like(identity)
+    return np.block(
+        [
+            [zero, 1j * identity],
+            [-1j * identity, zero],
+        ]
+    )
+
+
+def normalized_curvature(
+    channel_v: np.ndarray,
+    channel_w: np.ndarray,
+    rtol: float = 1e-12,
+    atol: float = 0.0,
+) -> NormalizedCurvature:
+    """Return ``Omega=Gamma^{-1/2} F Gamma^{-1/2}=Y J Y^dagger``."""
+
+    x, y = _validated_channel_pair(channel_v, channel_w)
+    if rtol < 0.0 or atol < 0.0:
+        raise ValueError("rank tolerances must be nonnegative")
+    doubled = np.concatenate([x, y], axis=1)
+    gamma = doubled @ doubled.conj().T
+    eigenvalues, eigenvectors = np.linalg.eigh(
+        0.5 * (gamma + gamma.conj().T)
+    )
+    scale = max(float(eigenvalues[-1]), 0.0)
+    cutoff = max(float(atol), float(rtol) * scale)
+    keep = eigenvalues > cutoff
+    active_values = eigenvalues[keep]
+    active_basis = eigenvectors[:, keep]
+    rank = int(active_values.size)
+    if rank == 0:
+        raise ValueError("the channel Gram matrix has empty support")
+    projected = active_basis.conj().T @ doubled
+    Y = projected / np.sqrt(active_values)[:, None]
+    J = canonical_channel_form(x.shape[1])
+    omega = Y @ J @ Y.conj().T
+    omega = 0.5 * (omega + omega.conj().T)
+    return NormalizedCurvature(
+        rank=rank,
+        kernel_dimension=x.shape[0] - rank,
+        cutoff=cutoff,
+        active_basis=active_basis,
+        gamma_eigenvalues=active_values,
+        Y=Y,
+        J=J,
+        omega=omega,
+    )
+
+
+def haar_row_isometry(
+    r: int,
+    doubled_channels: int,
+    rng: np.random.Generator,
+) -> np.ndarray:
+    """Sample an ``r x doubled_channels`` complex Haar row isometry."""
+
+    rows = int(r)
+    columns = int(doubled_channels)
+    if rows < 1 or columns < 1 or rows > columns:
+        raise ValueError("require 1 <= r <= doubled_channels")
+    gaussian = (
+        rng.normal(size=(columns, rows))
+        + 1j * rng.normal(size=(columns, rows))
+    ) / np.sqrt(2.0)
+    q, r_factor = np.linalg.qr(gaussian, mode="reduced")
+    phases = np.diag(r_factor)
+    phases = np.where(
+        np.abs(phases) > 0.0,
+        phases / np.abs(phases),
+        1.0,
+    )
+    q = q * phases.conj()[None, :]
+    return q.conj().T
+
+
+def jacobi_parameters(r: int, M: int) -> JacobiParameters:
+    """Return interior Jacobi size/exponent and forced boundary atoms."""
+
+    rank = int(r)
+    channels = int(M)
+    if channels < 1 or rank < 1 or rank > 2 * channels:
+        raise ValueError("require M>=1 and 1<=r<=2M")
+    if rank <= channels:
+        interior = rank
+        exponent = channels - rank
+        atoms = 0
+    else:
+        interior = 2 * channels - rank
+        exponent = rank - channels
+        atoms = rank - channels
+    return JacobiParameters(
+        r=rank,
+        M=channels,
+        interior_dimension=interior,
+        exponent=exponent,
+        plus_atoms=atoms,
+        minus_atoms=atoms,
+    )
+
+
+def _jacobi_norm(order: int, exponent: int) -> float:
+    degree = int(order)
+    alpha = int(exponent)
+    log_norm = (
+        (2 * alpha + 1) * np.log(2.0)
+        - np.log(2 * degree + 2 * alpha + 1)
+        + 2 * gammaln(degree + alpha + 1)
+        - gammaln(degree + 1)
+        - gammaln(degree + 2 * alpha + 1)
+    )
+    return float(np.exp(log_norm))
+
+
+def jacobi_one_point_density(
+    x: np.ndarray,
+    r: int,
+    M: int,
+) -> np.ndarray:
+    """Return the normalized interior one-eigenvalue Jacobi density."""
+
+    parameters = jacobi_parameters(r, M)
+    values = np.asarray(x, dtype=float)
+    density = np.zeros_like(values)
+    interior = parameters.interior_dimension
+    if interior == 0:
+        return density
+    mask = np.abs(values) <= 1.0
+    points = values[mask]
+    weight = np.maximum(1.0 - points * points, 0.0) ** (
+        parameters.exponent
+    )
+    kernel = np.zeros_like(points)
+    for order in range(interior):
+        polynomial = eval_jacobi(
+            order,
+            parameters.exponent,
+            parameters.exponent,
+            points,
+        )
+        kernel += polynomial * polynomial / _jacobi_norm(
+            order,
+            parameters.exponent,
+        )
+    density[mask] = weight * kernel / interior
+    density = np.maximum(density, 0.0)
+    return density
+
+
+def sample_jacobi_compression(
+    r: int,
+    M: int,
+    samples: int,
+    seed: int,
+) -> np.ndarray:
+    """Sample spectra of a Haar compression of ``diag(+1_M,-1_M)``."""
+
+    parameters = jacobi_parameters(r, M)
+    count = int(samples)
+    if count < 1:
+        raise ValueError("samples must be positive")
+    rng = np.random.default_rng(int(seed))
+    signature = np.concatenate(
+        [
+            np.ones(parameters.M, dtype=float),
+            -np.ones(parameters.M, dtype=float),
+        ]
+    )
+    spectra = np.empty((count, parameters.r), dtype=float)
+    for sample in range(count):
+        rows = haar_row_isometry(
+            parameters.r,
+            2 * parameters.M,
+            rng,
+        )
+        omega = (rows * signature[None, :]) @ rows.conj().T
+        spectra[sample] = np.linalg.eigvalsh(
+            0.5 * (omega + omega.conj().T)
+        )
+    return spectra
+
+
+def sample_jacobi_interior(
+    r: int,
+    M: int,
+    samples: int,
+    seed: int,
+) -> tuple[np.ndarray, np.ndarray]:
+    """Sample the finite Jacobi law and remove only algebraically forced atoms.
+
+    The Boolean labels are fixed by the exact intersection dimensions, not by
+    a floating-point threshold.  The full spectra are ordered, so the first
+    ``minus_atoms`` and last ``plus_atoms`` entries carry the labels.
+    """
+
+    parameters = jacobi_parameters(r, M)
+    full = sample_jacobi_compression(r, M, samples, seed)
+    labels = np.zeros_like(full, dtype=bool)
+    if parameters.minus_atoms:
+        labels[:, : parameters.minus_atoms] = True
+        labels[:, -parameters.plus_atoms :] = True
+        if not np.allclose(
+            full[:, : parameters.minus_atoms], -1.0, atol=2e-10, rtol=0.0
+        ):
+            raise RuntimeError("negative Jacobi atoms failed the exact label audit")
+        if not np.allclose(
+            full[:, -parameters.plus_atoms :], 1.0, atol=2e-10, rtol=0.0
+        ):
+            raise RuntimeError("positive Jacobi atoms failed the exact label audit")
+    interior = full[~labels].reshape(
+        int(samples), parameters.interior_dimension
+    )
+    return interior, labels
+
+
+def sample_jacobi_wishart(
+    r: int,
+    M: int,
+    samples: int,
+    seed: int,
+) -> tuple[np.ndarray, np.ndarray, np.ndarray]:
+    """Sample the exact complex Jacobi law via a matrix-beta construction.
+
+    For interior size ``k`` and exponent ``a``, two independent complex
+    Wishart matrices with ``k+a=M`` columns generate the eigenvalues on
+    ``[0,1]``.  The affine map ``lambda=2t-1`` gives the signature-compression
+    spectrum; the intersection-theorem atoms are then inserted explicitly.
+    """
+
+    parameters = jacobi_parameters(r, M)
+    count = int(samples)
+    if count < 1:
+        raise ValueError("samples must be positive")
+    k = parameters.interior_dimension
+    full = np.empty((count, parameters.r), dtype=float)
+    interior = np.empty((count, k), dtype=float)
+    labels = np.zeros_like(full, dtype=bool)
+    rng = np.random.default_rng(int(seed))
+    for sample in range(count):
+        if k:
+            gaussian_x = (
+                rng.normal(size=(k, parameters.M))
+                + 1j * rng.normal(size=(k, parameters.M))
+            ) / np.sqrt(2.0)
+            gaussian_y = (
+                rng.normal(size=(k, parameters.M))
+                + 1j * rng.normal(size=(k, parameters.M))
+            ) / np.sqrt(2.0)
+            first = gaussian_x @ gaussian_x.conj().T
+            second = gaussian_y @ gaussian_y.conj().T
+            beta_values = linalg.eigvalsh(
+                first,
+                first + second,
+                check_finite=False,
+                driver="gvd",
+            )
+            interior[sample] = 2.0 * beta_values - 1.0
+        if parameters.minus_atoms:
+            full[sample, : parameters.minus_atoms] = -1.0
+            labels[sample, : parameters.minus_atoms] = True
+        start = parameters.minus_atoms
+        full[sample, start : start + k] = interior[sample]
+        if parameters.plus_atoms:
+            full[sample, -parameters.plus_atoms :] = 1.0
+            labels[sample, -parameters.plus_atoms :] = True
+    return full, interior, labels
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/lgeth/lattice.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/lgeth/lattice.py
new file mode 100644
index 000000000..574dbdf78
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/lgeth/lattice.py
@@ -0,0 +1,489 @@
+"""Independent Kapit--Mueller projected-contact lattice backend.
+
+The algorithms are task-local rewrites of the prior ``qgeom/models.py``,
+``qgeom/projected.py``, ``qgeom/softcore.py``, and ``qgeom/operators.py``
+implementations at provenance commit ``e4ee4c9``.  This module imports no
+code or data from that implementation.
+"""
+
+from __future__ import annotations
+
+from dataclasses import dataclass
+from math import floor, sqrt
+
+import numpy as np
+from scipy import sparse
+
+from .combinatorics import occupation_states
+
+
+@dataclass(frozen=True)
+class Bond:
+    """Directed hopping record with integer torus windings."""
+
+    destination: int
+    source: int
+    amplitude: complex
+    winding_x: int
+    winding_y: int
+
+
+@dataclass(frozen=True)
+class BosonBasis:
+    """Normalized occupation basis at fixed boson number."""
+
+    n_orbitals: int
+    n_particles: int
+
+    def __post_init__(self) -> None:
+        if self.n_orbitals < 1:
+            raise ValueError("n_orbitals must be positive")
+        if self.n_particles < 0:
+            raise ValueError("n_particles must be nonnegative")
+        states = tuple(
+            occupation_states(self.n_particles, self.n_orbitals)
+        )
+        object.__setattr__(self, "states", states)
+        object.__setattr__(
+            self,
+            "index",
+            {state: index for index, state in enumerate(states)},
+        )
+
+    @property
+    def dimension(self) -> int:
+        return len(self.states)
+
+
+@dataclass(frozen=True)
+class KapitLaughlinParent:
+    """Lowest-band frame and factorized projected contact parent."""
+
+    n_particles: int
+    n_flux: int
+    length: int
+    theta_x: float
+    theta_y: float
+    basis: BosonBasis
+    intermediate_basis: BosonBasis
+    bonds: tuple[Bond, ...]
+    onebody_energies: np.ndarray
+    orbitals: np.ndarray
+    constraints: sparse.csr_matrix
+    parent: sparse.csr_matrix
+
+
+def _kapit_mueller_sign(displacement: complex) -> int:
+    x = int(round(displacement.real))
+    y = int(round(displacement.imag))
+    return -1 if (x + y + x * y) % 2 else 1
+
+
+def kapit_mueller_bonds(
+    length: int,
+    flux_density: float | None = None,
+    image_cutoff: int = 2,
+    amplitude_cutoff: float = 1e-13,
+) -> tuple[Bond, ...]:
+    """Return magneto-periodic Kapit--Mueller hoppings on a square torus."""
+
+    linear_size = int(length)
+    density = (
+        2.0 / linear_size
+        if flux_density is None
+        else float(flux_density)
+    )
+    if linear_size <= 2:
+        raise ValueError("length must exceed two")
+    if not 0.0 < density < 1.0:
+        raise ValueError("flux_density must lie in (0,1)")
+    if image_cutoff < 0:
+        raise ValueError("image_cutoff must be nonnegative")
+    positions = tuple(
+        complex(x, y)
+        for y in range(linear_size)
+        for x in range(linear_size)
+    )
+    bonds: list[Bond] = []
+    for destination, z_destination in enumerate(positions):
+        for source in range(destination + 1, len(positions)):
+            base = positions[source] - z_destination
+            for winding_x in range(-image_cutoff, image_cutoff + 1):
+                for winding_y in range(
+                    -image_cutoff,
+                    image_cutoff + 1,
+                ):
+                    image = complex(
+                        winding_x * linear_size,
+                        winding_y * linear_size,
+                    )
+                    displacement = base + image
+                    if abs(displacement) < 1e-14:
+                        continue
+                    envelope = np.exp(
+                        -0.5
+                        * np.pi
+                        * (1.0 - density)
+                        * abs(displacement) ** 2
+                    )
+                    gauge_phase = np.exp(
+                        0.5
+                        * np.pi
+                        * density
+                        * (
+                            z_destination
+                            * np.conjugate(displacement)
+                            - np.conjugate(z_destination)
+                            * displacement
+                        )
+                    )
+                    extension_phase = np.exp(
+                        0.5
+                        * np.pi
+                        * density
+                        * (
+                            z_destination * np.conjugate(image)
+                            - np.conjugate(z_destination) * image
+                        )
+                    )
+                    amplitude = (
+                        _kapit_mueller_sign(displacement)
+                        * envelope
+                        * gauge_phase
+                        * extension_phase
+                    )
+                    if abs(amplitude) >= amplitude_cutoff:
+                        bonds.append(
+                            Bond(
+                                destination=destination,
+                                source=source,
+                                amplitude=complex(amplitude),
+                                winding_x=winding_x,
+                                winding_y=winding_y,
+                            )
+                        )
+    return tuple(bonds)
+
+
+def one_body_hamiltonian(
+    n_sites: int,
+    bonds: tuple[Bond, ...],
+    theta_x: float = 0.0,
+    theta_y: float = 0.0,
+) -> sparse.csr_matrix:
+    """Assemble the twist-dependent Hermitian single-particle matrix."""
+
+    sites = int(n_sites)
+    if sites < 1:
+        raise ValueError("n_sites must be positive")
+    rows: list[int] = []
+    columns: list[int] = []
+    data: list[complex] = []
+    for bond in bonds:
+        if not (
+            0 <= bond.destination < sites
+            and 0 <= bond.source < sites
+        ):
+            raise IndexError("bond endpoint is outside the lattice")
+        phase = np.exp(
+            1j
+            * (
+                bond.winding_x * float(theta_x)
+                + bond.winding_y * float(theta_y)
+            )
+        )
+        amplitude = bond.amplitude * phase
+        rows.extend((bond.destination, bond.source))
+        columns.extend((bond.source, bond.destination))
+        data.extend((amplitude, np.conjugate(amplitude)))
+    matrix = sparse.coo_matrix(
+        (np.asarray(data, dtype=complex), (rows, columns)),
+        shape=(sites, sites),
+    ).tocsr()
+    matrix.sum_duplicates()
+    return matrix
+
+
+def lowest_band_frame(
+    n_sites: int,
+    bonds: tuple[Bond, ...],
+    n_orbitals: int,
+    theta_x: float,
+    theta_y: float,
+) -> tuple[np.ndarray, np.ndarray]:
+    """Diagonalize the one-body problem and return its lowest-band frame."""
+
+    orbitals = int(n_orbitals)
+    if not 0 < orbitals < n_sites:
+        raise ValueError("require 0<n_orbitals<n_sites")
+    matrix = one_body_hamiltonian(
+        n_sites,
+        bonds,
+        theta_x,
+        theta_y,
+    ).toarray()
+    energies, frame = np.linalg.eigh(matrix)
+    return energies, frame[:, :orbitals]
+
+
+def projected_contact_constraints(
+    basis: BosonBasis,
+    orbitals: np.ndarray,
+    onsite_u: float = 1.0,
+    amplitude_cutoff: float = 1e-14,
+) -> tuple[sparse.csr_matrix, BosonBasis]:
+    """Return ``C`` such that the projected contact parent is ``C^dagger C``."""
+
+    frame = np.asarray(orbitals, dtype=complex)
+    if basis.n_particles < 2:
+        raise ValueError("contact constraints require at least two particles")
+    if frame.ndim != 2 or frame.shape[1] != basis.n_orbitals:
+        raise ValueError("orbital frame and basis disagree")
+    if onsite_u <= 0.0:
+        raise ValueError("onsite_u must be positive")
+    if not np.allclose(
+        frame.conj().T @ frame,
+        np.eye(basis.n_orbitals),
+        atol=1e-11,
+    ):
+        raise ValueError("orbitals must have orthonormal columns")
+    intermediate = BosonBasis(
+        basis.n_orbitals,
+        basis.n_particles - 2,
+    )
+    physical_sites = frame.shape[0]
+    rows: list[int] = []
+    columns: list[int] = []
+    data: list[complex] = []
+    prefactor = sqrt(0.5 * float(onsite_u))
+    for column, state in enumerate(basis.states):
+        for left in range(basis.n_orbitals):
+            if state[left] >= 2:
+                updated = list(state)
+                updated[left] -= 2
+                intermediate_index = intermediate.index[tuple(updated)]
+                occupation_factor = sqrt(
+                    state[left] * (state[left] - 1)
+                )
+                for physical in range(physical_sites):
+                    coefficient = (
+                        prefactor
+                        * frame[physical, left] ** 2
+                        * occupation_factor
+                    )
+                    if abs(coefficient) > amplitude_cutoff:
+                        rows.append(
+                            physical * intermediate.dimension
+                            + intermediate_index
+                        )
+                        columns.append(column)
+                        data.append(coefficient)
+            if state[left] == 0:
+                continue
+            for right in range(left + 1, basis.n_orbitals):
+                if state[right] == 0:
+                    continue
+                updated = list(state)
+                updated[left] -= 1
+                updated[right] -= 1
+                intermediate_index = intermediate.index[tuple(updated)]
+                occupation_factor = sqrt(state[left] * state[right])
+                for physical in range(physical_sites):
+                    coefficient = (
+                        2.0
+                        * prefactor
+                        * frame[physical, left]
+                        * frame[physical, right]
+                        * occupation_factor
+                    )
+                    if abs(coefficient) > amplitude_cutoff:
+                        rows.append(
+                            physical * intermediate.dimension
+                            + intermediate_index
+                        )
+                        columns.append(column)
+                        data.append(coefficient)
+    constraints = sparse.coo_matrix(
+        (
+            np.asarray(data, dtype=complex),
+            (rows, columns),
+        ),
+        shape=(
+            physical_sites * intermediate.dimension,
+            basis.dimension,
+        ),
+    ).tocsr()
+    constraints.sum_duplicates()
+    return constraints, intermediate
+
+
+def projected_contact_parent(
+    basis: BosonBasis,
+    orbitals: np.ndarray,
+) -> tuple[sparse.csr_matrix, sparse.csr_matrix, BosonBasis]:
+    """Return the positive projected parent, its factor, and lower basis."""
+
+    constraints, intermediate = projected_contact_constraints(
+        basis,
+        orbitals,
+    )
+    parent = (constraints.conj().T @ constraints).tocsr()
+    parent.sum_duplicates()
+    return parent, constraints, intermediate
+
+
+def build_kapit_laughlin_parent(
+    n_particles: int,
+    n_flux: int,
+    theta_x: float,
+    theta_y: float,
+) -> KapitLaughlinParent:
+    """Build a commensurate Kapit--Mueller projected-contact parent."""
+
+    flux = int(n_flux)
+    if flux % 2:
+        raise ValueError("the registered sequence requires even n_flux")
+    length = flux // 2
+    if length <= 2:
+        raise ValueError("the registered sequence requires n_flux>=8")
+    bonds = kapit_mueller_bonds(length)
+    energies, orbitals = lowest_band_frame(
+        length * length,
+        bonds,
+        flux,
+        theta_x,
+        theta_y,
+    )
+    basis = BosonBasis(flux, int(n_particles))
+    parent, constraints, intermediate = projected_contact_parent(
+        basis,
+        orbitals,
+    )
+    return KapitLaughlinParent(
+        n_particles=int(n_particles),
+        n_flux=flux,
+        length=length,
+        theta_x=float(theta_x),
+        theta_y=float(theta_y),
+        basis=basis,
+        intermediate_basis=intermediate,
+        bonds=bonds,
+        onebody_energies=energies,
+        orbitals=orbitals,
+        constraints=constraints,
+        parent=parent,
+    )
+
+
+def projected_site_potential(
+    orbitals: np.ndarray,
+    potential: np.ndarray,
+) -> np.ndarray:
+    """Project a real physical-site potential into the Chern band."""
+
+    frame = np.asarray(orbitals, dtype=complex)
+    values = np.asarray(potential, dtype=float)
+    if frame.ndim != 2 or values.shape != (frame.shape[0],):
+        raise ValueError("potential and orbital frame disagree")
+    projected = frame.conj().T @ (values[:, None] * frame)
+    return 0.5 * (projected + projected.conj().T)
+
+
+def manybody_one_body_operator(
+    basis: BosonBasis,
+    one_body: np.ndarray,
+    amplitude_cutoff: float = 1e-14,
+) -> sparse.csr_matrix:
+    """Second-quantize a Hermitian one-body operator."""
+
+    matrix = np.asarray(one_body, dtype=complex)
+    if matrix.shape != (basis.n_orbitals, basis.n_orbitals):
+        raise ValueError("one-body matrix has the wrong shape")
+    if not np.allclose(matrix, matrix.conj().T, atol=1e-11):
+        raise ValueError("one-body matrix must be Hermitian")
+    rows: list[int] = []
+    columns: list[int] = []
+    data: list[complex] = []
+    for column, state in enumerate(basis.states):
+        for source, population in enumerate(state):
+            if population == 0:
+                continue
+            for destination in range(basis.n_orbitals):
+                coefficient = matrix[destination, source]
+                if abs(coefficient) <= amplitude_cutoff:
+                    continue
+                if destination == source:
+                    target = state
+                    factor = float(population)
+                else:
+                    updated = list(state)
+                    factor = sqrt(
+                        population * (updated[destination] + 1)
+                    )
+                    updated[source] -= 1
+                    updated[destination] += 1
+                    target = tuple(updated)
+                rows.append(basis.index[target])
+                columns.append(column)
+                data.append(coefficient * factor)
+    operator = sparse.coo_matrix(
+        (
+            np.asarray(data, dtype=complex),
+            (rows, columns),
+        ),
+        shape=(basis.dimension, basis.dimension),
+    ).tocsr()
+    operator.sum_duplicates()
+    return operator
+
+
+def channel_matrix(
+    energies_p: np.ndarray,
+    vectors_p: np.ndarray,
+    energies_q: np.ndarray,
+    vectors_q: np.ndarray,
+    tangent: sparse.spmatrix,
+) -> np.ndarray:
+    """Return the external Kubo response channel of an isolated multiplet."""
+
+    ep = np.asarray(energies_p, dtype=float)
+    eq = np.asarray(energies_q, dtype=float)
+    frame_p = np.asarray(vectors_p, dtype=complex)
+    frame_q = np.asarray(vectors_q, dtype=complex)
+    if ep.size == 0 or eq.size == 0:
+        raise ValueError("both target and external sectors must be nonempty")
+    reference = float(np.mean(ep))
+    denominators = reference - eq
+    scale = max(1.0, abs(reference), float(np.max(np.abs(eq))))
+    if np.any(np.abs(denominators) <= 1e-12 * scale):
+        raise ValueError("external denominator closes")
+    applied = tangent @ frame_q
+    elements = frame_p.conj().T @ np.asarray(applied)
+    return np.asarray(elements / denominators[None, :], dtype=complex)
+
+
+def random_local_potential(n_sites: int, seed: int) -> np.ndarray:
+    """Return a deterministic normalized zero-mean local potential."""
+
+    rng = np.random.default_rng(int(seed))
+    values = rng.normal(size=int(n_sites))
+    values -= np.mean(values)
+    norm = np.linalg.norm(values)
+    if norm <= 0.0:
+        raise RuntimeError("random potential has zero norm")
+    return values / norm
+
+
+def numerical_rank(
+    matrix: np.ndarray,
+    rtol: float = 1e-10,
+) -> int:
+    """Return a scale-aware singular-value rank."""
+
+    values = np.linalg.svd(
+        np.asarray(matrix, dtype=complex),
+        compute_uv=False,
+    )
+    if values.size == 0:
+        return 0
+    return int(np.count_nonzero(values > rtol * values[0]))
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/lgeth/manybody_response.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/lgeth/manybody_response.py
new file mode 100644
index 000000000..52d413959
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/lgeth/manybody_response.py
@@ -0,0 +1,459 @@
+"""Sparse resolvent responses on a genuine fixed-quasihole sequence."""
+
+from __future__ import annotations
+
+import warnings
+from dataclasses import dataclass, replace
+
+import numpy as np
+from scipy import sparse
+from scipy.sparse.linalg import eigsh, lobpcg, splu
+
+from .combinatorics import laughlin_zero_mode_count
+from .lattice import (
+    KapitLaughlinParent,
+    build_kapit_laughlin_parent,
+    manybody_one_body_operator,
+    projected_site_potential,
+)
+
+
+@dataclass(frozen=True)
+class ManyBodyCase:
+    """One registered physical fixed-two-quasihole system."""
+
+    N: int
+    n_flux: int
+    expected_rank: int
+    theta_x: float
+    theta_y: float
+
+
+@dataclass(frozen=True)
+class SmallCaseAudit:
+    """Reason an unregistered small physical system is excluded."""
+
+    N: int
+    n_flux: int
+    expected_rank: int
+    observed_rank: int
+    accepted: bool
+
+
+@dataclass(frozen=True)
+class KernelFrame:
+    """Numerically complete orthonormal frame for one exact zero-mode space."""
+
+    frame: np.ndarray
+    zero_eigenvalues: np.ndarray
+    external_gap: float
+    residual_norm: float
+    orthonormality_error: float
+    method: str
+    observed_rank: int
+
+
+@dataclass(frozen=True)
+class SiteResponseCache:
+    """Resolvent solutions for a selected physical-site tangent basis."""
+
+    case: ManyBodyCase
+    site_indices: tuple[int, ...]
+    solutions: np.ndarray
+    tangent_gram: np.ndarray
+    external_gap: float
+    shift_values: tuple[float, float]
+    maximum_relative_residual: float
+    maximum_shift_difference: float
+    maximum_kernel_leakage: float
+
+
+def registered_fixed_two_qh_cases() -> tuple[ManyBodyCase, ...]:
+    """Return the preregistered genuine particle-number sequence."""
+
+    return tuple(
+        ManyBodyCase(
+            N=N,
+            n_flux=2 * N + 2,
+            expected_rank=laughlin_zero_mode_count(N, 2 * N + 2),
+            theta_x=0.17,
+            theta_y=0.29,
+        )
+        for N in (3, 4, 5)
+    )
+
+
+def _zero_tolerance(eigenvalues: np.ndarray) -> float:
+    values = np.asarray(eigenvalues, dtype=float)
+    scale = max(float(np.max(np.abs(values))), 1.0)
+    return 1e-9 * scale
+
+
+def audit_unregistered_small_case(
+    N: int,
+    n_flux: int,
+    theta_x: float,
+    theta_y: float,
+) -> SmallCaseAudit:
+    """Return the exact-count audit for a proposed small physical parent."""
+
+    system = build_kapit_laughlin_parent(
+        int(N),
+        int(n_flux),
+        float(theta_x),
+        float(theta_y),
+    )
+    eigenvalues = np.linalg.eigvalsh(system.parent.toarray())
+    expected = laughlin_zero_mode_count(int(N), int(n_flux))
+    observed = int(
+        np.count_nonzero(np.abs(eigenvalues) < _zero_tolerance(eigenvalues))
+    )
+    return SmallCaseAudit(
+        N=int(N),
+        n_flux=int(n_flux),
+        expected_rank=expected,
+        observed_rank=observed,
+        accepted=observed == expected,
+    )
+
+
+def _dense_kernel_frame(
+    system: KapitLaughlinParent,
+    case: ManyBodyCase,
+) -> KernelFrame:
+    parent = system.parent.toarray()
+    parent = 0.5 * (parent + parent.conj().T)
+    eigenvalues, eigenvectors = np.linalg.eigh(parent)
+    tolerance = _zero_tolerance(eigenvalues)
+    observed = int(np.count_nonzero(np.abs(eigenvalues) < tolerance))
+    if observed != case.expected_rank:
+        raise RuntimeError(
+            f"zero-mode count mismatch: expected {case.expected_rank}, "
+            f"observed {observed}"
+        )
+    frame = eigenvectors[:, :observed]
+    gap = float(eigenvalues[observed] - eigenvalues[observed - 1])
+    residual = float(np.linalg.norm(system.parent @ frame))
+    orthonormality = float(
+        np.linalg.norm(frame.conj().T @ frame - np.eye(observed))
+    )
+    return KernelFrame(
+        frame=frame,
+        zero_eigenvalues=np.asarray(eigenvalues[:observed], dtype=float),
+        external_gap=gap,
+        residual_norm=residual,
+        orthonormality_error=orthonormality,
+        method="dense",
+        observed_rank=observed,
+    )
+
+
+def _sparse_kernel_frame(
+    system: KapitLaughlinParent,
+    case: ManyBodyCase,
+    seed: int,
+) -> KernelFrame:
+    dimension = system.basis.dimension
+    rank = case.expected_rank
+    rng = np.random.default_rng(int(seed))
+    initial = (
+        rng.normal(size=(dimension, rank))
+        + 1j * rng.normal(size=(dimension, rank))
+    )
+    initial, _ = np.linalg.qr(initial)
+    with warnings.catch_warnings():
+        warnings.simplefilter("ignore", UserWarning)
+        values, frame = lobpcg(
+            system.parent,
+            initial,
+            largest=False,
+            tol=1e-9,
+            maxiter=600,
+        )
+    frame, _ = np.linalg.qr(frame)
+    residual = float(np.linalg.norm(system.parent @ frame))
+    orthonormality = float(
+        np.linalg.norm(frame.conj().T @ frame - np.eye(rank))
+    )
+    audit_values = eigsh(
+        system.parent,
+        k=rank + 4,
+        which="SM",
+        return_eigenvectors=False,
+        tol=1e-9,
+        maxiter=12_000,
+        ncv=min(dimension, max(2 * (rank + 4) + 1, 100)),
+    )
+    audit_values = np.sort(np.real(audit_values))
+    tolerance = _zero_tolerance(audit_values)
+    observed = int(np.count_nonzero(np.abs(audit_values) < tolerance))
+    if observed != rank:
+        raise RuntimeError(
+            f"sparse zero-mode count mismatch: expected {rank}, observed {observed}"
+        )
+    gap = float(audit_values[rank] - audit_values[rank - 1])
+    if gap <= 0.0:
+        raise RuntimeError("sparse kernel has no open external gap")
+    return KernelFrame(
+        frame=frame,
+        zero_eigenvalues=np.sort(np.real(values)),
+        external_gap=gap,
+        residual_norm=residual,
+        orthonormality_error=orthonormality,
+        method="lobpcg",
+        observed_rank=observed,
+    )
+
+
+def solve_kernel_frame(
+    system: KapitLaughlinParent,
+    case: ManyBodyCase,
+    seed: int,
+) -> KernelFrame:
+    """Return a complete target frame and a separately audited external gap."""
+
+    if system.n_particles != case.N or system.n_flux != case.n_flux:
+        raise ValueError("system and many-body case disagree")
+    if case.expected_rank != laughlin_zero_mode_count(case.N, case.n_flux):
+        raise ValueError("case rank disagrees with exact Laughlin counting")
+    if system.basis.dimension <= 2_000:
+        return _dense_kernel_frame(system, case)
+    return _sparse_kernel_frame(system, case, seed)
+
+
+def _site_tangent_operators(
+    system: KapitLaughlinParent,
+    site_indices: tuple[int, ...],
+) -> list[sparse.csr_matrix]:
+    physical_sites = int(system.orbitals.shape[0])
+    operators: list[sparse.csr_matrix] = []
+    for site in site_indices:
+        if not 0 <= site < physical_sites:
+            raise IndexError("physical site index is outside the lattice")
+        potential = np.zeros(physical_sites, dtype=float)
+        potential[site] = 1.0
+        one_body = projected_site_potential(system.orbitals, potential)
+        operators.append(manybody_one_body_operator(system.basis, one_body))
+    return operators
+
+
+def _tangent_gram(operators: list[sparse.csr_matrix]) -> np.ndarray:
+    count = len(operators)
+    gram = np.empty((count, count), dtype=complex)
+    for left in range(count):
+        for right in range(left, count):
+            value = (
+                operators[left]
+                .conjugate()
+                .multiply(operators[right])
+                .sum()
+            )
+            gram[left, right] = value
+            gram[right, left] = np.conjugate(value)
+    gram = 0.5 * (gram + gram.conj().T)
+    if np.max(np.abs(gram.imag)) < 1e-10:
+        return gram.real
+    return gram
+
+
+def _project_complement(frame: np.ndarray, values: np.ndarray) -> np.ndarray:
+    return values - frame @ (frame.conj().T @ values)
+
+
+def _reshape_site_solutions(
+    matrix: np.ndarray,
+    sites: int,
+    dimension: int,
+    rank: int,
+) -> np.ndarray:
+    return (
+        np.asarray(matrix)
+        .reshape(dimension, sites, rank)
+        .transpose(1, 0, 2)
+    )
+
+
+def build_site_response_cache(
+    system: KapitLaughlinParent,
+    kernel: KernelFrame,
+    relative_shifts: tuple[float, float] = (1e-3, 5e-4),
+    site_indices: tuple[int, ...] | None = None,
+) -> SiteResponseCache:
+    """Build selected site responses by two-shift sparse extrapolation."""
+
+    relative = tuple(float(value) for value in relative_shifts)
+    if len(relative) != 2 or not (relative[0] > relative[1] > 0.0):
+        raise ValueError("require two positive descending relative shifts")
+    if not np.isclose(relative[1], 0.5 * relative[0]):
+        raise ValueError("Richardson extrapolation requires a half shift")
+    chosen = (
+        tuple(range(system.orbitals.shape[0]))
+        if site_indices is None
+        else tuple(int(index) for index in site_indices)
+    )
+    if not chosen or len(set(chosen)) != len(chosen):
+        raise ValueError("site indices must be nonempty and distinct")
+    operators = _site_tangent_operators(system, chosen)
+    frame = np.asarray(kernel.frame, dtype=complex)
+    right_hand_sides = [
+        _project_complement(frame, np.asarray(operator @ frame))
+        for operator in operators
+    ]
+    combined_rhs = np.concatenate(right_hand_sides, axis=1)
+    identity = sparse.eye(
+        system.basis.dimension,
+        format="csc",
+        dtype=complex,
+    )
+    absolute = (
+        relative[0] * kernel.external_gap,
+        relative[1] * kernel.external_gap,
+    )
+    first_solver = splu(
+        (system.parent + absolute[0] * identity).tocsc()
+    )
+    first = first_solver.solve(combined_rhs)
+    del first_solver
+    second_solver = splu(
+        (system.parent + absolute[1] * identity).tocsc()
+    )
+    second = second_solver.solve(combined_rhs)
+    del second_solver
+    first = _project_complement(frame, first)
+    second = _project_complement(frame, second)
+    extrapolated = _project_complement(frame, 2.0 * second - first)
+    sites = len(chosen)
+    dimension = system.basis.dimension
+    rank = kernel.frame.shape[1]
+    solutions = _reshape_site_solutions(
+        extrapolated,
+        sites,
+        dimension,
+        rank,
+    )
+    first_by_site = _reshape_site_solutions(
+        first,
+        sites,
+        dimension,
+        rank,
+    )
+    second_by_site = _reshape_site_solutions(
+        second,
+        sites,
+        dimension,
+        rank,
+    )
+    relative_residuals: list[float] = []
+    shift_differences: list[float] = []
+    kernel_leakage: list[float] = []
+    for index, rhs in enumerate(right_hand_sides):
+        solution = solutions[index]
+        rhs_norm = float(np.linalg.norm(rhs))
+        solution_norm = max(float(np.linalg.norm(solution)), 1e-30)
+        relative_residuals.append(
+            float(np.linalg.norm(system.parent @ solution - rhs))
+            / rhs_norm
+        )
+        shift_differences.append(
+            float(
+                np.linalg.norm(
+                    second_by_site[index] - first_by_site[index]
+                )
+            )
+            / solution_norm
+        )
+        kernel_leakage.append(
+            float(np.linalg.norm(frame.conj().T @ solution))
+        )
+    case = ManyBodyCase(
+        N=system.n_particles,
+        n_flux=system.n_flux,
+        expected_rank=rank,
+        theta_x=system.theta_x,
+        theta_y=system.theta_y,
+    )
+    return SiteResponseCache(
+        case=case,
+        site_indices=chosen,
+        solutions=solutions,
+        tangent_gram=_tangent_gram(operators),
+        external_gap=kernel.external_gap,
+        shift_values=absolute,
+        maximum_relative_residual=max(relative_residuals),
+        maximum_shift_difference=max(shift_differences),
+        maximum_kernel_leakage=max(kernel_leakage),
+    )
+
+
+def dense_resolvent_response(
+    system: KapitLaughlinParent,
+    kernel: KernelFrame,
+    site_indices: tuple[int, ...] | None = None,
+) -> np.ndarray:
+    """Return exact dense complement responses in the supplied target gauge."""
+
+    chosen = (
+        tuple(range(system.orbitals.shape[0]))
+        if site_indices is None
+        else tuple(int(index) for index in site_indices)
+    )
+    operators = _site_tangent_operators(system, chosen)
+    eigenvalues, eigenvectors = np.linalg.eigh(system.parent.toarray())
+    rank = kernel.frame.shape[1]
+    external_values = eigenvalues[rank:]
+    external_frame = eigenvectors[:, rank:]
+    if external_values.size == 0 or external_values[0] <= 0.0:
+        raise RuntimeError("dense spectral inverse has no external sector")
+    responses: list[np.ndarray] = []
+    for operator in operators:
+        rhs = _project_complement(
+            kernel.frame,
+            np.asarray(operator @ kernel.frame),
+        )
+        coefficients = external_frame.conj().T @ rhs
+        responses.append(
+            external_frame
+            @ (coefficients / external_values[:, None])
+        )
+    return np.asarray(responses)
+
+
+def response_pair_grams(solutions: np.ndarray) -> np.ndarray:
+    """Return all target-space products ``A_s^dagger A_t``."""
+
+    values = np.asarray(solutions, dtype=complex)
+    if values.ndim != 3:
+        raise ValueError("solutions must have shape (site, ambient, rank)")
+    return np.einsum(
+        "sai,taj->stij",
+        values.conj(),
+        values,
+        optimize=True,
+    )
+
+
+def rotate_response_target_gauge(
+    cache: SiteResponseCache,
+    unitary: np.ndarray,
+) -> SiteResponseCache:
+    """Return the same response cache in a rotated target frame."""
+
+    matrix = np.asarray(unitary, dtype=complex)
+    rank = cache.solutions.shape[-1]
+    if matrix.shape != (rank, rank):
+        raise ValueError("target unitary has the wrong shape")
+    if not np.allclose(
+        matrix.conj().T @ matrix,
+        np.eye(rank),
+        atol=1e-10,
+    ):
+        raise ValueError("target transformation must be unitary")
+    return replace(
+        cache,
+        solutions=np.einsum(
+            "sai,ij->saj",
+            cache.solutions,
+            matrix,
+            optimize=True,
+        ),
+    )
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/lgeth/root_operators.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/lgeth/root_operators.py
new file mode 100644
index 000000000..3f14fb3be
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/lgeth/root_operators.py
@@ -0,0 +1,142 @@
+"""Exact monomial one-body blocks and accessibility complexes."""
+
+from __future__ import annotations
+
+from dataclasses import dataclass
+
+import numpy as np
+
+from .combinatorics import RootPartition, root_descendant_partition
+
+
+@dataclass(frozen=True)
+class AccessibilityComplex:
+    """Two-tangent root-space accessibility complex."""
+
+    N: int
+    n: int
+    k: int
+    r: int
+    D: int
+    K1: int
+    Pi1: int
+    partition: RootPartition
+    response_v: np.ndarray
+    response_w: np.ndarray
+    primitive_v: np.ndarray
+    primitive_w: np.ndarray
+    stacked_response: np.ndarray
+    syzygy: np.ndarray
+
+
+def onebody_block(
+    states: tuple[tuple[int, ...], ...],
+    source_indices: tuple[int, ...],
+    target_indices: tuple[int, ...],
+    tangent: np.ndarray,
+) -> np.ndarray:
+    """Return an exact monomial-basis block of a one-body representation."""
+
+    matrix = np.asarray(tangent)
+    if matrix.ndim != 2 or matrix.shape[0] != matrix.shape[1]:
+        raise ValueError("tangent must be square")
+    if not np.issubdtype(matrix.dtype, np.integer):
+        raise ValueError("tangent must have integer entries")
+    n_flux = matrix.shape[0]
+    if any(len(state) != n_flux for state in states):
+        raise ValueError("state orbital count disagrees with tangent")
+    index_by_state = {state: index for index, state in enumerate(states)}
+    target_row = {
+        int(basis_index): row
+        for row, basis_index in enumerate(target_indices)
+    }
+    block = np.zeros(
+        (len(target_indices), len(source_indices)),
+        dtype=np.int64,
+    )
+    for column, basis_index in enumerate(source_indices):
+        state = states[int(basis_index)]
+        for source, population in enumerate(state):
+            if population == 0:
+                continue
+            for destination in range(n_flux):
+                if destination == source:
+                    continue
+                updated = list(state)
+                updated[source] -= 1
+                updated[destination] += 1
+                target_index = index_by_state[tuple(updated)]
+                row = target_row.get(target_index)
+                if row is not None:
+                    block[row, column] += (
+                        int(population)
+                        * int(matrix[destination, source])
+                    )
+    return block
+
+
+def accessibility_complex(
+    n_particles: int,
+    n_flux: int,
+    tangent_v: np.ndarray,
+    tangent_w: np.ndarray,
+    k: int = 1,
+    r: int = 2,
+) -> AccessibilityComplex:
+    """Construct ``P -> E+E -> Pi`` for two integer one-body tangents."""
+
+    partition = root_descendant_partition(
+        n_particles,
+        n_flux,
+        q=1,
+        k=k,
+        r=r,
+    )
+    response_v = onebody_block(
+        partition.states,
+        partition.zero_modes,
+        partition.descendant_external,
+        tangent_v,
+    )
+    response_w = onebody_block(
+        partition.states,
+        partition.zero_modes,
+        partition.descendant_external,
+        tangent_w,
+    )
+    primitive_v = onebody_block(
+        partition.states,
+        partition.descendant_external,
+        partition.primitive,
+        tangent_v,
+    )
+    primitive_w = onebody_block(
+        partition.states,
+        partition.descendant_external,
+        partition.primitive,
+        tangent_w,
+    )
+    stacked_response = np.concatenate(
+        [response_v, response_w],
+        axis=0,
+    )
+    syzygy = np.concatenate(
+        [-primitive_w, primitive_v],
+        axis=1,
+    )
+    return AccessibilityComplex(
+        N=int(n_particles),
+        n=int(n_flux),
+        k=int(k),
+        r=int(r),
+        D=len(partition.zero_modes),
+        K1=len(partition.descendant_external),
+        Pi1=len(partition.primitive),
+        partition=partition,
+        response_v=response_v,
+        response_w=response_w,
+        primitive_v=primitive_v,
+        primitive_w=primitive_w,
+        stacked_response=stacked_response,
+        syzygy=syzygy,
+    )
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/lgeth/statistics.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/lgeth/statistics.py
new file mode 100644
index 000000000..53a574a16
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/lgeth/statistics.py
@@ -0,0 +1,570 @@
+"""Controlled spectral estimators for active geometric statistics."""
+
+from __future__ import annotations
+
+from dataclasses import dataclass
+from typing import Iterable
+
+import numpy as np
+from scipy.optimize import curve_fit, lsq_linear
+
+
+@dataclass(frozen=True)
+class BootstrapInterval:
+    """Bootstrap summary of a scalar sample mean."""
+
+    mean: float
+    lower: float
+    upper: float
+    standard_error: float
+    replicates: int
+
+
+@dataclass(frozen=True)
+class CurveBand:
+    """Matrix- or block-level simultaneous confidence band."""
+
+    mean: np.ndarray
+    lower: np.ndarray
+    upper: np.ndarray
+    pointwise_lower: np.ndarray
+    pointwise_upper: np.ndarray
+    standard_error: np.ndarray
+    critical_value: float
+    replicates: int
+    units: int
+    method: str
+
+
+def sample_poisson_spectra(
+    samples: int,
+    levels: int,
+    seed: int,
+) -> np.ndarray:
+    """Sample independent exponential-spacing spectra."""
+
+    rng = np.random.default_rng(int(seed))
+    spacings = rng.exponential(size=(int(samples), int(levels)))
+    spectra = np.cumsum(spacings, axis=1)
+    spectra -= np.mean(spectra, axis=1, keepdims=True)
+    return spectra
+
+
+def sample_gue_spectra(
+    samples: int,
+    levels: int,
+    seed: int,
+) -> np.ndarray:
+    """Sample finite complex Hermitian Gaussian spectra."""
+
+    count = int(samples)
+    dimension = int(levels)
+    if count < 1 or dimension < 3:
+        raise ValueError("require samples>=1 and levels>=3")
+    rng = np.random.default_rng(int(seed))
+    spectra = np.empty((count, dimension), dtype=float)
+    for sample in range(count):
+        gaussian = (
+            rng.normal(size=(dimension, dimension))
+            + 1j * rng.normal(size=(dimension, dimension))
+        )
+        matrix = (gaussian + gaussian.conj().T) / np.sqrt(
+            4.0 * dimension
+        )
+        spectra[sample] = np.linalg.eigvalsh(matrix)
+    return spectra
+
+
+def bulk_gap_ratio_per_spectrum(
+    spectra: np.ndarray,
+    bulk_fraction: float = 0.7,
+) -> np.ndarray:
+    """Return one adjacent-gap-ratio mean per spectrum."""
+
+    values = np.asarray(spectra, dtype=float)
+    if values.ndim != 2 or values.shape[1] < 3:
+        raise ValueError("spectra must have shape (samples, levels>=3)")
+    fraction = float(bulk_fraction)
+    if not 0.2 <= fraction <= 1.0:
+        raise ValueError("bulk_fraction must lie in [0.2,1]")
+    result = np.empty(values.shape[0], dtype=float)
+    trim = int(np.floor(0.5 * (1.0 - fraction) * values.shape[1]))
+    for sample, spectrum in enumerate(values):
+        ordered = np.sort(spectrum)
+        bulk = ordered[
+            trim : values.shape[1] - trim if trim else values.shape[1]
+        ]
+        spacings = np.diff(bulk)
+        if spacings.size < 2 or np.any(spacings <= 0.0):
+            raise ValueError("bulk spectrum has degenerate or too few levels")
+        ratios = np.minimum(spacings[:-1], spacings[1:]) / np.maximum(
+            spacings[:-1],
+            spacings[1:],
+        )
+        result[sample] = float(np.mean(ratios))
+    return result
+
+
+def unfold_spectra(
+    spectra: np.ndarray,
+    method: str,
+) -> np.ndarray:
+    """Unfold spectra by pooled CDF or per-spectrum polynomial counting."""
+
+    values = np.asarray(spectra, dtype=float)
+    if values.ndim != 2 or values.shape[1] < 4:
+        raise ValueError("spectra must have shape (samples,levels>=4)")
+    ordered = np.sort(values, axis=1)
+    if method == "ensemble_cdf":
+        pooled = np.sort(ordered.ravel())
+        quantiles = np.linspace(
+            0.0,
+            float(values.shape[1]),
+            pooled.size,
+        )
+        return np.asarray(
+            [
+                np.interp(spectrum, pooled, quantiles)
+                for spectrum in ordered
+            ]
+        )
+    if method == "polynomial":
+        unfolded = np.empty_like(ordered)
+        target = np.arange(values.shape[1], dtype=float)
+        degree = min(5, values.shape[1] - 1)
+        for sample, spectrum in enumerate(ordered):
+            center = float(np.mean(spectrum))
+            scale = float(np.std(spectrum))
+            if scale <= 0.0:
+                raise ValueError("cannot unfold a constant spectrum")
+            standardized = (spectrum - center) / scale
+            coefficients = np.polynomial.chebyshev.chebfit(
+                standardized,
+                target,
+                degree,
+            )
+            mapped = np.polynomial.chebyshev.chebval(
+                standardized,
+                coefficients,
+            )
+            if np.any(np.diff(mapped) <= 0.0):
+                raise ValueError("polynomial unfolding is not monotone")
+            unfolded[sample] = mapped
+        return unfolded
+    raise ValueError("unknown unfolding method")
+
+
+def number_variance(
+    unfolded_spectra: np.ndarray,
+    lengths: Iterable[float],
+    windows_per_spectrum: int = 48,
+) -> dict[str, float]:
+    """Estimate number variance from sliding unfolded windows."""
+
+    spectra = np.asarray(unfolded_spectra, dtype=float)
+    if spectra.ndim != 2:
+        raise ValueError("unfolded_spectra must be two-dimensional")
+    result: dict[str, float] = {}
+    for raw_length in lengths:
+        length = float(raw_length)
+        if length <= 0.0:
+            raise ValueError("window lengths must be positive")
+        counts: list[int] = []
+        for spectrum in spectra:
+            ordered = np.sort(spectrum)
+            lower = float(ordered[1])
+            upper = float(ordered[-2] - length)
+            if upper <= lower:
+                continue
+            starts = np.linspace(
+                lower,
+                upper,
+                int(windows_per_spectrum),
+            )
+            for start in starts:
+                counts.append(
+                    int(
+                        np.count_nonzero(
+                            (ordered >= start)
+                            & (ordered < start + length)
+                        )
+                    )
+                )
+        if not counts:
+            raise ValueError("no number-variance windows were available")
+        result[str(length)] = float(np.var(counts, ddof=1))
+    return result
+
+
+def bootstrap_mean_interval(
+    values: np.ndarray,
+    replicates: int,
+    seed: int,
+) -> BootstrapInterval:
+    """Return a percentile bootstrap interval for the mean."""
+
+    sample = np.asarray(values, dtype=float).ravel()
+    draws = int(replicates)
+    if sample.size < 2 or draws < 100:
+        raise ValueError("need at least two values and 100 replicates")
+    rng = np.random.default_rng(int(seed))
+    indices = rng.integers(
+        0,
+        sample.size,
+        size=(draws, sample.size),
+    )
+    means = np.mean(sample[indices], axis=1)
+    lower, upper = np.quantile(means, (0.025, 0.975))
+    return BootstrapInterval(
+        mean=float(np.mean(sample)),
+        lower=float(lower),
+        upper=float(upper),
+        standard_error=float(np.std(means, ddof=1)),
+        replicates=draws,
+    )
+
+
+def intervals_overlap(
+    first: BootstrapInterval,
+    second: BootstrapInterval,
+) -> bool:
+    """Return whether two closed bootstrap intervals overlap."""
+
+    return bool(
+        max(first.lower, second.lower)
+        <= min(first.upper, second.upper)
+    )
+
+
+def remove_labeled_atoms(
+    spectrum: np.ndarray,
+    atom_labels: np.ndarray,
+) -> np.ndarray:
+    """Remove only levels carrying explicit algebraic atom labels."""
+
+    values = np.asarray(spectrum)
+    labels = np.asarray(atom_labels, dtype=bool)
+    if values.shape != labels.shape:
+        raise ValueError("spectrum and labels must have matching shapes")
+    return values[~labels]
+
+
+def histogram_l1(
+    first: np.ndarray,
+    second: np.ndarray,
+    edges: np.ndarray,
+) -> float:
+    """Return the histogram probability-density L1 distance."""
+
+    bins = np.asarray(edges, dtype=float)
+    density_first, _ = np.histogram(
+        np.asarray(first).ravel(),
+        bins=bins,
+        density=True,
+    )
+    density_second, _ = np.histogram(
+        np.asarray(second).ravel(),
+        bins=bins,
+        density=True,
+    )
+    return float(
+        np.sum(
+            np.abs(density_first - density_second) * np.diff(bins)
+        )
+    )
+
+
+def matrix_bootstrap_band(
+    curves: np.ndarray,
+    replicates: int,
+    seed: int,
+    groups: np.ndarray | None = None,
+) -> CurveBand:
+    """Return a simultaneous band using matrices or independent seed blocks.
+
+    Exact resampling is used for at most 512 independent units.  Larger
+    matrix ensembles use the Gaussian multiplier limit of the matrix-mean
+    process, estimated from the full between-matrix covariance.
+    """
+
+    values = np.asarray(curves, dtype=float)
+    draws = int(replicates)
+    if values.ndim != 2 or values.shape[0] < 2 or draws < 100:
+        raise ValueError("require curves=(units,grid), units>=2, draws>=100")
+    if groups is not None:
+        labels = np.asarray(groups)
+        if labels.shape != (values.shape[0],):
+            raise ValueError("groups must provide one label per curve")
+        unique = np.unique(labels)
+        units = np.asarray(
+            [np.mean(values[labels == label], axis=0) for label in unique]
+        )
+        method = "hierarchical_seed_block_bootstrap"
+    else:
+        units = values
+        method = "matrix_bootstrap"
+    count, grid = units.shape
+    rng = np.random.default_rng(int(seed))
+    mean = np.mean(units, axis=0)
+    if count <= 512:
+        bootstrap = np.empty((draws, grid), dtype=float)
+        batch = 256
+        for start in range(0, draws, batch):
+            stop = min(start + batch, draws)
+            indices = rng.integers(
+                0,
+                count,
+                size=(stop - start, count),
+            )
+            bootstrap[start:stop] = np.mean(units[indices], axis=1)
+    else:
+        centered = units - mean
+        covariance_mean = (
+            centered.T @ centered / (count * (count - 1))
+        )
+        eigenvalues, eigenvectors = np.linalg.eigh(
+            0.5 * (covariance_mean + covariance_mean.T)
+        )
+        keep = eigenvalues > max(
+            float(eigenvalues[-1]) * 1e-12,
+            0.0,
+        )
+        factor = eigenvectors[:, keep] * np.sqrt(eigenvalues[keep])[None, :]
+        bootstrap = mean + rng.normal(
+            size=(draws, int(np.count_nonzero(keep)))
+        ) @ factor.T
+        method = "matrix_gaussian_multiplier_bootstrap"
+    pointwise_lower, pointwise_upper = np.quantile(
+        bootstrap,
+        (0.025, 0.975),
+        axis=0,
+    )
+    standard_error = np.std(bootstrap, axis=0, ddof=1)
+    safe_error = np.maximum(standard_error, 1e-15)
+    maximum = np.max(
+        np.abs((bootstrap - mean) / safe_error),
+        axis=1,
+    )
+    critical = float(np.quantile(maximum, 0.95))
+    return CurveBand(
+        mean=mean,
+        lower=mean - critical * standard_error,
+        upper=mean + critical * standard_error,
+        pointwise_lower=pointwise_lower,
+        pointwise_upper=pointwise_upper,
+        standard_error=standard_error,
+        critical_value=critical,
+        replicates=draws,
+        units=count,
+        method=method,
+    )
+
+
+def _number_variance_matrix_curves(
+    unfolded_spectra: np.ndarray,
+    lengths: np.ndarray,
+    windows_per_spectrum: int = 24,
+) -> np.ndarray:
+    spectra = np.sort(np.asarray(unfolded_spectra, dtype=float), axis=1)
+    scales = np.asarray(lengths, dtype=float)
+    if spectra.ndim != 2 or spectra.shape[1] < 8:
+        raise ValueError("unfolded spectra require at least eight levels")
+    if np.any(scales <= 0.0):
+        raise ValueError("lengths must be positive")
+    curves = np.empty((spectra.shape[0], scales.size), dtype=float)
+    for matrix, levels in enumerate(spectra):
+        for column, length in enumerate(scales):
+            lower = float(levels[1])
+            upper = float(levels[-2] - length)
+            if upper <= lower:
+                curves[matrix, column] = np.nan
+                continue
+            starts = np.linspace(lower, upper, int(windows_per_spectrum))
+            left = np.searchsorted(levels, starts, side="left")
+            right = np.searchsorted(
+                levels,
+                starts + length,
+                side="left",
+            )
+            counts = right - left
+            curves[matrix, column] = float(np.var(counts, ddof=1))
+    if np.any(~np.isfinite(curves)):
+        raise ValueError("requested length exceeds the usable bulk")
+    return curves
+
+
+def number_variance_matrix_curves(
+    unfolded_spectra: np.ndarray,
+    lengths: Iterable[float],
+    windows_per_spectrum: int = 24,
+) -> np.ndarray:
+    """Return one number-variance curve per input matrix."""
+
+    return _number_variance_matrix_curves(
+        unfolded_spectra,
+        np.asarray(tuple(float(value) for value in lengths)),
+        windows_per_spectrum=windows_per_spectrum,
+    )
+
+
+def spectral_rigidity(
+    unfolded_spectra: np.ndarray,
+    lengths: Iterable[float],
+) -> np.ndarray:
+    """Estimate Dyson--Mehta rigidity from the number-variance identity."""
+
+    scales = np.asarray(tuple(float(value) for value in lengths))
+    sigma = np.mean(
+        _number_variance_matrix_curves(unfolded_spectra, scales),
+        axis=0,
+    )
+    result = np.empty_like(scales)
+    extended_x = np.concatenate([[0.0], scales])
+    extended_sigma = np.concatenate([[0.0], sigma])
+    for index, length in enumerate(scales):
+        mask = extended_x <= length
+        x = extended_x[mask]
+        values = extended_sigma[mask]
+        kernel = length**3 - 2.0 * length * length * x + x**3
+        result[index] = (
+            2.0
+            / length**4
+            * np.trapezoid(kernel * values, x)
+        )
+    return result
+
+
+def connected_form_factor(
+    unfolded_spectra: np.ndarray,
+    times: Iterable[float],
+) -> np.ndarray:
+    """Return the connected spectral form factor normalized by level count."""
+
+    spectra = np.asarray(unfolded_spectra, dtype=float)
+    time_grid = np.asarray(tuple(float(value) for value in times))
+    if spectra.ndim != 2 or spectra.shape[1] < 2:
+        raise ValueError("unfolded spectra must be two-dimensional")
+    phases = np.exp(
+        -2j
+        * np.pi
+        * spectra[:, :, None]
+        * time_grid[None, None, :]
+    )
+    partition = np.sum(phases, axis=1)
+    return (
+        np.mean(np.abs(partition) ** 2, axis=0)
+        - np.abs(np.mean(partition, axis=0)) ** 2
+    ) / spectra.shape[1]
+
+
+def fit_size_models(
+    dimensions: np.ndarray,
+    values: np.ndarray,
+    sigma: np.ndarray,
+) -> dict[str, dict[str, float | list[float]] | str]:
+    """Fit offset power laws and compare them by leave-one-size-out error."""
+
+    D = np.asarray(dimensions, dtype=float)
+    y = np.asarray(values, dtype=float)
+    uncertainty = np.asarray(sigma, dtype=float)
+    if D.ndim != 1 or D.size < 5 or y.shape != D.shape:
+        raise ValueError("at least five one-dimensional size points required")
+    if uncertainty.shape != D.shape or np.any(uncertainty <= 0.0):
+        raise ValueError("sigma must be positive and match dimensions")
+
+    def fixed_fit(
+        x: np.ndarray,
+        target: np.ndarray,
+        error: np.ndarray,
+        exponent: float,
+    ) -> tuple[np.ndarray, np.ndarray]:
+        design = np.column_stack([np.ones_like(x), x ** (-exponent)])
+        weighted = design / error[:, None]
+        rhs = target / error
+        solution = lsq_linear(
+            weighted,
+            rhs,
+            bounds=(0.0, np.inf),
+        )
+        if not solution.success:
+            raise RuntimeError("bounded fixed-exponent fit failed")
+        parameters = solution.x
+        covariance = np.linalg.pinv(weighted.T @ weighted)
+        return parameters, covariance
+
+    models: dict[str, dict[str, float | list[float]]] = {}
+    for label, exponent in (("D^-1/2", 0.5), ("D^-1", 1.0)):
+        parameters, covariance = fixed_fit(D, y, uncertainty, exponent)
+        prediction = parameters[0] + parameters[1] * D ** (-exponent)
+        residual = (y - prediction) / uncertainty
+        rss = float(np.sum(residual * residual))
+        loo = []
+        for held_out in range(D.size):
+            keep = np.arange(D.size) != held_out
+            local, _ = fixed_fit(
+                D[keep],
+                y[keep],
+                uncertainty[keep],
+                exponent,
+            )
+            loo.append(
+                y[held_out]
+                - (
+                    local[0]
+                    + local[1] * D[held_out] ** (-exponent)
+                )
+            )
+        models[label] = {
+            "offset": float(parameters[0]),
+            "amplitude": float(parameters[1]),
+            "exponent": exponent,
+            "offset_standard_error": float(np.sqrt(covariance[0, 0])),
+            "weighted_rss": rss,
+            "loo_rmse": float(np.sqrt(np.mean(np.square(loo)))),
+            "prediction": prediction.tolist(),
+        }
+
+    def free_model(x, offset, amplitude, exponent):
+        return offset + amplitude * x ** (-exponent)
+
+    parameters, covariance = curve_fit(
+        free_model,
+        D,
+        y,
+        sigma=uncertainty,
+        absolute_sigma=True,
+        p0=(max(0.0, float(np.min(y)) * 0.5), float(y[0]), 0.5),
+        bounds=([0.0, 0.0, 0.1], [np.inf, np.inf, 3.0]),
+        maxfev=50_000,
+    )
+    prediction = free_model(D, *parameters)
+    residual = (y - prediction) / uncertainty
+    loo = []
+    for held_out in range(D.size):
+        keep = np.arange(D.size) != held_out
+        try:
+            local, _ = curve_fit(
+                free_model,
+                D[keep],
+                y[keep],
+                sigma=uncertainty[keep],
+                absolute_sigma=True,
+                p0=parameters,
+                bounds=([0.0, 0.0, 0.1], [np.inf, np.inf, 3.0]),
+                maxfev=50_000,
+            )
+            loo.append(y[held_out] - free_model(D[held_out], *local))
+        except RuntimeError:
+            loo.append(np.nan)
+    models["free"] = {
+        "offset": float(parameters[0]),
+        "amplitude": float(parameters[1]),
+        "exponent": float(parameters[2]),
+        "offset_standard_error": float(np.sqrt(covariance[0, 0])),
+        "exponent_standard_error": float(np.sqrt(covariance[2, 2])),
+        "weighted_rss": float(np.sum(residual * residual)),
+        "loo_rmse": float(np.sqrt(np.nanmean(np.square(loo)))),
+        "prediction": prediction.tolist(),
+    }
+    best = min(models, key=lambda key: float(models[key]["loo_rmse"]))
+    return {"models": models, "best_by_loo": best}
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/lgeth/twist_bundle.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/lgeth/twist_bundle.py
new file mode 100644
index 000000000..3aa471aad
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/lgeth/twist_bundle.py
@@ -0,0 +1,332 @@
+"""Physical projected-contact zero-mode bundles over the closed twist torus."""
+
+from __future__ import annotations
+
+import argparse
+import hashlib
+import json
+import time
+from dataclasses import dataclass
+from pathlib import Path
+from typing import Any, Callable
+
+import numpy as np
+
+from .bundle_geometry import BundleGeometry, analyze_frame_bundle
+from .lattice import BosonBasis, build_kapit_laughlin_parent
+
+
+MODULE_ROOT = Path(__file__).resolve().parent
+SCRIPT_ROOT = MODULE_ROOT.parent
+DEFAULT_CHECKPOINT_ROOT = SCRIPT_ROOT / "output" / "topology_v3_checkpoints"
+
+
+@dataclass(frozen=True)
+class TwistBundle:
+    """One exact quasihole bundle sampled over a periodic twist mesh."""
+
+    N: int
+    n_flux: int
+    rank: int
+    mesh: int
+    energies: np.ndarray
+    kernel_bandwidth: np.ndarray
+    external_gap: np.ndarray
+    coefficient_frames: np.ndarray
+    orbital_frames: np.ndarray
+    geometry: BundleGeometry
+    observed_rank_min: int
+    observed_rank_max: int
+    runtime_seconds: float
+    identity: dict[str, Any]
+
+
+def _sha256(path: Path) -> str:
+    return hashlib.sha256(path.read_bytes()).hexdigest()
+
+
+def _identity(
+    N: int,
+    n_flux: int,
+    rank: int,
+    mesh: int,
+) -> dict[str, Any]:
+    sources = (
+        MODULE_ROOT / "twist_bundle.py",
+        MODULE_ROOT / "bundle_geometry.py",
+        MODULE_ROOT / "lattice.py",
+    )
+    return {
+        "version": "v3",
+        "N": int(N),
+        "n_flux": int(n_flux),
+        "rank": int(rank),
+        "mesh": int(mesh),
+        "sources": {
+            path.name: _sha256(path)
+            for path in sources
+        },
+        "numpy": np.__version__,
+    }
+
+
+def _identity_hash(identity: dict[str, Any]) -> str:
+    encoded = json.dumps(
+        identity,
+        sort_keys=True,
+        separators=(",", ":"),
+    ).encode("utf-8")
+    return hashlib.sha256(encoded).hexdigest()
+
+
+def build_twist_bundle(
+    N: int,
+    n_flux: int,
+    rank: int,
+    mesh: int,
+    progress: Callable[[str], None] | None = None,
+) -> TwistBundle:
+    """Diagonalize an exact projected-contact bundle on a periodic mesh."""
+
+    particles = int(N)
+    flux = int(n_flux)
+    target_rank = int(rank)
+    grid = int(mesh)
+    if particles < 2 or flux < 2 * particles or target_rank < 1:
+        raise ValueError("invalid quasihole bundle parameters")
+    if grid < 3:
+        raise ValueError("twist mesh must be at least three")
+    seed_system = build_kapit_laughlin_parent(
+        particles,
+        flux,
+        0.0,
+        0.0,
+    )
+    basis_dimension = seed_system.basis.dimension
+    physical_sites = seed_system.orbitals.shape[0]
+    energies = np.empty((grid, grid, target_rank + 1), dtype=float)
+    bandwidth = np.empty((grid, grid), dtype=float)
+    gap = np.empty_like(bandwidth)
+    coefficient_frames = np.empty(
+        (grid, grid, basis_dimension, target_rank),
+        dtype=complex,
+    )
+    orbital_frames = np.empty(
+        (grid, grid, physical_sites, flux),
+        dtype=complex,
+    )
+    observed_ranks: list[int] = []
+    twists = 2.0 * np.pi * np.arange(grid) / grid
+    started = time.perf_counter()
+    for ix, theta_x in enumerate(twists):
+        for iy, theta_y in enumerate(twists):
+            system = build_kapit_laughlin_parent(
+                particles,
+                flux,
+                float(theta_x),
+                float(theta_y),
+            )
+            parent = system.parent.toarray()
+            parent = 0.5 * (parent + parent.conj().T)
+            values, vectors = np.linalg.eigh(parent)
+            tolerance = 1e-9 * max(float(np.max(np.abs(values))), 1.0)
+            observed = int(
+                np.count_nonzero(np.abs(values) < tolerance)
+            )
+            observed_ranks.append(observed)
+            if observed != target_rank:
+                raise RuntimeError(
+                    f"twist ({ix},{iy}) has {observed} zero modes, "
+                    f"expected {target_rank}"
+                )
+            energies[ix, iy] = values[: target_rank + 1]
+            bandwidth[ix, iy] = float(np.ptp(values[:target_rank]))
+            gap[ix, iy] = float(
+                values[target_rank] - values[target_rank - 1]
+            )
+            coefficient_frames[ix, iy] = vectors[:, :target_rank]
+            orbital_frames[ix, iy] = system.orbitals
+        if progress is not None:
+            progress(f"N={particles}, mesh={grid}: row {ix + 1}/{grid}")
+    basis = BosonBasis(flux, particles)
+    geometry = analyze_frame_bundle(
+        coefficient_frames,
+        orbital_frames,
+        basis,
+    )
+    return TwistBundle(
+        N=particles,
+        n_flux=flux,
+        rank=target_rank,
+        mesh=grid,
+        energies=energies,
+        kernel_bandwidth=bandwidth,
+        external_gap=gap,
+        coefficient_frames=coefficient_frames,
+        orbital_frames=orbital_frames,
+        geometry=geometry,
+        observed_rank_min=min(observed_ranks),
+        observed_rank_max=max(observed_ranks),
+        runtime_seconds=time.perf_counter() - started,
+        identity=_identity(particles, flux, target_rank, grid),
+    )
+
+
+def save_twist_bundle(
+    bundle: TwistBundle,
+    metadata_path: Path,
+) -> None:
+    """Save a bundle and its hash-locked array checkpoint."""
+
+    metadata = Path(metadata_path)
+    arrays_path = metadata.with_suffix(".npz")
+    metadata.parent.mkdir(parents=True, exist_ok=True)
+    temporary_arrays = arrays_path.with_suffix(".npz.tmp")
+    with temporary_arrays.open("wb") as handle:
+        np.savez_compressed(
+            handle,
+            energies=bundle.energies,
+            kernel_bandwidth=bundle.kernel_bandwidth,
+            external_gap=bundle.external_gap,
+            coefficient_frames=bundle.coefficient_frames,
+            orbital_frames=bundle.orbital_frames,
+        )
+    temporary_arrays.replace(arrays_path)
+    payload = {
+        "identity": bundle.identity,
+        "identity_hash": _identity_hash(bundle.identity),
+        "arrays": arrays_path.name,
+        "arrays_sha256": _sha256(arrays_path),
+        "observed_rank_min": bundle.observed_rank_min,
+        "observed_rank_max": bundle.observed_rank_max,
+        "runtime_seconds": bundle.runtime_seconds,
+        "geometry": {
+            "chern_determinant": bundle.geometry.chern_determinant,
+            "chern_trace_log": bundle.geometry.chern_trace_log,
+            "determinant_branch_margin": (
+                bundle.geometry.determinant_branch_margin
+            ),
+            "minimum_overlap_singular_value": (
+                bundle.geometry.minimum_overlap_singular_value
+            ),
+            "maximum_link_unitarity_error": (
+                bundle.geometry.maximum_link_unitarity_error
+            ),
+            "maximum_plaquette_unitarity_error": (
+                bundle.geometry.maximum_plaquette_unitarity_error
+            ),
+        },
+    }
+    temporary_metadata = metadata.with_suffix(".json.tmp")
+    temporary_metadata.write_text(
+        json.dumps(payload, indent=2, sort_keys=True),
+        encoding="utf-8",
+    )
+    temporary_metadata.replace(metadata)
+
+
+def load_twist_bundle(
+    metadata_path: Path,
+    expected_N: int,
+    expected_n_flux: int,
+    expected_rank: int,
+    expected_mesh: int,
+) -> TwistBundle:
+    """Load a checkpoint only if its identity and array hash match."""
+
+    metadata = Path(metadata_path)
+    payload = json.loads(metadata.read_text(encoding="utf-8"))
+    expected_identity = _identity(
+        expected_N,
+        expected_n_flux,
+        expected_rank,
+        expected_mesh,
+    )
+    if (
+        payload.get("identity") != expected_identity
+        or payload.get("identity_hash") != _identity_hash(expected_identity)
+    ):
+        raise ValueError("checkpoint identity mismatch")
+    arrays_path = metadata.with_name(payload["arrays"])
+    if payload.get("arrays_sha256") != _sha256(arrays_path):
+        raise ValueError("checkpoint array hash mismatch")
+    with np.load(arrays_path, allow_pickle=False) as arrays:
+        energies = np.asarray(arrays["energies"], dtype=float)
+        bandwidth = np.asarray(arrays["kernel_bandwidth"], dtype=float)
+        gap = np.asarray(arrays["external_gap"], dtype=float)
+        coefficient_frames = np.asarray(
+            arrays["coefficient_frames"],
+            dtype=complex,
+        )
+        orbital_frames = np.asarray(
+            arrays["orbital_frames"],
+            dtype=complex,
+        )
+    basis = BosonBasis(expected_n_flux, expected_N)
+    geometry = analyze_frame_bundle(
+        coefficient_frames,
+        orbital_frames,
+        basis,
+    )
+    return TwistBundle(
+        N=int(expected_N),
+        n_flux=int(expected_n_flux),
+        rank=int(expected_rank),
+        mesh=int(expected_mesh),
+        energies=energies,
+        kernel_bandwidth=bandwidth,
+        external_gap=gap,
+        coefficient_frames=coefficient_frames,
+        orbital_frames=orbital_frames,
+        geometry=geometry,
+        observed_rank_min=int(payload["observed_rank_min"]),
+        observed_rank_max=int(payload["observed_rank_max"]),
+        runtime_seconds=float(payload["runtime_seconds"]),
+        identity=expected_identity,
+    )
+
+
+def default_checkpoint_path(
+    N: int,
+    mesh: int,
+) -> Path:
+    return DEFAULT_CHECKPOINT_ROOT / f"N{int(N)}_mesh{int(mesh)}_twist_bundle_v3.json"
+
+
+def main() -> None:
+    parser = argparse.ArgumentParser()
+    parser.add_argument("--N", type=int, required=True)
+    parser.add_argument("--n-flux", type=int, required=True)
+    parser.add_argument("--rank", type=int, required=True)
+    parser.add_argument("--mesh", type=int, required=True)
+    parser.add_argument("--output", type=Path)
+    arguments = parser.parse_args()
+    bundle = build_twist_bundle(
+        arguments.N,
+        arguments.n_flux,
+        arguments.rank,
+        arguments.mesh,
+        progress=print,
+    )
+    output = arguments.output or default_checkpoint_path(
+        arguments.N,
+        arguments.mesh,
+    )
+    save_twist_bundle(bundle, output)
+    print(json.dumps(
+        {
+            "output": str(output),
+            "chern_determinant": bundle.geometry.chern_determinant,
+            "chern_trace_log": bundle.geometry.chern_trace_log,
+            "minimum_gap": float(np.min(bundle.external_gap)),
+            "minimum_overlap_singular_value": (
+                bundle.geometry.minimum_overlap_singular_value
+            ),
+        },
+        indent=2,
+        sort_keys=True,
+    ))
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/lgeth/wick_channels.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/lgeth/wick_channels.py
new file mode 100644
index 000000000..89f47f39b
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/lgeth/wick_channels.py
@@ -0,0 +1,442 @@
+"""Gauge-invariant covariance-matched four-channel Wick statistics."""
+
+from __future__ import annotations
+
+from dataclasses import dataclass
+
+import numpy as np
+
+from .manybody_response import SiteResponseCache
+
+
+@dataclass(frozen=True)
+class WhitenedChannels:
+    """Channel tensor after exact whitening on its label support."""
+
+    channels: np.ndarray
+    covariance: np.ndarray
+    covariance_eigenvalues: np.ndarray
+    inverse_sqrt: np.ndarray
+
+
+@dataclass(frozen=True)
+class WickResult:
+    """Four-channel tensor, separable Wick prediction, and residual."""
+
+    tensor: np.ndarray
+    wick_tensor: np.ndarray
+    connected: np.ndarray
+    R4: float
+    A_left: float
+    B_right: float
+    left_eigenvalues: np.ndarray
+    right_eigenvalues: np.ndarray
+    channel_covariance_eigenvalues: np.ndarray
+
+
+def _toroidal_distance_squared(
+    first: int,
+    second: int,
+    length: int,
+) -> float:
+    ax, ay = first % length, first // length
+    bx, by = second % length, second // length
+    dx = min(abs(ax - bx), length - abs(ax - bx))
+    dy = min(abs(ay - by), length - abs(ay - by))
+    return float(dx * dx + dy * dy)
+
+
+def _farthest_site_subset(
+    length: int,
+    count: int,
+    start: int,
+    tie_order: np.ndarray,
+) -> tuple[int, ...]:
+    sites = length * length
+    chosen = [int(start)]
+    priority = {int(site): index for index, site in enumerate(tie_order)}
+    while len(chosen) < count:
+        candidates = [site for site in range(sites) if site not in chosen]
+        scores = {
+            site: min(
+                _toroidal_distance_squared(site, selected, length)
+                for selected in chosen
+            )
+            for site in candidates
+        }
+        best_score = max(scores.values())
+        best = [site for site in candidates if scores[site] == best_score]
+        chosen.append(min(best, key=priority.__getitem__))
+    return tuple(chosen)
+
+
+def local_density_panels(
+    length: int,
+    panel_size: int,
+    panels: int,
+    seed: int,
+) -> np.ndarray:
+    """Return deterministic balanced panels of mean-zero site densities."""
+
+    linear = int(length)
+    size = int(panel_size)
+    count = int(panels)
+    sites = linear * linear
+    if linear < 2 or not 1 <= size < sites or count < 1:
+        raise ValueError("invalid local-density panel dimensions")
+    rng = np.random.default_rng(int(seed))
+    result = np.empty((count, size, sites), dtype=float)
+    starts = np.resize(rng.permutation(sites), count)
+    for panel in range(count):
+        tie_order = rng.permutation(sites)
+        chosen = _farthest_site_subset(
+            linear,
+            size,
+            int(starts[panel]),
+            tie_order,
+        )
+        for row, site in enumerate(chosen):
+            result[panel, row] = -np.ones(sites, dtype=float) / sites
+            result[panel, row, site] += 1.0
+    return result
+
+
+def fourier_density_panel(
+    length: int,
+    panel_size: int,
+) -> np.ndarray:
+    """Return a deterministic real low-momentum density panel."""
+
+    linear = int(length)
+    size = int(panel_size)
+    sites = linear * linear
+    if linear < 2 or not 1 <= size < sites:
+        raise ValueError("invalid Fourier-panel dimensions")
+    coordinates = np.asarray(
+        [(x, y) for y in range(linear) for x in range(linear)],
+        dtype=float,
+    )
+    momenta = [
+        (kx, ky)
+        for ky in range(linear)
+        for kx in range(linear)
+        if (kx, ky) != (0, 0)
+    ]
+    momenta.sort(
+        key=lambda momentum: (
+            min(momentum[0], linear - momentum[0]) ** 2
+            + min(momentum[1], linear - momentum[1]) ** 2,
+            momentum[1],
+            momentum[0],
+        )
+    )
+    selected: list[np.ndarray] = []
+    for kx, ky in momenta:
+        phase = (
+            2.0
+            * np.pi
+            * (kx * coordinates[:, 0] + ky * coordinates[:, 1])
+            / linear
+        )
+        for candidate in (np.cos(phase), np.sin(phase)):
+            vector = candidate - np.mean(candidate)
+            for existing in selected:
+                vector = vector - (existing @ vector) * existing
+            norm = float(np.linalg.norm(vector))
+            if norm <= 1e-10:
+                continue
+            selected.append(vector / norm)
+            if len(selected) == size:
+                return np.asarray(selected)
+    raise RuntimeError("Fourier panel did not reach the requested rank")
+
+
+def assemble_channels(
+    cache: SiteResponseCache,
+    coefficients: np.ndarray,
+) -> np.ndarray:
+    """Combine and tangent-normalize cached site responses."""
+
+    values = np.asarray(coefficients, dtype=complex)
+    sites = cache.solutions.shape[0]
+    if values.ndim != 2 or values.shape[1] != sites:
+        raise ValueError("coefficients and site-response cache disagree")
+    gram = np.asarray(cache.tangent_gram, dtype=complex)
+    if gram.shape != (sites, sites):
+        raise ValueError("tangent Gram matrix has the wrong shape")
+    channels = np.empty(
+        (values.shape[0], cache.solutions.shape[1], cache.solutions.shape[2]),
+        dtype=complex,
+    )
+    for index, vector in enumerate(values):
+        norm_squared = float(np.real(vector.conj() @ gram @ vector))
+        if norm_squared <= 1e-20:
+            raise ValueError("operator panel contains a null tangent")
+        channels[index] = np.tensordot(
+            vector,
+            cache.solutions,
+            axes=(0, 0),
+        ) / np.sqrt(norm_squared)
+    return channels
+
+
+def channel_covariance(channels: np.ndarray) -> np.ndarray:
+    """Return ``Tr(A_mu A_nu^dagger)/D`` on channel-label space."""
+
+    values = np.asarray(channels, dtype=complex)
+    if values.ndim != 3 or min(values.shape) < 1:
+        raise ValueError("channels must have shape (label, ambient, rank)")
+    rank = values.shape[-1]
+    covariance = np.einsum(
+        "mai,nai->mn",
+        values,
+        values.conj(),
+        optimize=True,
+    ) / rank
+    return 0.5 * (covariance + covariance.conj().T)
+
+
+def whiten_channel_labels(
+    channels: np.ndarray,
+    rtol: float = 1e-10,
+) -> WhitenedChannels:
+    """Whiten the complete numerically supported channel-label covariance."""
+
+    values = np.asarray(channels, dtype=complex)
+    covariance = channel_covariance(values)
+    eigenvalues, eigenvectors = np.linalg.eigh(covariance)
+    largest = float(eigenvalues[-1])
+    if largest <= 0.0:
+        raise ValueError("channel-label covariance has no positive support")
+    if float(eigenvalues[0]) <= float(rtol) * largest:
+        raise ValueError("channel-label support is singular")
+    inverse_sqrt = (
+        eigenvectors * (eigenvalues ** -0.5)[None, :]
+    ) @ eigenvectors.conj().T
+    whitened = np.einsum(
+        "mn,nai->mai",
+        inverse_sqrt,
+        values,
+        optimize=True,
+    )
+    observed = channel_covariance(whitened)
+    if not np.allclose(
+        observed,
+        np.eye(values.shape[0]),
+        atol=2e-9,
+        rtol=2e-9,
+    ):
+        raise RuntimeError("channel-label whitening failed")
+    return WhitenedChannels(
+        channels=whitened,
+        covariance=covariance,
+        covariance_eigenvalues=eigenvalues,
+        inverse_sqrt=inverse_sqrt,
+    )
+
+
+def target_covariance(channels: np.ndarray) -> np.ndarray:
+    """Return the mean target-space covariance ``A_mu^dagger A_mu``."""
+
+    values = np.asarray(channels, dtype=complex)
+    covariance = np.mean(
+        np.einsum(
+            "mai,maj->mij",
+            values.conj(),
+            values,
+            optimize=True,
+        ),
+        axis=0,
+    )
+    return 0.5 * (covariance + covariance.conj().T)
+
+
+def external_covariance_eigenvalues(
+    channels: np.ndarray,
+    rtol: float = 1e-12,
+) -> np.ndarray:
+    """Return nonzero eigenvalues of the mean external covariance by Gram reduction."""
+
+    values = np.asarray(channels, dtype=complex)
+    if values.ndim != 3:
+        raise ValueError("channels must have shape (label, ambient, rank)")
+    labels, ambient, rank = values.shape
+    stacked = values.transpose(1, 0, 2).reshape(ambient, labels * rank)
+    gram = stacked.conj().T @ stacked / labels
+    eigenvalues = np.linalg.eigvalsh(0.5 * (gram + gram.conj().T))
+    largest = max(float(eigenvalues[-1]), 0.0)
+    if largest <= 0.0:
+        raise ValueError("external covariance has no positive support")
+    return eigenvalues[eigenvalues > float(rtol) * largest]
+
+
+def four_channel_tensor(channels: np.ndarray) -> np.ndarray:
+    """Return ``Tr(X_mu X_nu^dagger X_rho X_sigma^dagger)/D``."""
+
+    values = np.asarray(channels, dtype=complex)
+    if values.ndim != 3:
+        raise ValueError("channels must have shape (label, ambient, rank)")
+    rank = values.shape[-1]
+    pair_grams = np.einsum(
+        "mai,naj->mnij",
+        values.conj(),
+        values,
+        optimize=True,
+    )
+    return np.einsum(
+        "mnij,rsji->mnrs",
+        pair_grams,
+        pair_grams,
+        optimize=True,
+    ) / rank
+
+
+def covariance_matched_wick(
+    channels: np.ndarray,
+    rtol: float = 1e-10,
+) -> WickResult:
+    """Return the separable covariance-matched Wick residual."""
+
+    whitened = whiten_channel_labels(channels, rtol=rtol)
+    values = whitened.channels
+    rank = values.shape[-1]
+    left = target_covariance(values)
+    left_eigenvalues = np.linalg.eigvalsh(left)
+    right_eigenvalues = external_covariance_eigenvalues(values)
+    left_trace = float(np.sum(left_eigenvalues))
+    right_trace = float(np.sum(right_eigenvalues))
+    A_left = (
+        rank
+        * float(np.sum(left_eigenvalues**2))
+        / (left_trace * left_trace)
+    )
+    B_right = (
+        rank
+        * float(np.sum(right_eigenvalues**2))
+        / (right_trace * right_trace)
+    )
+    tensor = four_channel_tensor(values)
+    identity = np.eye(values.shape[0])
+    wick = (
+        A_left * np.einsum("mn,rs->mnrs", identity, identity)
+        + B_right * np.einsum("ms,rn->mnrs", identity, identity)
+    )
+    connected = tensor - wick
+    denominator = float(np.linalg.norm(wick))
+    if denominator <= 0.0:
+        raise RuntimeError("Wick tensor has zero norm")
+    return WickResult(
+        tensor=tensor,
+        wick_tensor=wick,
+        connected=connected,
+        R4=float(np.linalg.norm(connected) / denominator),
+        A_left=A_left,
+        B_right=B_right,
+        left_eigenvalues=left_eigenvalues,
+        right_eigenvalues=right_eigenvalues,
+        channel_covariance_eigenvalues=whitened.covariance_eigenvalues,
+    )
+
+
+def sample_matched_gaussian_channels(
+    left_eigenvalues: np.ndarray,
+    right_eigenvalues: np.ndarray,
+    channel_count: int,
+    rng: np.random.Generator,
+) -> np.ndarray:
+    """Draw a separable complex Gaussian response tensor."""
+
+    left = np.asarray(left_eigenvalues, dtype=float)
+    right = np.asarray(right_eigenvalues, dtype=float)
+    labels = int(channel_count)
+    if (
+        left.ndim != 1
+        or right.ndim != 1
+        or left.size == 0
+        or right.size == 0
+        or labels < 1
+        or np.any(left <= 0.0)
+        or np.any(right <= 0.0)
+    ):
+        raise ValueError("Gaussian covariance spectra must be positive vectors")
+    left = left / np.sum(left)
+    right = right / np.sum(right)
+    gaussian = (
+        rng.normal(size=(labels, right.size, left.size))
+        + 1j * rng.normal(size=(labels, right.size, left.size))
+    ) / np.sqrt(2.0)
+    return (
+        np.sqrt(right)[None, :, None]
+        * gaussian
+        * np.sqrt(left)[None, None, :]
+    )
+
+
+def _fast_covariance_matched_r4(
+    channels: np.ndarray,
+) -> float:
+    """Return ``R4`` without diagonalizing the external covariance."""
+
+    values = whiten_channel_labels(channels).channels
+    labels = values.shape[0]
+    rank = values.shape[-1]
+    pair_grams = np.einsum(
+        "mai,naj->mnij",
+        values.conj(),
+        values,
+        optimize=True,
+    )
+    left = np.mean(
+        pair_grams[np.arange(labels), np.arange(labels)],
+        axis=0,
+    )
+    left_trace = float(np.trace(left).real)
+    A_left = (
+        rank
+        * float(np.trace(left @ left).real)
+        / (left_trace * left_trace)
+    )
+    right_trace = left_trace
+    right_trace_square = (
+        float(np.sum(np.abs(pair_grams) ** 2)) / (labels * labels)
+    )
+    B_right = (
+        rank * right_trace_square / (right_trace * right_trace)
+    )
+    tensor = np.einsum(
+        "mnij,rsji->mnrs",
+        pair_grams,
+        pair_grams,
+        optimize=True,
+    ) / rank
+    identity = np.eye(labels)
+    wick = (
+        A_left * np.einsum("mn,rs->mnrs", identity, identity)
+        + B_right * np.einsum("ms,rn->mnrs", identity, identity)
+    )
+    return float(np.linalg.norm(tensor - wick) / np.linalg.norm(wick))
+
+
+def gaussian_r4_reference(
+    left_eigenvalues: np.ndarray,
+    right_eigenvalues: np.ndarray,
+    channel_count: int,
+    samples: int,
+    seed: int,
+) -> np.ndarray:
+    """Return finite-size covariance-matched Gaussian ``R4`` samples."""
+
+    count = int(samples)
+    if count < 1:
+        raise ValueError("Gaussian reference requires at least one sample")
+    rng = np.random.default_rng(int(seed))
+    result = np.empty(count, dtype=float)
+    for sample in range(count):
+        channels = sample_matched_gaussian_channels(
+            left_eigenvalues,
+            right_eigenvalues,
+            channel_count,
+            rng,
+        )
+        result[sample] = _fast_covariance_matched_r4(channels)
+    return result
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/make_geometric_eth_topology_assets_v3.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/make_geometric_eth_topology_assets_v3.py
new file mode 100644
index 000000000..eb055ee65
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/make_geometric_eth_topology_assets_v3.py
@@ -0,0 +1,272 @@
+#!/usr/bin/env python3
+"""Generate manuscript-facing v3 macros, tables, and provenance."""
+
+from __future__ import annotations
+
+import hashlib
+import json
+import subprocess
+from datetime import datetime, timezone
+from pathlib import Path
+from typing import Any
+
+
+SCRIPT_ROOT = Path(__file__).resolve().parent
+REPO_ROOT = SCRIPT_ROOT.parents[2]
+OUTPUT = SCRIPT_ROOT / "output"
+MATRIX_JSON = OUTPUT / "matrix_element_geometric_eth_v3.json"
+TOPOLOGY_JSON = OUTPUT / "topological_holonomy_v3.json"
+MATRIX_AUDIT = OUTPUT / "matrix_element_delivery_audit_v3.json"
+TOPOLOGY_AUDIT = OUTPUT / "topological_holonomy_delivery_audit_v3.json"
+FIGURE_6 = OUTPUT / "figure_6_wick_factorization_v3.pdf"
+FIGURE_7 = OUTPUT / "figure_7_topological_holonomy_v3.pdf"
+NUMBERS = OUTPUT / "generated_numbers_v3.tex"
+TABLES = OUTPUT / "generated_tables_v3.tex"
+MANIFEST = OUTPUT / "geometric_eth_topology_assets_v3.json"
+OVERLEAF_GENERATED = (
+    REPO_ROOT / "overleaf_sync" / "geometric_eth_large_scale" / "generated"
+)
+
+
+def _sha256(path: Path) -> str:
+    return hashlib.sha256(path.read_bytes()).hexdigest()
+
+
+def _atomic_text(path: Path, text: str) -> None:
+    path.parent.mkdir(parents=True, exist_ok=True)
+    temporary = path.with_suffix(path.suffix + ".tmp")
+    temporary.write_text(text, encoding="utf-8")
+    temporary.replace(path)
+
+
+def _atomic_json(path: Path, payload: dict[str, Any]) -> None:
+    _atomic_text(path, json.dumps(payload, indent=2, sort_keys=True))
+
+
+def _fmt(value: float, digits: int = 5) -> str:
+    return f"{float(value):.{digits}f}"
+
+
+def _macro(name: str, value: str) -> str:
+    return rf"\newcommand{{\{name}}}{{{value}}}"
+
+
+def generate_assets() -> dict[str, Any]:
+    matrix = json.loads(MATRIX_JSON.read_text(encoding="utf-8"))
+    topology = json.loads(TOPOLOGY_JSON.read_text(encoding="utf-8"))
+    matrix_audit = json.loads(MATRIX_AUDIT.read_text(encoding="utf-8"))
+    topology_audit = json.loads(
+        TOPOLOGY_AUDIT.read_text(encoding="utf-8")
+    )
+    if not matrix_audit["passed"] or not topology_audit["passed"]:
+        raise RuntimeError("independent v3 audits must pass before assets")
+    largest = matrix["cases"][-1]
+    top3, top4 = topology["sizes"]
+    macros = [
+        "% Generated from audited v3 artifacts by the release pipeline.",
+        _macro(
+            "MatrixElementBranch",
+            matrix["result_branch"].replace("_", r"\_"),
+        ),
+        _macro(
+            "MatrixElementBranchText",
+            (
+                "The four-channel residual decreases along the genuine "
+                "many-body sequence and retains a resolved connected "
+                "component at the largest size."
+            ),
+        ),
+        _macro("LargestManyBodyN", str(largest["N"])),
+        _macro("LargestManyBodyRank", str(largest["rank"])),
+        _macro("LargestManyBodyDimension", str(largest["basis_dimension"])),
+        _macro("LargestNRFour", _fmt(largest["physical_R4_median"])),
+        _macro("LargestGaussianRFour", _fmt(largest["gaussian_R4_interval"][1])),
+        _macro(
+            "LargestGaussianRFourLow",
+            _fmt(largest["gaussian_R4_interval"][0]),
+        ),
+        _macro(
+            "LargestGaussianRFourHigh",
+            _fmt(largest["gaussian_R4_interval"][2]),
+        ),
+        _macro(
+            "LargestRFourExcess",
+            _fmt(largest["physical_excess"]),
+        ),
+        _macro(
+            "TopologyBranch",
+            topology["result_branch"].replace("_", r"\_"),
+        ),
+        _macro(
+            "TopologyBranchText",
+            (
+                "The Chern class and complete spectrum remain fixed while "
+                "Wilson statistics change significantly and occupy a "
+                "structured class distinct from the circular-unitary "
+                "reference."
+            ),
+        ),
+        _macro("TopologyPrimaryMesh", str(topology["configuration"]["primary_mesh"])),
+        _macro(
+            "TopologyConvergenceMesh",
+            str(topology["configuration"]["convergence_mesh"]),
+        ),
+        _macro("TopologyNThreeChern", str(top3["base_chern_integer"])),
+        _macro("TopologyNFourChern", str(top4["base_chern_integer"])),
+        _macro("TopologyNThreeGap", _fmt(top3["minimum_external_gap"], 6)),
+        _macro("TopologyNFourGap", _fmt(top4["minimum_external_gap"], 6)),
+        _macro(
+            "TopologyNThreeGapChangeLow",
+            _fmt(top3["gap_change_interval"][0]),
+        ),
+        _macro(
+            "TopologyNThreeGapChangeHigh",
+            _fmt(top3["gap_change_interval"][2]),
+        ),
+        _macro(
+            "TopologyNFourGapChangeLow",
+            _fmt(top4["gap_change_interval"][0]),
+        ),
+        _macro(
+            "TopologyNFourGapChangeHigh",
+            _fmt(top4["gap_change_interval"][2]),
+        ),
+        _macro(
+            "TopologyNThreeFinalGapRatio",
+            _fmt(top3["final_gap_ratio_interval"][1]),
+        ),
+        _macro(
+            "TopologyNFourFinalGapRatio",
+            _fmt(top4["final_gap_ratio_interval"][1]),
+        ),
+        _macro(
+            "TopologyNThreeCUERatio",
+            _fmt(top3["cue_gap_ratio_interval"][1]),
+        ),
+        _macro(
+            "TopologyNFourCUERatio",
+            _fmt(top4["cue_gap_ratio_interval"][1]),
+        ),
+        _macro(
+            "TopologyMinimumBranchMargin",
+            _fmt(
+                min(
+                    top3["minimum_branch_margin"],
+                    top4["minimum_branch_margin"],
+                )
+            ),
+        ),
+        _macro(
+            "TopologyMinimumOverlap",
+            _fmt(
+                min(
+                    top3["minimum_overlap_singular_value"],
+                    top4["minimum_overlap_singular_value"],
+                )
+            ),
+        ),
+        _macro(
+            "TopologyGaugeError",
+            f"{topology['random_gauge_errors']['wilson_phase_error']:.2e}",
+        ),
+        "",
+    ]
+    matrix_rows = []
+    for case in matrix["cases"]:
+        matrix_rows.append(
+            " & ".join(
+                [
+                    str(case["N"]),
+                    str(case["n_flux"]),
+                    str(case["rank"]),
+                    str(case["basis_dimension"]),
+                    _fmt(case["external_gap"], 6),
+                    _fmt(case["physical_R4_median"]),
+                    _fmt(case["gaussian_R4_interval"][1]),
+                    _fmt(case["physical_excess"]),
+                ]
+            )
+            + r" \\"
+        )
+    topology_rows = []
+    for size in topology["sizes"]:
+        topology_rows.append(
+            " & ".join(
+                [
+                    str(size["N"]),
+                    str(size["rank"]),
+                    str(size["base_chern_integer"]),
+                    _fmt(size["minimum_external_gap"], 6),
+                    _fmt(size["minimum_branch_margin"]),
+                    _fmt(size["minimum_overlap_singular_value"]),
+                    _fmt(size["final_gap_ratio_interval"][1]),
+                    _fmt(size["cue_gap_ratio_interval"][1]),
+                ]
+            )
+            + r" \\"
+        )
+    tables = "\n".join(
+        [
+            "% Generated from audited v3 artifacts by the release pipeline.",
+            r"\newcommand{\MatrixElementResultRows}{%",
+            *matrix_rows,
+            "}",
+            r"\newcommand{\TopologyResultRows}{%",
+            *topology_rows,
+            "}",
+            "",
+        ]
+    )
+    number_text = "\n".join(macros)
+    _atomic_text(NUMBERS, number_text)
+    _atomic_text(TABLES, tables)
+    _atomic_text(OVERLEAF_GENERATED / NUMBERS.name, number_text)
+    _atomic_text(OVERLEAF_GENERATED / TABLES.name, tables)
+    commit = subprocess.run(
+        ["git", "rev-parse", "HEAD"],
+        cwd=REPO_ROOT,
+        check=True,
+        capture_output=True,
+        text=True,
+    ).stdout.strip()
+    inputs = (
+        MATRIX_JSON,
+        TOPOLOGY_JSON,
+        MATRIX_AUDIT,
+        TOPOLOGY_AUDIT,
+        FIGURE_6,
+        FIGURE_7,
+    )
+    result = {
+        "version": "v3",
+        "generated_utc": datetime.now(timezone.utc).isoformat(),
+        "git_commit": commit,
+        "matrix_branch": matrix["result_branch"],
+        "topology_branch": topology["result_branch"],
+        "input_hashes": {
+            str(path.relative_to(SCRIPT_ROOT)): _sha256(path)
+            for path in inputs
+        },
+        "output_hashes": {
+            str(path.relative_to(SCRIPT_ROOT)): _sha256(path)
+            for path in (NUMBERS, TABLES)
+        },
+        "overleaf_hashes": {
+            str(path.relative_to(REPO_ROOT)): _sha256(path)
+            for path in (
+                OVERLEAF_GENERATED / NUMBERS.name,
+                OVERLEAF_GENERATED / TABLES.name,
+            )
+        },
+        "source_sha256": _sha256(Path(__file__)),
+    }
+    _atomic_json(MANIFEST, result)
+    return result
+
+
+def main() -> None:
+    print(json.dumps(generate_assets(), indent=2, sort_keys=True))
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/make_large_scale_figures_v1.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/make_large_scale_figures_v1.py
new file mode 100644
index 000000000..98154e733
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/make_large_scale_figures_v1.py
@@ -0,0 +1,811 @@
+#!/usr/bin/env python3
+"""Create the five publication figures and generated LaTeX inputs."""
+
+from __future__ import annotations
+
+import argparse
+import hashlib
+import json
+from pathlib import Path
+from typing import Any
+
+import matplotlib
+
+matplotlib.use("Agg")
+import matplotlib.pyplot as plt
+import numpy as np
+from scipy.ndimage import gaussian_filter1d
+
+
+VERSION = "v1"
+FIGURE_WIDTH = 7.0
+DPI = 300
+COLORS = {
+    "physical": "#0072B2",
+    "haar": "#222222",
+    "deformed": "#E69F00",
+    "atom": "#CC79A7",
+    "reference": "#666666",
+    "accent": "#009E73",
+}
+LABELS = {
+    "physical": "physical",
+    "haar": "Haar--Jacobi",
+    "deformed": "covariance model",
+}
+
+
+def _style() -> None:
+    plt.rcParams.update(
+        {
+            "font.family": "serif",
+            "font.serif": ["STIX Two Text", "STIXGeneral", "DejaVu Serif"],
+            "mathtext.fontset": "stix",
+            "font.size": 8.2,
+            "axes.labelsize": 8.5,
+            "axes.titlesize": 9.0,
+            "legend.fontsize": 7.2,
+            "xtick.labelsize": 7.4,
+            "ytick.labelsize": 7.4,
+            "axes.linewidth": 0.75,
+            "lines.linewidth": 1.35,
+            "savefig.facecolor": "white",
+            "figure.facecolor": "white",
+            "axes.facecolor": "white",
+            "axes.spines.top": False,
+            "axes.spines.right": False,
+        }
+    )
+
+
+def _panel(ax, label: str, title: str) -> None:
+    ax.text(
+        -0.12,
+        1.04,
+        f"({label})",
+        transform=ax.transAxes,
+        fontweight="bold",
+        va="bottom",
+    )
+    ax.set_title(title, loc="left", pad=5.0)
+
+
+def _band(
+    ax,
+    x: np.ndarray,
+    arrays: Any,
+    prefix: str,
+    color: str,
+    label: str,
+) -> None:
+    mean = arrays[f"{prefix}_mean"]
+    lower = arrays[f"{prefix}_lower"]
+    upper = arrays[f"{prefix}_upper"]
+    ax.fill_between(x, lower, upper, color=color, alpha=0.16, linewidth=0)
+    ax.plot(x, mean, color=color, label=label)
+
+
+def _save(fig, output_dir: Path, stem: str) -> dict[str, Any]:
+    pdf = output_dir / f"{stem}.pdf"
+    png = output_dir / f"{stem}.png"
+    fig.savefig(pdf, format="pdf")
+    fig.savefig(png, format="png", dpi=DPI)
+    plt.close(fig)
+    return {
+        "pdf": str(pdf),
+        "png": str(png),
+        "width_inches": FIGURE_WIDTH,
+        "png_width_pixels": int(round(FIGURE_WIDTH * DPI)),
+        "dpi": DPI,
+    }
+
+
+def _figure_physical_law(
+    stat: Any,
+    covariance: dict[str, Any],
+    output_dir: Path,
+) -> dict[str, Any]:
+    grid = stat["density_grid"]
+    fig = plt.figure(figsize=(FIGURE_WIDTH, 4.65), layout="constrained")
+    axes = fig.subplot_mosaic(
+        [["density", "density"], ["residual", "moments"]],
+        height_ratios=[1.25, 1.0],
+    )
+    ax = axes["density"]
+    for name in ("haar", "deformed", "physical"):
+        _band(
+            ax,
+            grid,
+            stat,
+            f"{name}_density",
+            COLORS[name],
+            LABELS[name],
+        )
+    ax.set_xlim(-1.0, 1.0)
+    ax.set_ylabel(r"one-point density $\rho(\lambda)$")
+    ax.set_xlabel(r"normalized curvature eigenvalue $\lambda$")
+    ax.legend(frameon=False, ncol=3, loc="upper center")
+    _panel(ax, "a", "High-statistics physical law")
+
+    ax = axes["residual"]
+    physical = stat["physical_density_mean"]
+    for name in ("haar", "deformed"):
+        difference = physical - stat[f"{name}_density_mean"]
+        standard_error = np.sqrt(
+            stat["physical_density_standard_error"] ** 2
+            + stat[f"{name}_density_standard_error"] ** 2
+        )
+        color = COLORS[name]
+        ax.fill_between(
+            grid,
+            difference - 2.5 * standard_error,
+            difference + 2.5 * standard_error,
+            color=color,
+            alpha=0.16,
+            linewidth=0,
+        )
+        ax.plot(
+            grid,
+            difference,
+            color=color,
+            label=f"physical $-$ {LABELS[name]}",
+        )
+    ax.axhline(0.0, color="#777777", linewidth=0.7)
+    ax.set_xlim(-1.0, 1.0)
+    ax.set_xlabel(r"$\lambda$")
+    ax.set_ylabel(r"density residual")
+    ax.legend(frameon=False, loc="upper left")
+    _panel(ax, "b", "Resolved global deformation")
+
+    ax = axes["moments"]
+    orders = stat["moment_orders"]
+    width = 0.22
+    positions = np.arange(orders.size)
+    for shift, name in zip(
+        (-width, 0.0, width),
+        ("haar", "deformed", "physical"),
+        strict=True,
+    ):
+        mean = stat[f"{name}_moments_mean"]
+        error = stat[f"{name}_moments_standard_error"]
+        ax.bar(
+            positions + shift,
+            mean,
+            width=width,
+            color=COLORS[name],
+            alpha=0.82,
+            label=LABELS[name],
+            yerr=1.96 * error,
+            capsize=2,
+            linewidth=0,
+        )
+    ax.set_xticks(positions, [rf"$m_{{{int(order)}}}$" for order in orders])
+    ax.set_ylabel(r"$D^{-1}\langle\mathrm{Tr}\,\Omega^k\rangle$")
+    ax.set_yscale("log")
+    ax.legend(frameon=False, ncol=1, loc="upper right")
+    _panel(ax, "c", "Moments through eighth order")
+    return _save(fig, output_dir, "figure_1_physical_law_v1")
+
+
+def _figure_scale_hierarchy(
+    stat: Any,
+    output_dir: Path,
+) -> dict[str, Any]:
+    fig, axes = plt.subplots(
+        2,
+        2,
+        figsize=(FIGURE_WIDTH, 5.2),
+        layout="constrained",
+    )
+    configurations = (
+        (
+            axes[0, 0],
+            stat["ratio_centers"],
+            "ratio",
+            r"$P(r)$",
+            r"adjacent-gap ratio $r$",
+            "a",
+            "Local level repulsion",
+        ),
+        (
+            axes[0, 1],
+            stat["lengths"],
+            "number",
+            r"$\Sigma^2(L)$",
+            r"window length $L$",
+            "b",
+            "Number variance",
+        ),
+        (
+            axes[1, 0],
+            stat["lengths"],
+            "rigidity",
+            r"$\Delta_3(L)$",
+            r"window length $L$",
+            "c",
+            "Spectral rigidity",
+        ),
+        (
+            axes[1, 1],
+            stat["form_factor_times"],
+            "form_factor",
+            r"$K_c(\tau)$",
+            r"scaled time $\tau$",
+            "d",
+            "Connected form factor",
+        ),
+    )
+    for ax, x, metric, ylabel, xlabel, label, title in configurations:
+        for name in ("haar", "deformed", "physical"):
+            _band(
+                ax,
+                x,
+                stat,
+                f"{name}_{metric}",
+                COLORS[name],
+                LABELS[name],
+            )
+        ax.set_xlabel(xlabel)
+        ax.set_ylabel(ylabel)
+        _panel(ax, label, title)
+    axes[0, 0].legend(frameon=False, loc="lower right")
+    axes[1, 1].set_xlim(0.0, 1.5)
+    axes[1, 1].set_ylim(bottom=-0.04)
+    return _save(fig, output_dir, "figure_2_scale_hierarchy_v1")
+
+
+def _hist_density(values: np.ndarray, grid: np.ndarray) -> np.ndarray:
+    edges = np.linspace(-1.02, 1.02, 409)
+    density, _ = np.histogram(values.ravel(), bins=edges, density=True)
+    centers = 0.5 * (edges[:-1] + edges[1:])
+    smoothed = gaussian_filter1d(density, 2.0)
+    curve = np.interp(grid, centers, smoothed)
+    return curve / np.trapezoid(curve, grid)
+
+
+def _figure_atom_crossover(
+    scaling_json: dict[str, Any],
+    scaling: Any,
+    output_dir: Path,
+) -> dict[str, Any]:
+    cases = scaling_json["cases"]
+    grid = np.linspace(-1.0, 1.0, 500)
+    fig, (ax, atom_ax) = plt.subplots(
+        1,
+        2,
+        figsize=(FIGURE_WIDTH, 4.7),
+        gridspec_kw={"width_ratios": [2.2, 1.0]},
+        layout="constrained",
+    )
+    colors = plt.cm.viridis(np.linspace(0.12, 0.9, len(cases)))
+    offset = 0.9
+    for index, (case, color) in enumerate(
+        zip(cases, colors, strict=True)
+    ):
+        n = case["n"]
+        physical = _hist_density(
+            scaling[f"n{n}_interior_spectra"],
+            grid,
+        )
+        reference = _hist_density(
+            scaling[f"n{n}_reference_interior_spectra"],
+            grid,
+        )
+        baseline = index * offset
+        ax.fill_between(
+            grid,
+            baseline,
+            baseline + 0.52 * physical / np.max(physical),
+            color=color,
+            alpha=0.60,
+            linewidth=0,
+        )
+        ax.plot(
+            grid,
+            baseline + 0.52 * physical / np.max(physical),
+            color=color,
+            linewidth=1.15,
+        )
+        ax.plot(
+            grid,
+            baseline + 0.52 * reference / np.max(reference),
+            color=COLORS["reference"],
+            linewidth=0.75,
+            linestyle=(0, (2, 2)),
+        )
+    ax.set_yticks(
+        np.arange(len(cases)) * offset + 0.16,
+        [
+            rf"$D={case['D']}$" + (
+                rf", $a={case['plus_atoms_per_matrix']}$"
+                if case["plus_atoms_per_matrix"]
+                else ""
+            )
+            for case in cases
+        ],
+    )
+    ax.set_xlabel(r"interior eigenvalue $\lambda$")
+    ax.set_ylabel("increasing root rank")
+    ax.set_xlim(-1.0, 1.0)
+    ax.set_ylim(-0.08, (len(cases) - 1) * offset + 0.72)
+    ax.plot([], [], color=COLORS["reference"], linestyle=(0, (2, 2)),
+            label="exact Jacobi")
+    ax.plot([], [], color=colors[-1], label="root response")
+    ax.legend(
+        frameon=False,
+        loc="center",
+        bbox_to_anchor=(0.53, 0.105),
+        ncol=2,
+    )
+    _panel(ax, "a", "Continuous spectrum across the capacity boundary")
+
+    D = np.asarray([case["D"] for case in cases], dtype=float)
+    M = np.asarray([case["M"] for case in cases], dtype=float)
+    atom_weight = np.asarray(
+        [
+            2.0 * case["plus_atoms_per_matrix"] / case["D"]
+            for case in cases
+        ]
+    )
+    atom_ax.plot(
+        D,
+        D / M,
+        color=COLORS["accent"],
+        marker="o",
+        label=r"capacity ratio $D/M$",
+    )
+    atom_ax.axhline(1.0, color="#777777", linestyle="--", linewidth=0.8)
+    atom_ax.set_xscale("log")
+    atom_ax.set_xlabel(r"active rank $D$")
+    atom_ax.set_ylabel(r"$D/M$")
+    atom_ax.set_ylim(0.0, 1.35)
+    twin = atom_ax.twinx()
+    twin.plot(
+        D,
+        atom_weight,
+        color=COLORS["atom"],
+        marker="s",
+        label="total atom weight",
+    )
+    twin.set_ylabel(r"$2(D-M)_+/D$", color=COLORS["atom"])
+    twin.tick_params(axis="y", colors=COLORS["atom"])
+    twin.set_ylim(0.0, 0.36)
+    handles, labels = atom_ax.get_legend_handles_labels()
+    handles2, labels2 = twin.get_legend_handles_labels()
+    atom_ax.legend(
+        handles + handles2,
+        labels + labels2,
+        frameon=False,
+        loc="upper left",
+    )
+    _panel(atom_ax, "b", "Exact atom onset at $D=M$")
+    return _save(fig, output_dir, "figure_3_atom_crossover_v1")
+
+
+def _fit_curve(model: dict[str, Any], grid: np.ndarray) -> np.ndarray:
+    return (
+        model["offset"]
+        + model["amplitude"] * grid ** (-model["exponent"])
+    )
+
+
+def _figure_finite_size(
+    statistical_json: dict[str, Any],
+    stat: Any,
+    output_dir: Path,
+) -> dict[str, Any]:
+    D = stat["scaling_D"]
+    grid = np.geomspace(float(np.min(D)), float(np.max(D)), 300)
+    fig, axes = plt.subplots(
+        1,
+        3,
+        figsize=(FIGURE_WIDTH, 2.75),
+        layout="constrained",
+    )
+    panels = (
+        (
+            axes[0],
+            "density_l1",
+            stat["scaling_density_l1"],
+            stat["scaling_density_se"],
+            r"interior density $L^1$",
+            "a",
+            "Global density",
+        ),
+        (
+            axes[1],
+            "gap_ratio_difference",
+            stat["scaling_gap_difference"],
+            stat["scaling_gap_se"],
+            r"$|\Delta\langle r\rangle|$",
+            "b",
+            "Local repulsion",
+        ),
+        (
+            axes[2],
+            "participation_deficit",
+            1.0 - stat["scaling_participation"],
+            stat["scaling_participation_se"],
+            r"$1-\mathcal{P}$",
+            "c",
+            "Channel participation",
+        ),
+    )
+    atom_mask = stat["scaling_atom_weight"] > 0
+    for ax, key, y, error, ylabel, label, title in panels:
+        fit = statistical_json["finite_size_fits"][key]
+        best = fit["best_by_loo"]
+        model = fit["models"][best]
+        ax.errorbar(
+            D[~atom_mask],
+            y[~atom_mask],
+            yerr=1.96 * error[~atom_mask],
+            fmt="o",
+            color=COLORS["physical"],
+            capsize=2,
+            label="atom free",
+        )
+        ax.errorbar(
+            D[atom_mask],
+            y[atom_mask],
+            yerr=1.96 * error[atom_mask],
+            fmt="s",
+            color=COLORS["atom"],
+            capsize=2,
+            label="atom sector present",
+        )
+        ax.plot(
+            grid,
+            _fit_curve(model, grid),
+            color=COLORS["haar"],
+            linestyle="--",
+            label=rf"best LOO: $p={model['exponent']:.2f}$",
+        )
+        ax.set_xscale("log")
+        ax.set_yscale("log")
+        ax.set_xlabel(r"active rank $D$")
+        ax.set_ylabel(ylabel)
+        ax.legend(frameon=False, loc="upper right")
+        _panel(ax, label, title)
+    return _save(fig, output_dir, "figure_4_finite_size_v1")
+
+
+def _figure_covariance_mechanism(
+    covariance_json: dict[str, Any],
+    covariance: Any,
+    statistical_json: dict[str, Any],
+    stat: Any,
+    output_dir: Path,
+) -> dict[str, Any]:
+    fig, axes = plt.subplots(
+        2,
+        2,
+        figsize=(FIGURE_WIDTH, 5.0),
+        layout="constrained",
+    )
+    eigenvalues = np.sort(covariance["covariance_eigenvalues"])[::-1]
+    eigenvalues = eigenvalues / np.mean(eigenvalues)
+    ax = axes[0, 0]
+    ax.plot(
+        np.arange(1, eigenvalues.size + 1),
+        eigenvalues,
+        color=COLORS["physical"],
+    )
+    ax.axhline(1.0, color=COLORS["haar"], linestyle="--", linewidth=0.8)
+    ax.set_yscale("log")
+    ax.set_xlabel("covariance eigenvalue index")
+    ax.set_ylabel(r"$c_\alpha/\overline{c}$")
+    _panel(ax, "a", "Learned channel covariance")
+
+    ax = axes[0, 1]
+    floors = np.asarray(covariance_json["candidate_floors"])
+    density = np.asarray(
+        [
+            covariance_json["validation_scores"][str(value)][
+                "density_l1"
+            ]
+            for value in floors
+        ]
+    )
+    gap = np.asarray(
+        [
+            covariance_json["validation_scores"][str(value)][
+                "gap_ratio_difference"
+            ]
+            for value in floors
+        ]
+    )
+    ax.plot(
+        floors,
+        density,
+        marker="o",
+        color=COLORS["deformed"],
+        label="density $L^1$",
+    )
+    ax.set_xscale("log")
+    ax.set_xlabel("eigenvalue floor")
+    ax.set_ylabel(r"validation density $L^1$")
+    twin = ax.twinx()
+    twin.plot(
+        floors,
+        gap,
+        marker="s",
+        color=COLORS["physical"],
+        label=r"$|\Delta\langle r\rangle|$",
+    )
+    twin.set_ylabel(r"validation $|\Delta\langle r\rangle|$")
+    selected = covariance_json["selected_floor"]
+    ax.axvline(selected, color="#777777", linestyle=":", linewidth=0.9)
+    ax.text(
+        selected,
+        np.max(density),
+        f" selected {selected:g}",
+        ha="left",
+        va="top",
+        fontsize=7.0,
+    )
+    handles, labels = ax.get_legend_handles_labels()
+    handles2, labels2 = twin.get_legend_handles_labels()
+    ax.legend(
+        handles + handles2,
+        labels + labels2,
+        frameon=False,
+        loc="lower left",
+    )
+    _panel(ax, "b", "Validation-only regularization")
+
+    ax = axes[1, 0]
+    orders = stat["moment_orders"]
+    physical = stat["physical_moments_mean"]
+    for name, marker in (("haar", "o"), ("deformed", "s")):
+        ratio = stat[f"{name}_moments_mean"] / physical
+        ratio_error = stat[f"{name}_moments_standard_error"] / physical
+        ax.errorbar(
+            orders,
+            ratio,
+            yerr=1.96 * ratio_error,
+            marker=marker,
+            color=COLORS[name],
+            capsize=2,
+            label=LABELS[name],
+        )
+    ax.axhline(1.0, color=COLORS["physical"], linewidth=1.0,
+               label="physical target")
+    ax.set_xticks(orders)
+    ax.set_xlabel("moment order")
+    ax.set_ylabel("model / physical")
+    ax.legend(frameon=False, loc="best")
+    _panel(ax, "c", "Global moments")
+
+    ax = axes[1, 1]
+    bandwidth = statistical_json["sensitivity"]["bandwidth"]
+    widths = np.asarray([float(value) for value in bandwidth])
+    haar_l1 = np.asarray(
+        [bandwidth[str(value)]["physical_haar_l1"] for value in widths]
+    )
+    deformed_l1 = np.asarray(
+        [
+            bandwidth[str(value)]["physical_deformed_l1"]
+            for value in widths
+        ]
+    )
+    ax.plot(
+        widths,
+        haar_l1,
+        marker="o",
+        color=COLORS["haar"],
+        label=LABELS["haar"],
+    )
+    ax.plot(
+        widths,
+        deformed_l1,
+        marker="s",
+        color=COLORS["deformed"],
+        label=LABELS["deformed"],
+    )
+    ax.set_xlabel("KDE bandwidth")
+    ax.set_ylabel(r"test density $L^1$")
+    ax.legend(frameon=False, loc="best")
+    _panel(ax, "d", "Bandwidth-stable improvement")
+    return _save(fig, output_dir, "figure_5_covariance_mechanism_v1")
+
+
+def _sha256(path: Path) -> str:
+    digest = hashlib.sha256()
+    with path.open("rb") as handle:
+        for chunk in iter(lambda: handle.read(1024 * 1024), b""):
+            digest.update(chunk)
+    return digest.hexdigest()
+
+
+def _write_generated_inputs(
+    output_dir: Path,
+    physical_json: dict[str, Any],
+    covariance_json: dict[str, Any],
+    scaling_json: dict[str, Any],
+    statistical_json: dict[str, Any],
+    stat: Any,
+) -> None:
+    held_out = covariance_json["held_out_test"]
+    largest = scaling_json["cases"][-1]
+    physical_case = physical_json["physical_case"]
+    density_fit = statistical_json["finite_size_fits"]["density_l1"][
+        "models"
+    ]["free"]
+    length_index = int(np.argmin(np.abs(stat["lengths"] - 8.0)))
+    time_index = int(
+        np.argmin(np.abs(stat["form_factor_times"] - 0.5))
+    )
+    lines = [
+        rf"\newcommand{{\PhysicalMatrices}}{{{physical_json['sample_count']}}}",
+        rf"\newcommand{{\PhysicalTestMatrices}}{{{statistical_json['physical_test_matrices']}}}",
+        rf"\newcommand{{\PhysicalRank}}{{{physical_case['D']}}}",
+        rf"\newcommand{{\PhysicalChannels}}{{{physical_case['M']}}}",
+        rf"\newcommand{{\TrainingRows}}{{{covariance_json['diagnostic_training_rows']}}}",
+        rf"\newcommand{{\HaarMatrices}}{{{statistical_json['haar_matrices']}}}",
+        rf"\newcommand{{\DeformedMatrices}}{{{statistical_json['deformed_matrices']}}}",
+        rf"\newcommand{{\SelectedCovFloor}}{{{covariance_json['selected_floor']:.3f}}}",
+        rf"\newcommand{{\DensityHaarLone}}{{{held_out['density_l1']['physical_vs_haar']:.4f}}}",
+        rf"\newcommand{{\DensityCovLone}}{{{held_out['density_l1']['physical_vs_deformed']:.4f}}}",
+        rf"\newcommand{{\DensityImprovementPercent}}{{{100.0 * held_out['density_l1']['relative_improvement']:.1f}\%}}",
+        rf"\newcommand{{\PhysicalGapRatio}}{{{held_out['mean_gap_ratio']['physical']:.6f}}}",
+        rf"\newcommand{{\HaarGapRatio}}{{{held_out['mean_gap_ratio']['haar']:.6f}}}",
+        rf"\newcommand{{\DeformedGapRatio}}{{{held_out['mean_gap_ratio']['deformed']:.6f}}}",
+        rf"\newcommand{{\LargestRank}}{{{largest['D']}}}",
+        rf"\newcommand{{\LargestChannels}}{{{largest['M']}}}",
+        rf"\newcommand{{\LargestAtomMultiplicity}}{{{largest['plus_atoms_per_matrix']}}}",
+        rf"\newcommand{{\LargestAtomWeightPercent}}{{{100.0 * 2 * largest['plus_atoms_per_matrix'] / largest['D']:.1f}\%}}",
+        rf"\newcommand{{\LargestInteriorDensityLone}}{{{largest['interior_density_l1']:.4f}}}",
+        rf"\newcommand{{\DensityFitExponent}}{{{density_fit['exponent']:.3f}}}",
+        rf"\newcommand{{\BootstrapReplicates}}{{{statistical_json['bootstrap_replicates']}}}",
+        rf"\newcommand{{\RootMatricesTotal}}{{{sum(case['samples'] for case in scaling_json['cases'])}}}",
+        rf"\newcommand{{\CovarianceAnisotropy}}{{{covariance_json['training_geometry']['relative_frobenius_anisotropy']:.3f}}}",
+        rf"\newcommand{{\PhysicalParticipation}}{{{covariance_json['training_geometry']['mean_participation_fraction']:.3f}}}",
+        rf"\newcommand{{\NumberVariancePhysEight}}{{{float(stat['physical_number_mean'][length_index]):.3f}}}",
+        rf"\newcommand{{\NumberVarianceHaarEight}}{{{float(stat['haar_number_mean'][length_index]):.3f}}}",
+        rf"\newcommand{{\NumberVarianceCovEight}}{{{float(stat['deformed_number_mean'][length_index]):.3f}}}",
+        rf"\newcommand{{\FormFactorPhysHalf}}{{{float(stat['physical_form_factor_mean'][time_index]):.3f}}}",
+        rf"\newcommand{{\FormFactorHaarHalf}}{{{float(stat['haar_form_factor_mean'][time_index]):.3f}}}",
+        rf"\newcommand{{\FormFactorCovHalf}}{{{float(stat['deformed_form_factor_mean'][time_index]):.3f}}}",
+    ]
+    (output_dir / "generated_numbers_v1.tex").write_text(
+        "\n".join(lines) + "\n",
+        encoding="utf-8",
+    )
+    table = [
+        r"\begin{tabular}{rrrrrr}",
+        r"\hline\hline",
+        r"$D$ & $M$ & samples & atoms/edge & $\Delta\langle r\rangle$ & $L^1_{\rm int}$ \\",
+        r"\hline",
+    ]
+    for case in scaling_json["cases"]:
+        table.append(
+            f"{case['D']} & {case['M']} & {case['samples']} & "
+            f"{case['plus_atoms_per_matrix']} & "
+            f"{case['gap_ratio_difference']:.5f} & "
+            f"{case['interior_density_l1']:.5f} \\\\"
+        )
+    table.extend([r"\hline\hline", r"\end{tabular}"])
+    (output_dir / "generated_tables_v1.tex").write_text(
+        "\n".join(table) + "\n",
+        encoding="utf-8",
+    )
+
+
+def run(
+    output_dir: Path,
+    physical_json_path: Path = Path("output/physical_ensemble_v1.json"),
+    covariance_json_path: Path = Path("output/covariance_model_v1.json"),
+    covariance_npz_path: Path = Path("output/covariance_model_v1.npz"),
+    scaling_json_path: Path = Path("output/rank_scaling_v1.json"),
+    scaling_npz_path: Path = Path("output/rank_scaling_v1.npz"),
+    statistical_json_path: Path = Path(
+        "output/statistical_analysis_v1.json"
+    ),
+    statistical_npz_path: Path = Path(
+        "output/statistical_analysis_v1.npz"
+    ),
+) -> dict[str, Any]:
+    """Generate figures, macros, tables, and a hash manifest."""
+
+    _style()
+    output_dir.mkdir(parents=True, exist_ok=True)
+    physical_json = json.loads(
+        physical_json_path.read_text(encoding="utf-8")
+    )
+    covariance_json = json.loads(
+        covariance_json_path.read_text(encoding="utf-8")
+    )
+    scaling_json = json.loads(
+        scaling_json_path.read_text(encoding="utf-8")
+    )
+    statistical_json = json.loads(
+        statistical_json_path.read_text(encoding="utf-8")
+    )
+    with (
+        np.load(covariance_npz_path) as covariance,
+        np.load(scaling_npz_path) as scaling,
+        np.load(statistical_npz_path) as stat,
+    ):
+        figures = {
+            "figure_1": _figure_physical_law(
+                stat,
+                covariance_json,
+                output_dir,
+            ),
+            "figure_2": _figure_scale_hierarchy(stat, output_dir),
+            "figure_3": _figure_atom_crossover(
+                scaling_json,
+                scaling,
+                output_dir,
+            ),
+            "figure_4": _figure_finite_size(
+                statistical_json,
+                stat,
+                output_dir,
+            ),
+            "figure_5": _figure_covariance_mechanism(
+                covariance_json,
+                covariance,
+                statistical_json,
+                stat,
+                output_dir,
+            ),
+        }
+        _write_generated_inputs(
+            output_dir,
+            physical_json,
+            covariance_json,
+            scaling_json,
+            statistical_json,
+            stat,
+        )
+    inputs = (
+        physical_json_path,
+        covariance_json_path,
+        covariance_npz_path,
+        scaling_json_path,
+        scaling_npz_path,
+        statistical_json_path,
+        statistical_npz_path,
+    )
+    manifest = {
+        "schema_version": 1,
+        "version": VERSION,
+        "figure_width_inches": FIGURE_WIDTH,
+        "png_dpi": DPI,
+        "inputs": {
+            str(path): _sha256(path) for path in inputs
+        },
+        "figures": figures,
+        "atom_annotations": {
+            "D546_each_boundary": 6,
+            "D800_each_boundary": 120,
+            "D800_total_weight": 0.30,
+        },
+    }
+    for figure in figures.values():
+        figure["pdf_sha256"] = _sha256(Path(figure["pdf"]))
+        figure["png_sha256"] = _sha256(Path(figure["png"]))
+    manifest_path = output_dir / "figure_manifest_v1.json"
+    manifest_path.write_text(
+        json.dumps(manifest, indent=2) + "\n",
+        encoding="utf-8",
+    )
+    return manifest
+
+
+def main() -> None:
+    parser = argparse.ArgumentParser()
+    parser.add_argument(
+        "--output-dir",
+        type=Path,
+        default=Path("output"),
+    )
+    args = parser.parse_args()
+    manifest = run(args.output_dir)
+    print(json.dumps(manifest, indent=2))
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/make_matrix_element_geometric_eth_figure_v3.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/make_matrix_element_geometric_eth_figure_v3.py
new file mode 100644
index 000000000..0db8996c8
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/make_matrix_element_geometric_eth_figure_v3.py
@@ -0,0 +1,334 @@
+#!/usr/bin/env python3
+"""Generate the publication figure for four-channel Wick factorization."""
+
+from __future__ import annotations
+
+import hashlib
+import json
+from pathlib import Path
+from typing import Any
+
+import matplotlib
+
+matplotlib.use("Agg")
+import matplotlib.pyplot as plt
+import numpy as np
+
+
+SCRIPT_ROOT = Path(__file__).resolve().parent
+OUTPUT = SCRIPT_ROOT / "output"
+SOURCE = OUTPUT / "matrix_element_geometric_eth_v3.json"
+FIGURE_PDF = OUTPUT / "figure_6_wick_factorization_v3.pdf"
+FIGURE_PNG = OUTPUT / "figure_6_wick_factorization_v3.png"
+MANIFEST = OUTPUT / "figure_manifest_v3.json"
+
+
+def _sha256(path: Path) -> str:
+    return hashlib.sha256(path.read_bytes()).hexdigest()
+
+
+def _atomic_json(path: Path, payload: dict[str, Any]) -> None:
+    temporary = path.with_suffix(path.suffix + ".tmp")
+    temporary.write_text(
+        json.dumps(payload, indent=2, sort_keys=True),
+        encoding="utf-8",
+    )
+    temporary.replace(path)
+
+
+def _style() -> None:
+    plt.rcParams.update(
+        {
+            "font.family": "serif",
+            "font.serif": ["STIXGeneral", "DejaVu Serif"],
+            "mathtext.fontset": "stix",
+            "font.size": 8.4,
+            "axes.titlesize": 9.2,
+            "axes.labelsize": 8.6,
+            "xtick.labelsize": 7.7,
+            "ytick.labelsize": 7.7,
+            "legend.fontsize": 7.1,
+            "axes.linewidth": 0.75,
+            "xtick.major.width": 0.65,
+            "ytick.major.width": 0.65,
+            "pdf.fonttype": 42,
+            "ps.fonttype": 42,
+        }
+    )
+
+
+def _panel_label(axis, label: str) -> None:
+    axis.text(
+        -0.15,
+        1.08,
+        label,
+        transform=axis.transAxes,
+        fontsize=9.2,
+        fontweight="bold",
+        va="top",
+    )
+
+
+def make_figure() -> dict[str, Any]:
+    payload = json.loads(SOURCE.read_text(encoding="utf-8"))
+    cases = payload["cases"]
+    if len(cases) != 3:
+        raise RuntimeError("Figure 6 requires the full three-case artifact")
+    _style()
+    navy = "#24476b"
+    orange = "#d8752d"
+    teal = "#228b8d"
+    grey = "#6d747d"
+    pale = "#dfe8ef"
+    N = np.asarray([case["N"] for case in cases], dtype=float)
+    ranks = np.asarray([case["rank"] for case in cases], dtype=float)
+    dimensions = np.asarray(
+        [case["basis_dimension"] for case in cases],
+        dtype=float,
+    )
+    gaps = np.asarray([case["external_gap"] for case in cases])
+    physical = np.asarray(
+        [case["physical_R4_median"] for case in cases]
+    )
+    physical_interval = np.asarray(
+        [case["physical_R4_interval"] for case in cases]
+    )
+    structured = np.asarray([case["structured_R4"] for case in cases])
+    gaussian = np.asarray(
+        [case["gaussian_R4_interval"] for case in cases]
+    )
+    A_left = np.asarray([case["A_left_median"] for case in cases])
+    B_right = np.asarray([case["B_right_median"] for case in cases])
+    effective_external = ranks / B_right
+
+    figure, axes = plt.subplots(
+        2,
+        2,
+        figsize=(7.0, 5.15),
+        constrained_layout=True,
+    )
+
+    axis = axes[0, 0]
+    _panel_label(axis, "(a)")
+    axis.plot(N, gaps, "o-", color=navy, lw=1.5, ms=4.3)
+    axis.set_xlabel("particle number $N$")
+    axis.set_ylabel("external gap $\\Delta$", color=navy)
+    axis.tick_params(axis="y", colors=navy)
+    axis.set_xticks(N)
+    axis.set_title("Exact fixed-two-quasihole manifolds", pad=5)
+    twin = axis.twinx()
+    twin.semilogy(
+        N,
+        dimensions,
+        "s--",
+        color=grey,
+        lw=1.2,
+        ms=4.0,
+    )
+    twin.set_ylabel("$\\dim\\mathcal{H}$", color=grey)
+    twin.tick_params(axis="y", colors=grey)
+    annotation_offsets = ((0, 9), (0, -17), (0, 9))
+    for x, gap, rank, offset in zip(
+        N,
+        gaps,
+        ranks,
+        annotation_offsets,
+        strict=True,
+    ):
+        axis.annotate(
+            f"$D={int(rank)}$",
+            (x, gap),
+            xytext=offset,
+            textcoords="offset points",
+            ha="center",
+            color=navy,
+            fontsize=7.1,
+        )
+    axis.grid(alpha=0.18, lw=0.55)
+
+    axis = axes[0, 1]
+    _panel_label(axis, "(b)")
+    axis.fill_between(
+        N,
+        gaussian[:, 0],
+        gaussian[:, 2],
+        color=pale,
+        label="covariance-matched Gaussian 95%",
+        zorder=1,
+    )
+    axis.plot(
+        N,
+        gaussian[:, 1],
+        "-",
+        color=grey,
+        lw=1.2,
+        label="Gaussian median",
+        zorder=2,
+    )
+    axis.errorbar(
+        N,
+        physical,
+        yerr=np.vstack(
+            [
+                physical - physical_interval[:, 0],
+                physical_interval[:, 1] - physical,
+            ]
+        ),
+        fmt="o-",
+        color=orange,
+        lw=1.6,
+        ms=4.5,
+        capsize=2.5,
+        label="local-density panels",
+        zorder=4,
+    )
+    axis.plot(
+        N,
+        structured,
+        "D--",
+        color=teal,
+        lw=1.25,
+        ms=3.8,
+        label="Fourier panel",
+        zorder=3,
+    )
+    axis.set_xlabel("particle number $N$")
+    axis.set_ylabel("four-channel residual $R_4$")
+    axis.set_xticks(N)
+    axis.set_title("Finite-size Wick test", pad=5)
+    axis.legend(frameon=False, loc="upper right")
+    axis.grid(alpha=0.18, lw=0.55)
+
+    axis = axes[1, 0]
+    _panel_label(axis, "(c)")
+    physical_excess = physical - gaussian[:, 1]
+    structured_excess = structured - gaussian[:, 1]
+    axis.axhline(0.0, color="black", lw=0.7, alpha=0.55)
+    axis.plot(
+        N,
+        physical_excess,
+        "o-",
+        color=orange,
+        lw=1.6,
+        ms=4.5,
+        label="local-density excess",
+    )
+    axis.plot(
+        N,
+        structured_excess,
+        "D--",
+        color=teal,
+        lw=1.25,
+        ms=3.8,
+        label="Fourier excess",
+    )
+    axis.set_xlabel("particle number $N$")
+    axis.set_ylabel("$R_4-\\mathrm{median}(R_4^{\\rm G})$")
+    axis.set_xticks(N)
+    axis.set_title("Connected channel memory", pad=5)
+    axis.legend(frameon=False)
+    axis.grid(alpha=0.18, lw=0.55)
+    axis.text(
+        0.04,
+        0.08,
+        "resolved connected component at $N=5$",
+        transform=axis.transAxes,
+        color=orange,
+        fontsize=7.3,
+    )
+
+    axis = axes[1, 1]
+    _panel_label(axis, "(d)")
+    axis.plot(
+        N,
+        A_left - 1.0,
+        "o-",
+        color=navy,
+        lw=1.5,
+        ms=4.2,
+    )
+    axis.set_xlabel("particle number $N$")
+    axis.set_ylabel("target anisotropy $A_L-1$", color=navy)
+    axis.tick_params(axis="y", colors=navy)
+    axis.set_xticks(N)
+    twin = axis.twinx()
+    twin.plot(
+        N,
+        effective_external,
+        "s--",
+        color=grey,
+        lw=1.25,
+        ms=4.0,
+    )
+    twin.set_ylabel(
+        "effective external dimension $M_{\\rm eff}=D/B_R$",
+        color=grey,
+    )
+    twin.tick_params(axis="y", colors=grey)
+    axis.set_title("Covariance envelope", pad=5)
+    axis.grid(alpha=0.18, lw=0.55)
+    axis.text(
+        0.04,
+        0.86,
+        "registered branch:\n$\\bf{deformed\\ geometric\\ ETH}$",
+        transform=axis.transAxes,
+        color=orange,
+        fontsize=7.5,
+        va="top",
+        bbox={
+            "facecolor": "white",
+            "edgecolor": "none",
+            "alpha": 0.88,
+            "pad": 1.5,
+        },
+    )
+    axis.text(
+        0.04,
+        0.10,
+        "$N=3,4,5$ finite-size baseline",
+        transform=axis.transAxes,
+        color="#444444",
+        fontsize=6.9,
+        bbox={
+            "facecolor": "white",
+            "edgecolor": "none",
+            "alpha": 0.82,
+            "pad": 1.2,
+        },
+    )
+
+    figure.savefig(FIGURE_PDF)
+    figure.savefig(FIGURE_PNG, dpi=300)
+    plt.close(figure)
+    manifest = (
+        json.loads(MANIFEST.read_text(encoding="utf-8"))
+        if MANIFEST.exists()
+        else {}
+    )
+    manifest["figure_6_wick_factorization_v3"] = {
+        "source": str(SOURCE.relative_to(SCRIPT_ROOT)),
+        "source_sha256": _sha256(SOURCE),
+        "pdf": str(FIGURE_PDF.relative_to(SCRIPT_ROOT)),
+        "pdf_sha256": _sha256(FIGURE_PDF),
+        "png": str(FIGURE_PNG.relative_to(SCRIPT_ROOT)),
+        "png_sha256": _sha256(FIGURE_PNG),
+        "width_inches": 7.0,
+        "png_width_pixels": 2100,
+        "result_branch": payload["result_branch"],
+        "panels": [
+            "genuine_manybody_sequence",
+            "four_channel_residual",
+            "non_gaussian_excess",
+            "covariance_geometry",
+        ],
+    }
+    _atomic_json(MANIFEST, manifest)
+    return manifest["figure_6_wick_factorization_v3"]
+
+
+def main() -> None:
+    print(json.dumps(make_figure(), indent=2, sort_keys=True))
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/make_release_manifest_v1.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/make_release_manifest_v1.py
new file mode 100644
index 000000000..25d813dd3
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/make_release_manifest_v1.py
@@ -0,0 +1,232 @@
+#!/usr/bin/env python3
+"""Build the machine-readable public release contract for task 05."""
+
+from __future__ import annotations
+
+import argparse
+import hashlib
+import json
+import subprocess
+from datetime import datetime, timezone
+from pathlib import Path
+from typing import Any
+
+
+SCRIPT_ROOT = Path(__file__).resolve().parent
+DEFAULT_REPO_ROOT = SCRIPT_ROOT.parents[2]
+DEFAULT_OUTPUT = SCRIPT_ROOT / "output"
+DEFAULT_MANIFEST = DEFAULT_OUTPUT / "release_manifest_v1.json"
+
+FIGURES = tuple(
+    f"figure_{index}_{name}"
+    for index, name in (
+        (1, "spectral_silence_v2.png"),
+        (2, "falsification_triangle_v2.png"),
+        (3, "independent_channels_v2.png"),
+        (4, "geometric_hierarchy_v2.png"),
+        (5, "jacobi_atoms_v2.png"),
+        (6, "wick_factorization_v3.png"),
+        (7, "topological_holonomy_v3.png"),
+    )
+)
+
+COMPACT_ARTIFACTS = (
+    "citation_audit_v1.json",
+    "geometric_eth_topology_assets_v3.json",
+    "geometric_eth_topology_delivery_audit_v3.json",
+    "matrix_element_delivery_audit_v3.json",
+    "matrix_element_geometric_eth_v3.json",
+    "matrix_element_geometric_eth_v3.npz",
+    "matrix_element_topology_theory_v3.json",
+    "spectral_silence_delivery_audit_v2.json",
+    "spectral_silence_statistics_v2.json",
+    "spectral_silence_statistics_v2.npz",
+    "spectral_silence_v2.json",
+    "topological_holonomy_delivery_audit_v3.json",
+    "topological_holonomy_v3.json",
+    "topological_holonomy_v3.npz",
+)
+
+
+def _sha256(path: Path) -> str:
+    digest = hashlib.sha256()
+    with path.open("rb") as handle:
+        for block in iter(lambda: handle.read(1024 * 1024), b""):
+            digest.update(block)
+    return digest.hexdigest()
+
+
+def _record(path: Path, repo_root: Path) -> dict[str, Any]:
+    return {
+        "path": path.relative_to(repo_root).as_posix(),
+        "size_bytes": path.stat().st_size,
+        "sha256": _sha256(path),
+    }
+
+
+def _producer_for(relative: str) -> str:
+    if relative.startswith(("physical_ensemble", "covariance_model")):
+        return "bash run_large_scale_article_v1.sh"
+    if relative.startswith(("rank_scaling", "statistical_analysis")):
+        return "bash run_large_scale_article_v1.sh"
+    if relative.startswith("spectral_silence"):
+        return "bash run_spectral_silence_article_v2.sh"
+    if "matrix_element" in relative:
+        return "FULL_RECOMPUTE=1 bash run_geometric_eth_topology_article_v3.sh"
+    if "topology" in relative or "topological_holonomy" in relative:
+        return "FULL_RECOMPUTE=1 bash run_geometric_eth_topology_article_v3.sh"
+    return "Run the registered task-05 production pipeline"
+
+
+def _tracked_relative_paths(repo_root: Path) -> set[str]:
+    result = subprocess.run(
+        ["git", "ls-files", "-z"],
+        cwd=repo_root,
+        check=True,
+        capture_output=True,
+    )
+    return {
+        item.decode("utf-8")
+        for item in result.stdout.split(b"\0")
+        if item
+    }
+
+
+def build_manifest(
+    *,
+    repo_root: Path,
+    bulk_output: Path,
+    generated_utc: str | None = None,
+) -> dict[str, Any]:
+    """Build a release manifest from current compact and optional bulk data."""
+    repo_root = repo_root.resolve()
+    compact_output = (
+        repo_root / "01_task_folder" / "task_05" / "script" / "output"
+    )
+    matrix = json.loads(
+        (compact_output / "matrix_element_geometric_eth_v3.json").read_text(
+            encoding="utf-8"
+        )
+    )
+    topology = json.loads(
+        (compact_output / "topological_holonomy_v3.json").read_text(
+            encoding="utf-8"
+        )
+    )
+    audit = json.loads(
+        (
+            compact_output / "geometric_eth_topology_delivery_audit_v3.json"
+        ).read_text(encoding="utf-8")
+    )
+    paper = compact_output / "spectral_silence_and_geometric_chaos_v3.pdf"
+
+    figures = []
+    for name in FIGURES:
+        record = _record(compact_output / name, repo_root)
+        record["role"] = (
+            "principal_result"
+            if name.startswith("figure_1_")
+            else "main_figure"
+        )
+        figures.append(record)
+
+    compact = [
+        {**_record(compact_output / name, repo_root), "storage_class": "git"}
+        for name in COMPACT_ARTIFACTS
+    ]
+
+    external = []
+    tracked = _tracked_relative_paths(repo_root)
+    bulk_output = bulk_output.resolve()
+    if bulk_output.is_dir():
+        for source in sorted(bulk_output.rglob("*.npz")):
+            relative = source.relative_to(bulk_output)
+            compact_path = compact_output / relative
+            compact_relative = compact_path.relative_to(repo_root).as_posix()
+            if (
+                compact_relative in tracked
+                and compact_path.is_file()
+                and _sha256(compact_path) == _sha256(source)
+            ):
+                continue
+            external.append(
+                {
+                    "path": (
+                        "01_task_folder/task_05/script/output/"
+                        + relative.as_posix()
+                    ),
+                    "size_bytes": source.stat().st_size,
+                    "sha256": _sha256(source),
+                    "storage_class": "recompute_or_release_asset",
+                    "producer": _producer_for(relative.as_posix()),
+                }
+            )
+
+    existing_manifest = compact_output / "release_manifest_v1.json"
+    existing: dict[str, Any] = {}
+    if existing_manifest.is_file():
+        existing = json.loads(existing_manifest.read_text(encoding="utf-8"))
+    if not external:
+        external = existing.get("external_artifacts", [])
+
+    timestamp = (
+        generated_utc
+        or existing.get("generated_utc")
+        or datetime.now(timezone.utc).isoformat()
+    )
+    return {
+        "schema_version": 1,
+        "release_id": "task05-geometric-chaos-v1",
+        "generated_utc": timestamp,
+        "headline": "Exact degeneracy turns quantum geometry into the signal.",
+        "result_branches": {
+            "matrix_element": matrix["result_branch"],
+            "topology": topology["result_branch"],
+        },
+        "paper": {
+            **_record(paper, repo_root),
+            "page_count": audit["page_count"],
+            "title": (
+                "Spectral Silence and Geometric Chaos in an Exactly "
+                "Degenerate Topological Manifold"
+            ),
+        },
+        "figures": figures,
+        "compact_artifacts": compact,
+        "external_artifacts": external,
+        "verification": {
+            "quick": "bash run_quick_verify_v1.sh",
+            "article": "bash run_geometric_eth_topology_article_v3.sh",
+            "full": "bash run_full_recompute_v1.sh",
+        },
+        "scientific_scope": [
+            "exact-degeneracy projector geometry",
+            "finite-rank local Jacobi universality",
+            "structured matrix-element and Wilson correlations",
+        ],
+    }
+
+
+def main() -> None:
+    parser = argparse.ArgumentParser()
+    parser.add_argument("--repo-root", type=Path, default=DEFAULT_REPO_ROOT)
+    parser.add_argument("--bulk-output", type=Path, default=DEFAULT_OUTPUT)
+    parser.add_argument("--output", type=Path, default=DEFAULT_MANIFEST)
+    parser.add_argument("--generated-utc")
+    args = parser.parse_args()
+
+    manifest = build_manifest(
+        repo_root=args.repo_root,
+        bulk_output=args.bulk_output,
+        generated_utc=args.generated_utc,
+    )
+    args.output.parent.mkdir(parents=True, exist_ok=True)
+    args.output.write_text(
+        json.dumps(manifest, indent=2, sort_keys=True) + "\n",
+        encoding="utf-8",
+    )
+    print(args.output)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/make_spectral_silence_figures_v2.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/make_spectral_silence_figures_v2.py
new file mode 100644
index 000000000..842e34339
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/make_spectral_silence_figures_v2.py
@@ -0,0 +1,1088 @@
+#!/usr/bin/env python3
+"""Create the argument-ordered v2 publication figures and TeX inputs."""
+
+from __future__ import annotations
+
+import argparse
+import hashlib
+import json
+import shutil
+from pathlib import Path
+from typing import Any
+
+import matplotlib
+
+matplotlib.use("Agg")
+import matplotlib.pyplot as plt
+from matplotlib.colors import TwoSlopeNorm
+import numpy as np
+
+
+VERSION = "v2"
+FIGURE_WIDTH = 7.0
+DPI = 300
+COLORS = {
+    "structured": "#CC79A7",
+    "physical": "#0072B2",
+    "haar": "#222222",
+    "jacobi": "#009E73",
+    "spectral": "#E69F00",
+    "residual": "#D55E00",
+    "gray": "#777777",
+    "light": "#D9D9D9",
+}
+
+
+def _style() -> None:
+    plt.rcParams.update(
+        {
+            "font.family": "serif",
+            "font.serif": [
+                "STIX Two Text",
+                "STIXGeneral",
+                "DejaVu Serif",
+            ],
+            "mathtext.fontset": "stix",
+            "font.size": 8.2,
+            "axes.labelsize": 8.5,
+            "axes.titlesize": 9.0,
+            "legend.fontsize": 7.0,
+            "xtick.labelsize": 7.3,
+            "ytick.labelsize": 7.3,
+            "axes.linewidth": 0.75,
+            "lines.linewidth": 1.35,
+            "savefig.facecolor": "white",
+            "figure.facecolor": "white",
+            "axes.facecolor": "white",
+            "axes.spines.top": False,
+            "axes.spines.right": False,
+        }
+    )
+
+
+def _panel(ax, label: str, title: str) -> None:
+    ax.text(
+        -0.12,
+        1.04,
+        f"({label})",
+        transform=ax.transAxes,
+        fontweight="bold",
+        va="bottom",
+    )
+    ax.set_title(title, loc="left", pad=5.0)
+
+
+def _band(
+    ax,
+    x: np.ndarray,
+    arrays: Any,
+    prefix: str,
+    color: str,
+    label: str,
+    alpha: float = 0.16,
+    linestyle: str = "-",
+) -> None:
+    ax.fill_between(
+        x,
+        arrays[f"{prefix}_lower"],
+        arrays[f"{prefix}_upper"],
+        color=color,
+        alpha=alpha,
+        linewidth=0,
+    )
+    ax.plot(
+        x,
+        arrays[f"{prefix}_mean"],
+        color=color,
+        label=label,
+        linestyle=linestyle,
+    )
+
+
+def _sha256(path: Path) -> str:
+    digest = hashlib.sha256()
+    with path.open("rb") as handle:
+        for block in iter(lambda: handle.read(1024 * 1024), b""):
+            digest.update(block)
+    return digest.hexdigest()
+
+
+def _save(
+    fig,
+    output_dir: Path,
+    stem: str,
+) -> dict[str, Any]:
+    pdf = (output_dir / f"{stem}.pdf").resolve()
+    png = (output_dir / f"{stem}.png").resolve()
+    fig.savefig(pdf, format="pdf")
+    fig.savefig(png, format="png", dpi=DPI)
+    plt.close(fig)
+    return {
+        "pdf": str(pdf),
+        "png": str(png),
+        "pdf_sha256": _sha256(pdf),
+        "png_sha256": _sha256(png),
+        "width_inches": FIGURE_WIDTH,
+        "png_width_pixels": int(round(FIGURE_WIDTH * DPI)),
+        "dpi": DPI,
+    }
+
+
+def _combined_legend(ax, twin=None, **kwargs) -> None:
+    handles, labels = ax.get_legend_handles_labels()
+    if twin is not None:
+        twin_handles, twin_labels = twin.get_legend_handles_labels()
+        handles += twin_handles
+        labels += twin_labels
+    ax.legend(handles, labels, frameon=False, **kwargs)
+
+
+def _figure_spectral_silence(
+    source: Any,
+    stat: Any,
+    output_dir: Path,
+) -> dict[str, Any]:
+    times = stat["times"]
+    fig, axes = plt.subplots(
+        2,
+        2,
+        figsize=(FIGURE_WIDTH, 5.15),
+        layout="constrained",
+    )
+    ax = axes[0, 0]
+    ax.plot(
+        times,
+        source["energy_raw"],
+        color=COLORS["haar"],
+        label=r"raw energy SFF $K_{E,\rm raw}=D$",
+    )
+    ax.plot(
+        times,
+        source["energy_connected"],
+        color=COLORS["residual"],
+        label=r"connected energy SFF $K_{E,c}=0$",
+    )
+    ax.scatter(
+        np.linspace(0.25, 2.75, 22),
+        np.full(22, 43.0),
+        marker="_",
+        color=COLORS["gray"],
+        s=18,
+        linewidths=0.75,
+        label=r"$E_a=E_0$ (exactly degenerate)",
+    )
+    ax.set_xlim(0.0, 3.0)
+    ax.set_ylim(-2.0, 54.0)
+    ax.set_xlabel(r"Fourier variable $t$")
+    ax.set_ylabel(r"$K_E(t)$")
+    ax.legend(frameon=False, loc="center right")
+    _panel(ax, "a", "Exact degeneracy: spectral silence")
+
+    ax = axes[0, 1]
+    rows = (
+        (
+            source["structured_spectra"][0],
+            2.0,
+            COLORS["structured"],
+            "structured Fourier",
+        ),
+        (
+            source["physical_test_spectra"][0],
+            1.0,
+            COLORS["physical"],
+            "physical random local",
+        ),
+        (
+            source["haar_spectra"][0],
+            0.0,
+            COLORS["haar"],
+            "Haar--Jacobi",
+        ),
+    )
+    for spectrum, baseline, color, label in rows:
+        ax.eventplot(
+            np.asarray(spectrum, dtype=float),
+            lineoffsets=baseline,
+            linelengths=0.62,
+            linewidths=0.72,
+            colors=color,
+            label=label,
+        )
+    ax.set_yticks([0, 1, 2], ["Jacobi", "physical", "structured"])
+    ax.set_xlim(-1.02, 1.02)
+    ax.set_ylim(-0.55, 2.55)
+    ax.set_xlabel(r"metric-normalized curvature eigenvalue $\lambda$")
+    _panel(ax, "b", "Same rank, different geometry")
+
+    ax = axes[1, 0]
+    _band(
+        ax,
+        times,
+        stat,
+        "physical_form",
+        COLORS["physical"],
+        "physical",
+    )
+    ax.plot(
+        times,
+        stat["jacobi_connected_D50"],
+        color=COLORS["jacobi"],
+        linestyle="--",
+        label="finite-$D$ Jacobi",
+    )
+    ax.set_xlim(0.0, 1.5)
+    ax.set_ylim(-0.04, 1.12)
+    ax.set_xlabel(r"dimensionless Fourier scale $\tau$")
+    ax.set_ylabel(r"$K_{F,c}(\tau)$")
+    twin = ax.twinx()
+    twin.plot(
+        times,
+        stat["structured_form_mean"],
+        color=COLORS["structured"],
+        alpha=0.82,
+        label="structured (right axis)",
+    )
+    twin.fill_between(
+        times,
+        stat["structured_form_lower"],
+        stat["structured_form_upper"],
+        color=COLORS["structured"],
+        alpha=0.10,
+        linewidth=0,
+    )
+    twin.set_ylim(-0.2, 6.2)
+    twin.set_ylabel(
+        r"structured $K_{F,c}$",
+        color=COLORS["structured"],
+    )
+    twin.tick_params(axis="y", colors=COLORS["structured"])
+    _combined_legend(ax, twin, loc="lower right")
+    _panel(ax, "c", "Geometry restores a correlation ramp")
+
+    ax = axes[1, 1]
+    _band(
+        ax,
+        times,
+        stat,
+        "physical_form_residual",
+        COLORS["residual"],
+        r"physical $-$ finite-$D$ Jacobi",
+        alpha=0.18,
+    )
+    ax.axhline(0.0, color=COLORS["gray"], linewidth=0.75)
+    ax.axvspan(0.25, 1.5, color=COLORS["jacobi"], alpha=0.06)
+    ax.set_xlim(0.0, 1.55)
+    ax.set_xlabel(r"$\tau$")
+    ax.set_ylabel(r"$\delta K_{F,c}$")
+    ax.legend(frameon=False, loc="upper right")
+    inset = ax.inset_axes([0.50, 0.12, 0.47, 0.42])
+    inset.fill_between(
+        stat["lengths"],
+        stat["physical_haar_number_residual_lower"],
+        stat["physical_haar_number_residual_upper"],
+        color=COLORS["physical"],
+        alpha=0.18,
+        linewidth=0,
+    )
+    inset.plot(
+        stat["lengths"],
+        stat["physical_haar_number_residual_mean"],
+        color=COLORS["physical"],
+        linewidth=1.0,
+    )
+    inset.axhline(0.0, color=COLORS["gray"], linewidth=0.6)
+    inset.axvline(1.0, color=COLORS["residual"], linestyle=":", linewidth=0.8)
+    inset.set_xlabel(r"$L$", fontsize=6.8)
+    inset.set_ylabel(r"$\Delta\Sigma^2$", fontsize=6.8)
+    inset.tick_params(labelsize=6.2)
+    _panel(ax, "d", "Ramp universal, long range nonuniversal")
+    return _save(
+        fig,
+        output_dir,
+        "figure_1_spectral_silence_v2",
+    )
+
+
+def _figure_falsification_triangle(
+    stat: Any,
+    output_dir: Path,
+) -> dict[str, Any]:
+    fig, axes = plt.subplots(
+        1,
+        3,
+        figsize=(FIGURE_WIDTH, 2.75),
+        layout="constrained",
+    )
+    ax = axes[0]
+    for prefix, color, label in (
+        ("structured", COLORS["structured"], "structured"),
+        ("physical", COLORS["physical"], "physical"),
+        ("haar", COLORS["haar"], "Haar--Jacobi"),
+    ):
+        _band(
+            ax,
+            stat["ratio_centers"],
+            stat,
+            f"{prefix}_ratio",
+            color,
+            label,
+            alpha=0.13,
+        )
+    ax.set_yscale("log")
+    ax.set_ylim(2e-2, 80)
+    ax.set_xlabel(r"adjacent-gap ratio $r$")
+    ax.set_ylabel(r"$P(r)$")
+    ax.legend(frameon=False, loc="upper right")
+    _panel(ax, "a", "Local repulsion")
+
+    ax = axes[1]
+    for prefix, color, label in (
+        ("physical", COLORS["physical"], "physical"),
+        ("haar", COLORS["haar"], "Haar--Jacobi"),
+    ):
+        _band(
+            ax,
+            stat["times"],
+            stat,
+            f"{prefix}_form",
+            color,
+            label,
+            alpha=0.13,
+        )
+    ax.plot(
+        stat["times"],
+        stat["jacobi_connected_D50"],
+        color=COLORS["jacobi"],
+        linestyle="--",
+        label="exact finite-$D$",
+    )
+    twin = ax.twinx()
+    twin.plot(
+        stat["times"],
+        stat["structured_form_mean"],
+        color=COLORS["structured"],
+        label="structured (right)",
+    )
+    twin.set_ylim(-0.2, 6.2)
+    twin.tick_params(axis="y", colors=COLORS["structured"])
+    ax.set_xlim(0.0, 1.5)
+    ax.set_ylim(-0.04, 1.12)
+    ax.set_xlabel(r"$\tau$")
+    ax.set_ylabel(r"$K_{F,c}(\tau)$")
+    _combined_legend(ax, twin, loc="lower right")
+    _panel(ax, "b", "Connected curvature SFF")
+
+    ax = axes[2]
+    for prefix, color, label in (
+        ("structured", COLORS["structured"], "structured"),
+        ("physical", COLORS["physical"], "physical"),
+        ("haar", COLORS["haar"], "Haar--Jacobi"),
+    ):
+        _band(
+            ax,
+            stat["lengths"],
+            stat,
+            f"{prefix}_number",
+            color,
+            label,
+            alpha=0.13,
+        )
+    ax.set_yscale("log")
+    ax.set_xlabel(r"window length $L$")
+    ax.set_ylabel(r"$\Sigma^2(L)$")
+    ax.legend(frameon=False, loc="lower right")
+    _panel(ax, "c", "Long-range memory")
+    return _save(
+        fig,
+        output_dir,
+        "figure_2_falsification_triangle_v2",
+    )
+
+
+def _figure_independent_channels(
+    stat: Any,
+    statistical_json: dict[str, Any],
+    output_dir: Path,
+) -> dict[str, Any]:
+    fig, axes = plt.subplots(
+        2,
+        2,
+        figsize=(FIGURE_WIDTH, 5.0),
+        layout="constrained",
+    )
+    alpha = stat["alpha_values"]
+    ax = axes[0, 0]
+    ax.fill_between(
+        alpha,
+        stat["energy_gap_ratio_lower"],
+        stat["energy_gap_ratio_upper"],
+        color=COLORS["spectral"],
+        alpha=0.18,
+        linewidth=0,
+    )
+    ax.plot(
+        alpha,
+        stat["energy_gap_ratio_mean"],
+        color=COLORS["spectral"],
+        marker="o",
+        markersize=3.3,
+        label=r"energy spectrum of $PHP$",
+    )
+    ax.axhspan(
+        float(stat["haar_ratio_mean_lower"][0]),
+        float(stat["haar_ratio_mean_upper"][0]),
+        color=COLORS["haar"],
+        alpha=0.10,
+        label="Haar/GUE interval",
+    )
+    ax.axvline(0.5, color=COLORS["gray"], linestyle=":", linewidth=0.8)
+    ax.set_xlabel(r"intrafiber interpolation $\alpha$")
+    ax.set_ylabel(r"$\langle r_E\rangle$")
+    ax.legend(frameon=False, loc="lower right")
+    _panel(ax, "a", r"Spectral channel: change $PHP$")
+
+    ax = axes[0, 1]
+    projector = np.maximum(stat["projector_distance_alpha"], 1e-18)
+    curvature = np.maximum(stat["curvature_error_alpha"], 1e-18)
+    ax.plot(
+        alpha,
+        projector,
+        color=COLORS["physical"],
+        marker="o",
+        markersize=3.0,
+        label=r"$\|P_\alpha-P_0\|_F$",
+    )
+    ax.plot(
+        alpha,
+        curvature,
+        color=COLORS["jacobi"],
+        marker="s",
+        markersize=3.0,
+        label=r"curvature-spectrum error",
+    )
+    ax.set_yscale("log")
+    ax.set_ylim(3e-19, 3e-13)
+    ax.set_xlabel(r"$\alpha$")
+    ax.set_ylabel("invariance error")
+    ax.legend(frameon=False, loc="upper left")
+    _panel(ax, "b", "Projector geometry does not move")
+
+    ax = axes[1, 0]
+    g = np.concatenate([[0.0], stat["g_values"]])
+    structured_ratio = float(stat["structured_ratio_mean_mean"][0])
+    mean = np.concatenate(
+        [[structured_ratio], stat["g_ratio_scalar_mean"]]
+    )
+    lower = np.concatenate(
+        [[structured_ratio], stat["g_ratio_scalar_lower"]]
+    )
+    upper = np.concatenate(
+        [[structured_ratio], stat["g_ratio_scalar_upper"]]
+    )
+    ax.fill_between(
+        g,
+        lower,
+        upper,
+        color=COLORS["physical"],
+        alpha=0.18,
+        linewidth=0,
+    )
+    ax.plot(
+        g,
+        mean,
+        color=COLORS["physical"],
+        marker="o",
+        markersize=3.3,
+        label=r"curvature spectrum",
+    )
+    ax.axhspan(
+        float(stat["haar_ratio_mean_lower"][0]),
+        float(stat["haar_ratio_mean_upper"][0]),
+        color=COLORS["haar"],
+        alpha=0.10,
+        label="Haar--Jacobi interval",
+    )
+    ax.axvline(
+        0.2,
+        color=COLORS["jacobi"],
+        linestyle=":",
+        linewidth=0.9,
+        label=r"$g_{\rm local}=0.20$",
+    )
+    ax.axvline(
+        0.4,
+        color=COLORS["residual"],
+        linestyle="--",
+        linewidth=0.9,
+        label=r"$g_{\rm ramp}=0.40$",
+    )
+    ax.set_xlabel(r"geometric scrambling $g$")
+    ax.set_ylabel(r"$\langle r_F\rangle$")
+    ax.legend(frameon=False, loc="lower right")
+    _panel(ax, "c", r"Geometric channel: change $P(\partial H)Q$")
+
+    ax = axes[1, 1]
+    ax.set_xlim(0.0, 1.0)
+    ax.set_ylim(0.0, 1.0)
+    ax.axvline(0.5, color="white", linewidth=1.3)
+    ax.axhline(0.4, color="white", linewidth=1.3)
+    colors = np.asarray(
+        [
+            [
+                matplotlib.colors.to_rgb("#ECECEC"),
+                matplotlib.colors.to_rgb("#F7DFB1"),
+            ],
+            [
+                matplotlib.colors.to_rgb("#B9DDED"),
+                matplotlib.colors.to_rgb("#C9E9D9"),
+            ],
+        ]
+    )
+    ax.imshow(
+        colors,
+        origin="lower",
+        extent=(0, 1, 0, 1),
+        aspect="auto",
+    )
+    labels = (
+        (0.25, 0.20, "neither"),
+        (0.75, 0.20, "spectral only"),
+        (0.25, 0.70, "geometric only"),
+        (0.75, 0.70, "both"),
+    )
+    for x, y, label in labels:
+        ax.text(x, y, label, ha="center", va="center", fontweight="bold")
+    ax.set_xticks([0.25, 0.75], ["regular", "GUE-like"])
+    ax.set_yticks([0.20, 0.70], ["structured", "Jacobi-like"])
+    ax.set_xlabel(r"intrafiber spectral channel $PHP$")
+    ax.set_ylabel(r"projector-geometric channel")
+    _panel(ax, "d", "Two independent notions of chaos")
+    return _save(
+        fig,
+        output_dir,
+        "figure_3_independent_channels_v2",
+    )
+
+
+def _figure_geometric_hierarchy(
+    source: Any,
+    stat: Any,
+    statistical_json: dict[str, Any],
+    output_dir: Path,
+) -> dict[str, Any]:
+    times = stat["times"]
+    all_g = np.concatenate([[0.0], stat["g_values"]])
+    residual = np.vstack(
+        [
+            stat["structured_form_mean"]
+            - stat["jacobi_connected_D50"],
+            stat["g_form_mean"]
+            - stat["jacobi_connected_D50"][None, :],
+        ]
+    )
+    fig, axes = plt.subplots(
+        2,
+        2,
+        figsize=(FIGURE_WIDTH, 5.0),
+        layout="constrained",
+    )
+    ax = axes[0, 0]
+    mask = times <= 1.5
+    image = ax.imshow(
+        residual[:, mask],
+        origin="lower",
+        aspect="auto",
+        extent=(
+            float(times[mask][0]),
+            float(times[mask][-1]),
+            -0.5,
+            all_g.size - 0.5,
+        ),
+        cmap="RdBu_r",
+        norm=TwoSlopeNorm(vmin=-0.25, vcenter=0.0, vmax=0.25),
+    )
+    ax.set_yticks(np.arange(all_g.size), [f"{value:g}" for value in all_g])
+    ax.set_xlabel(r"$\tau$")
+    ax.set_ylabel(r"scrambling $g$")
+    colorbar = fig.colorbar(image, ax=ax, pad=0.02)
+    colorbar.set_label(r"$K_{F,c}-K_{J,c}$")
+    _panel(ax, "a", "Residual flow toward finite-$D$ Jacobi")
+
+    ax = axes[0, 1]
+    registered_mask = (times >= 0.25) & (times <= 1.5)
+    rms_residual = np.sqrt(
+        np.mean(
+            (
+                stat["g_form_mean"][:, registered_mask]
+                - stat["jacobi_connected_D50"][
+                    None,
+                    registered_mask,
+                ]
+            )
+            ** 2,
+            axis=1,
+        )
+    )
+    ax.plot(
+        stat["g_values"],
+        rms_residual,
+        color=COLORS["residual"],
+        marker="o",
+        markersize=3.4,
+        label=r"RMS SFF residual, $0.25\leq\tau\leq1.5$",
+    )
+    ax.axvline(
+        0.2,
+        color=COLORS["jacobi"],
+        linestyle=":",
+        label=r"local $P(r)$ onset",
+    )
+    ax.axvline(
+        0.4,
+        color=COLORS["residual"],
+        linestyle="--",
+        label=r"first registered ramp window",
+    )
+    ax.set_xlim(0.0, 1.02)
+    ax.set_yscale("log")
+    ax.set_xlabel(r"$g$")
+    ax.set_ylabel(r"RMS$(K_{F,c}-K_{J,c})$")
+    ax.legend(frameon=False, loc="upper right")
+    _panel(ax, "b", "Local correlations precede the ramp")
+
+    ax = axes[1, 0]
+    _band(
+        ax,
+        times,
+        stat,
+        "physical_form_residual",
+        COLORS["residual"],
+        "physical $-$ finite-$D$ Jacobi",
+    )
+    ax.axhline(0.0, color=COLORS["gray"], linewidth=0.75)
+    ax.axvspan(0.25, 1.5, color=COLORS["jacobi"], alpha=0.07)
+    ax.set_xlim(0.0, 1.55)
+    ax.set_xlabel(r"$\tau$")
+    ax.set_ylabel(r"$\delta K_{F,c}$")
+    ax.legend(frameon=False, loc="upper right")
+    _panel(ax, "c", r"Physical ramp: compatible for $\tau\geq0.25$")
+
+    ax = axes[1, 1]
+    _band(
+        ax,
+        stat["lengths"],
+        stat,
+        "physical_haar_number_residual",
+        COLORS["physical"],
+        r"physical $-$ Haar--Jacobi",
+    )
+    ax.axhline(0.0, color=COLORS["gray"], linewidth=0.75)
+    ax.axvline(
+        1.0,
+        color=COLORS["residual"],
+        linestyle=":",
+        label=r"$L_{\rm universal}=1$",
+    )
+    ax.set_xlabel(r"window length $L$")
+    ax.set_ylabel(r"$\Delta\Sigma^2(L)$")
+    ax.legend(frameon=False, loc="upper left")
+    _panel(ax, "d", "Long-range memory survives")
+    return _save(
+        fig,
+        output_dir,
+        "figure_4_geometric_hierarchy_v2",
+    )
+
+
+def _figure_jacobi_atoms(
+    source: Any,
+    output_dir: Path,
+) -> dict[str, Any]:
+    times = source["times"]
+    D = np.asarray(source["rank_D"], dtype=float)
+    k = np.asarray(source["rank_interior"], dtype=float)
+    atoms = np.asarray(source["rank_atom_each"], dtype=float)
+    fig, axes = plt.subplots(
+        2,
+        2,
+        figsize=(FIGURE_WIDTH, 5.0),
+        layout="constrained",
+    )
+    for ax, index, label, title in (
+        (axes[0, 0], 5, "a", r"$D=546$: six atoms per edge"),
+        (axes[0, 1], 6, "b", r"$D=800$: 120 atoms per edge"),
+    ):
+        ax.plot(
+            times,
+            source["rank_physical_connected_full"][index],
+            color=COLORS["physical"],
+            label="physical full spectrum",
+        )
+        ax.plot(
+            times,
+            source["rank_reference_connected_full"][index],
+            color=COLORS["haar"],
+            label="Jacobi full spectrum",
+        )
+        if index == 6:
+            ax.plot(
+                times,
+                source["rank_reference_connected_continuous"][index],
+                color=COLORS["jacobi"],
+                linestyle="--",
+                label="atom-stripped continuous",
+            )
+        plateau = k[index] / D[index]
+        ax.axhline(
+            plateau,
+            color=COLORS["structured"],
+            linestyle=":",
+            label=rf"full plateau $k/D={plateau:.3f}$",
+        )
+        ax.set_xlim(0.0, 2.0)
+        ax.set_ylim(-0.04, 1.08)
+        ax.set_xlabel(r"$\tau$")
+        ax.set_ylabel(r"$K_{F,c}(\tau)$")
+        ax.legend(frameon=False, loc="lower right")
+        _panel(ax, label, title)
+
+    ax = axes[1, 0]
+    plateau = k / D
+    ax.plot(
+        D,
+        plateau,
+        color=COLORS["jacobi"],
+        marker="o",
+        label=r"exact full connected plateau $k/D$",
+    )
+    ax.plot(
+        D,
+        2.0 * atoms / D,
+        color=COLORS["structured"],
+        marker="s",
+        label=r"total atom weight $2(D-M)_+/D$",
+    )
+    ax.set_xscale("log")
+    ax.set_xlabel(r"active rank $D$")
+    ax.set_ylabel("spectral weight")
+    ax.set_ylim(-0.03, 1.06)
+    ax.legend(frameon=False, loc="center left")
+    _panel(ax, "c", "Exact atom suppression of connected SFF")
+
+    ax = axes[1, 1]
+    index = 6
+    for key, color, label, linestyle in (
+        (
+            "rank_reference_raw_full",
+            COLORS["haar"],
+            "full raw SFF",
+            "-",
+        ),
+        (
+            "rank_reference_raw_atom_atom",
+            COLORS["structured"],
+            "atom--atom",
+            "--",
+        ),
+        (
+            "rank_reference_raw_atom_continuum",
+            COLORS["residual"],
+            "atom--continuum",
+            "-.",
+        ),
+        (
+            "rank_reference_raw_continuum_continuum",
+            COLORS["physical"],
+            "continuum--continuum",
+            ":",
+        ),
+    ):
+        ax.plot(
+            times,
+            source[key][index],
+            color=color,
+            label=label,
+            linestyle=linestyle,
+        )
+    ax.set_xlim(0.0, 1.5)
+    ax.set_xlabel(r"raw Fourier scale $\tau$")
+    ax.set_ylabel(r"raw $K_F(\tau)$")
+    ax.legend(frameon=False, loc="upper right")
+    _panel(ax, "d", "Raw atom decomposition closes exactly")
+    return _save(
+        fig,
+        output_dir,
+        "figure_5_jacobi_atoms_v2",
+    )
+
+
+def _write_generated_inputs(
+    output_dir: Path,
+    source_json: dict[str, Any],
+    statistical_json: dict[str, Any],
+    source: Any,
+    stat: Any,
+) -> None:
+    outcomes = statistical_json["outcomes"]
+    tau_half = int(np.argmin(np.abs(stat["times"] - 0.5)))
+    residual = outcomes["number_variance_L8_residual"]
+    energy = outcomes["energy_gap_ratio_endpoints"]
+    lines = [
+        r"\newcommand{\EnergyRawSFF}{50}",
+        r"\newcommand{\EnergyConnectedSFF}{0}",
+        rf"\newcommand{{\StructuredFormHalf}}{{{float(stat['structured_form_mean'][tau_half]):.3f}}}",
+        rf"\newcommand{{\PhysicalFormHalf}}{{{float(stat['physical_form_mean'][tau_half]):.3f}}}",
+        rf"\newcommand{{\JacobiFormHalf}}{{{float(stat['jacobi_connected_D50'][tau_half]):.3f}}}",
+        rf"\newcommand{{\GeometricTauOnset}}{{{outcomes['physical_tau_compatibility_onset']:.2f}}}",
+        rf"\newcommand{{\GeometricLocalOnset}}{{{outcomes['first_g_with_haar_gap_ratio_interval']:.2f}}}",
+        rf"\newcommand{{\GeometricRampOnset}}{{{outcomes['first_g_with_registered_jacobi_window']:.2f}}}",
+        rf"\newcommand{{\NumberVarianceExtent}}{{{outcomes['number_variance_compatibility_extent']:.1f}}}",
+        rf"\newcommand{{\NumberResidualEight}}{{{residual['mean']:.5f}}}",
+        rf"\newcommand{{\NumberResidualEightLower}}{{{residual['lower']:.5f}}}",
+        rf"\newcommand{{\NumberResidualEightUpper}}{{{residual['upper']:.5f}}}",
+        rf"\newcommand{{\PoissonEndpointRatio}}{{{energy['poisson']:.6f}}}",
+        rf"\newcommand{{\GUEEndpointRatio}}{{{energy['gue']:.6f}}}",
+        rf"\newcommand{{\StructuredMomenta}}{{{source_json['sample_counts']['structured_momenta']}}}",
+        rf"\newcommand{{\StructuredOrbits}}{{{source_json['sample_counts']['structured_orbits']}}}",
+        rf"\newcommand{{\GeometricSamplesPerPoint}}{{{source_json['sample_counts']['per_positive_g']}}}",
+        rf"\newcommand{{\SpectralSamplesPerPoint}}{{{source_json['sample_counts']['fixed_projector_per_alpha']}}}",
+        rf"\newcommand{{\BootstrapReplicatesVTwo}}{{{statistical_json['bootstrap_replicates']}}}",
+        rf"\newcommand{{\LargestRankVTwo}}{{{int(source['rank_D'][-1])}}}",
+        rf"\newcommand{{\LargestAtomEachVTwo}}{{{int(source['rank_atom_each'][-1])}}}",
+        rf"\newcommand{{\LargestConnectedPlateau}}{{{float(source['rank_interior'][-1] / source['rank_D'][-1]):.1f}}}",
+    ]
+    (output_dir / "generated_numbers_v2.tex").write_text(
+        "\n".join(lines) + "\n",
+        encoding="utf-8",
+    )
+    table = [
+        r"\begin{tabular}{rrrr}",
+        r"\hline\hline",
+        r"$g$ & $\langle r_F\rangle$ & lower & upper \\",
+        r"\hline",
+    ]
+    for index, g in enumerate(stat["g_values"]):
+        table.append(
+            f"{float(g):.2f} & "
+            f"{float(stat['g_ratio_scalar_mean'][index]):.6f} & "
+            f"{float(stat['g_ratio_scalar_lower'][index]):.6f} & "
+            f"{float(stat['g_ratio_scalar_upper'][index]):.6f} \\\\"
+        )
+    table.extend([r"\hline\hline", r"\end{tabular}"])
+    (output_dir / "generated_tables_v2.tex").write_text(
+        "\n".join(table) + "\n",
+        encoding="utf-8",
+    )
+
+
+def run(
+    output_dir: Path,
+    source_json_path: Path | None = None,
+    source_npz_path: Path | None = None,
+    statistical_json_path: Path | None = None,
+    statistical_npz_path: Path | None = None,
+    sync_overleaf: bool = False,
+) -> dict[str, Any]:
+    """Generate five figures, generated TeX, and a hash manifest."""
+
+    _style()
+    script_dir = Path(__file__).resolve().parent
+    output_dir = output_dir.resolve()
+    output_dir.mkdir(parents=True, exist_ok=True)
+    source_json_path = (
+        script_dir / "output" / "spectral_silence_v2.json"
+        if source_json_path is None
+        else source_json_path
+    )
+    source_npz_path = (
+        script_dir / "output" / "spectral_silence_v2.npz"
+        if source_npz_path is None
+        else source_npz_path
+    )
+    statistical_json_path = (
+        script_dir
+        / "output"
+        / "spectral_silence_statistics_v2.json"
+        if statistical_json_path is None
+        else statistical_json_path
+    )
+    statistical_npz_path = (
+        script_dir
+        / "output"
+        / "spectral_silence_statistics_v2.npz"
+        if statistical_npz_path is None
+        else statistical_npz_path
+    )
+    source_json = json.loads(
+        source_json_path.read_text(encoding="utf-8")
+    )
+    statistical_json = json.loads(
+        statistical_json_path.read_text(encoding="utf-8")
+    )
+    if not source_json["all_checks_pass"]:
+        raise RuntimeError("source scientific artifact failed")
+    if not statistical_json["all_checks_pass"]:
+        raise RuntimeError("statistical scientific artifact failed")
+    with (
+        np.load(source_npz_path, allow_pickle=False) as source,
+        np.load(statistical_npz_path, allow_pickle=False) as stat,
+    ):
+        figures = {
+            "figure_1": _figure_spectral_silence(
+                source,
+                stat,
+                output_dir,
+            ),
+            "figure_2": _figure_falsification_triangle(
+                stat,
+                output_dir,
+            ),
+            "figure_3": _figure_independent_channels(
+                stat,
+                statistical_json,
+                output_dir,
+            ),
+            "figure_4": _figure_geometric_hierarchy(
+                source,
+                stat,
+                statistical_json,
+                output_dir,
+            ),
+            "figure_5": _figure_jacobi_atoms(
+                source,
+                output_dir,
+            ),
+        }
+        _write_generated_inputs(
+            output_dir,
+            source_json,
+            statistical_json,
+            source,
+            stat,
+        )
+        annotations = {
+            "energy_raw": float(source["energy_raw"][0]),
+            "energy_connected": float(source["energy_connected"][0]),
+            "local_g": round(
+                statistical_json["outcomes"][
+                    "first_g_with_haar_gap_ratio_interval"
+                ],
+                2,
+            ),
+            "ramp_g": round(
+                statistical_json["outcomes"][
+                    "first_g_with_registered_jacobi_window"
+                ],
+                2,
+            ),
+            "number_extent": float(
+                statistical_json["outcomes"][
+                    "number_variance_compatibility_extent"
+                ]
+            ),
+            "D800_atom_each": int(source["rank_atom_each"][-1]),
+            "D800_connected_plateau": float(
+                source["rank_interior"][-1] / source["rank_D"][-1]
+            ),
+        }
+    if sync_overleaf:
+        project = (
+            script_dir.parents[2]
+            / "overleaf_sync"
+            / "geometric_eth_large_scale"
+        )
+        figure_target = project / "figures"
+        generated_target = project / "generated"
+        figure_target.mkdir(parents=True, exist_ok=True)
+        generated_target.mkdir(parents=True, exist_ok=True)
+        for figure in figures.values():
+            shutil.copy2(figure["pdf"], figure_target)
+        shutil.copy2(
+            output_dir / "generated_numbers_v2.tex",
+            generated_target / "generated_numbers_v2.tex",
+        )
+        shutil.copy2(
+            output_dir / "generated_tables_v2.tex",
+            generated_target / "generated_tables_v2.tex",
+        )
+    inputs = {
+        str(path.resolve()): _sha256(path)
+        for path in (
+            source_json_path,
+            source_npz_path,
+            statistical_json_path,
+            statistical_npz_path,
+        )
+    }
+    checks = {
+        "source_artifacts_pass": bool(
+            source_json["all_checks_pass"]
+            and statistical_json["all_checks_pass"]
+        ),
+        "five_figures_generated": len(figures) == 5,
+        "all_pdf_png_pairs_exist": all(
+            Path(figure["pdf"]).is_file()
+            and Path(figure["png"]).is_file()
+            for figure in figures.values()
+        ),
+        "registered_annotations_exact": bool(
+            annotations["energy_raw"] == 50.0
+            and annotations["energy_connected"] == 0.0
+            and annotations["local_g"] == 0.2
+            and annotations["ramp_g"] == 0.4
+            and annotations["number_extent"] == 1.0
+            and annotations["D800_atom_each"] == 120
+            and abs(
+                annotations["D800_connected_plateau"] - 0.7
+            )
+            < 1e-12
+        ),
+    }
+    manifest = {
+        "schema_version": 2,
+        "version": VERSION,
+        "inputs": inputs,
+        "figures": figures,
+        "generated_tex": {
+            "numbers": str(
+                (output_dir / "generated_numbers_v2.tex").resolve()
+            ),
+            "tables": str(
+                (output_dir / "generated_tables_v2.tex").resolve()
+            ),
+        },
+        "scientific_annotations": annotations,
+        "checks": checks,
+        "all_checks_pass": bool(all(checks.values())),
+    }
+    manifest_path = output_dir / "figure_manifest_v2.json"
+    manifest_path.write_text(
+        json.dumps(manifest, indent=2) + "\n",
+        encoding="utf-8",
+    )
+    return manifest
+
+
+def main() -> None:
+    parser = argparse.ArgumentParser()
+    parser.add_argument(
+        "--output-dir",
+        type=Path,
+        default=Path(__file__).resolve().parent / "output",
+    )
+    parser.add_argument(
+        "--no-sync-overleaf",
+        action="store_true",
+    )
+    args = parser.parse_args()
+    result = run(
+        args.output_dir,
+        sync_overleaf=not args.no_sync_overleaf,
+    )
+    print(json.dumps(result, indent=2))
+    if not result["all_checks_pass"]:
+        raise SystemExit("v2 figure audit failed")
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/make_topological_holonomy_figure_v3.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/make_topological_holonomy_figure_v3.py
new file mode 100644
index 000000000..49a2c1a2d
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/make_topological_holonomy_figure_v3.py
@@ -0,0 +1,454 @@
+#!/usr/bin/env python3
+"""Generate the fixed-Chern Wilson-holonomy publication figure."""
+
+from __future__ import annotations
+
+import hashlib
+import json
+from pathlib import Path
+from typing import Any
+
+import matplotlib
+
+matplotlib.use("Agg")
+import matplotlib.pyplot as plt
+import numpy as np
+
+from lgeth.bundle_geometry import analyze_frame_bundle
+from lgeth.holonomy import deform_orbital_mesh
+from lgeth.lattice import BosonBasis
+from lgeth.twist_bundle import default_checkpoint_path, load_twist_bundle
+
+
+SCRIPT_ROOT = Path(__file__).resolve().parent
+OUTPUT = SCRIPT_ROOT / "output"
+SOURCE_JSON = OUTPUT / "topological_holonomy_v3.json"
+SOURCE_NPZ = OUTPUT / "topological_holonomy_v3.npz"
+FIGURE_PDF = OUTPUT / "figure_7_topological_holonomy_v3.pdf"
+FIGURE_PNG = OUTPUT / "figure_7_topological_holonomy_v3.png"
+MANIFEST = OUTPUT / "figure_manifest_v3.json"
+
+
+def _sha256(path: Path) -> str:
+    return hashlib.sha256(path.read_bytes()).hexdigest()
+
+
+def _atomic_json(path: Path, payload: dict[str, Any]) -> None:
+    temporary = path.with_suffix(path.suffix + ".tmp")
+    temporary.write_text(
+        json.dumps(payload, indent=2, sort_keys=True),
+        encoding="utf-8",
+    )
+    temporary.replace(path)
+
+
+def _style() -> None:
+    plt.rcParams.update(
+        {
+            "font.family": "serif",
+            "font.serif": ["STIXGeneral", "DejaVu Serif"],
+            "mathtext.fontset": "stix",
+            "font.size": 8.4,
+            "axes.titlesize": 9.2,
+            "axes.labelsize": 8.6,
+            "xtick.labelsize": 7.7,
+            "ytick.labelsize": 7.7,
+            "legend.fontsize": 7.0,
+            "axes.linewidth": 0.75,
+            "xtick.major.width": 0.65,
+            "ytick.major.width": 0.65,
+            "pdf.fonttype": 42,
+            "ps.fonttype": 42,
+        }
+    )
+
+
+def _panel_label(axis, label: str) -> None:
+    axis.text(
+        -0.15,
+        1.08,
+        label,
+        transform=axis.transAxes,
+        fontsize=9.2,
+        fontweight="bold",
+        va="top",
+    )
+
+
+def _determinant_flow(
+    plaquettes: np.ndarray,
+) -> tuple[np.ndarray, np.ndarray]:
+    flux_by_transverse_slice = np.sum(
+        np.angle(np.linalg.det(np.asarray(plaquettes))),
+        axis=0,
+    )
+    transverse = np.arange(flux_by_transverse_slice.size + 1)
+    transverse = transverse / flux_by_transverse_slice.size
+    flow = np.concatenate(
+        [[0.0], np.cumsum(flux_by_transverse_slice)]
+    ) / (2.0 * np.pi)
+    return transverse, flow
+
+
+def _n4_determinant_flows(
+    mesh: int,
+    seed: int,
+) -> tuple[np.ndarray, np.ndarray, np.ndarray, dict[str, str]]:
+    bundle = load_twist_bundle(
+        default_checkpoint_path(4, mesh),
+        expected_N=4,
+        expected_n_flux=10,
+        expected_rank=25,
+        expected_mesh=mesh,
+    )
+    final_geometry = analyze_frame_bundle(
+        bundle.coefficient_frames,
+        deform_orbital_mesh(
+            bundle.orbital_frames,
+            g=1.0,
+            seed=seed,
+            commuting=False,
+        ),
+        BosonBasis(10, 4),
+    )
+    transverse, base_flow = _determinant_flow(
+        bundle.geometry.plaquette
+    )
+    final_transverse, final_flow = _determinant_flow(
+        final_geometry.plaquette
+    )
+    if not np.array_equal(transverse, final_transverse):
+        raise RuntimeError("base and deformed determinant grids disagree")
+    checkpoint_json = default_checkpoint_path(4, mesh)
+    checkpoint_npz = checkpoint_json.with_suffix(".npz")
+    return (
+        transverse,
+        base_flow,
+        final_flow,
+        {
+            str(checkpoint_json.relative_to(SCRIPT_ROOT)): _sha256(
+                checkpoint_json
+            ),
+            str(checkpoint_npz.relative_to(SCRIPT_ROOT)): _sha256(
+                checkpoint_npz
+            ),
+        },
+    )
+
+
+def make_figure() -> dict[str, Any]:
+    payload = json.loads(SOURCE_JSON.read_text(encoding="utf-8"))
+    if payload["result_branch"] != "fixed_chern_deformed_holonomy":
+        raise RuntimeError("Figure 7 requires the accepted deformed branch")
+    configuration = payload["configuration"]
+    g_values = np.asarray(configuration["g_values"], dtype=float)
+    seeds = np.asarray(configuration["generator_seeds"], dtype=np.int64)
+    transverse, base_flow, final_flow, checkpoint_hashes = (
+        _n4_determinant_flows(
+            mesh=int(configuration["primary_mesh"]),
+            seed=int(seeds[0]),
+        )
+    )
+    with np.load(SOURCE_NPZ, allow_pickle=False) as arrays:
+        gap_mean = [
+            np.asarray(arrays[f"size_{index}_gap_mean"])
+            for index in range(2)
+        ]
+        form_mean = [
+            np.asarray(arrays[f"size_{index}_form_mean"])
+            for index in range(2)
+        ]
+        commuting_gap = [
+            np.asarray(arrays[f"size_{index}_commuting_gap"])
+            for index in range(2)
+        ]
+        commuting_form = [
+            np.asarray(arrays[f"size_{index}_commuting_form"])
+            for index in range(2)
+        ]
+        cue_gap = [
+            np.asarray(arrays[f"size_{index}_cue_gap"])
+            for index in range(2)
+        ]
+        cue_form = [
+            np.asarray(arrays[f"size_{index}_cue_form"])
+            for index in range(2)
+        ]
+        cue_lower = [
+            np.asarray(
+                arrays[f"size_{index}_cue_form_simultaneous_lower"]
+            )
+            for index in range(2)
+        ]
+        cue_upper = [
+            np.asarray(
+                arrays[f"size_{index}_cue_form_simultaneous_upper"]
+            )
+            for index in range(2)
+        ]
+
+    _style()
+    navy = "#24476b"
+    orange = "#d8752d"
+    teal = "#228b8d"
+    grey = "#666b73"
+    pale_navy = "#dce7f0"
+    pale_orange = "#f3e3d7"
+    figure, axes = plt.subplots(
+        2,
+        2,
+        figsize=(7.0, 5.25),
+        constrained_layout=True,
+    )
+
+    axis = axes[0, 0]
+    _panel_label(axis, "(a)")
+    for index, (size, color, marker) in enumerate(
+        zip(payload["sizes"], (navy, orange), ("o", "s"), strict=True)
+    ):
+        chern = float(size["base_chern_integer"])
+        axis.plot(
+            g_values,
+            np.full_like(g_values, chern),
+            marker=marker,
+            color=color,
+            lw=1.45,
+            ms=3.7,
+            label=rf"$N={size['N']}$: $C_1={int(chern)}$",
+        )
+    axis.set_xlabel("isospectral deformation $g$")
+    axis.set_ylabel("first Chern number $C_1$")
+    axis.set_ylim(4.9, 11.0)
+    axis.set_title("Topology and spectrum remain fixed", pad=5)
+    axis.grid(alpha=0.18, lw=0.55)
+    twin = axis.twinx()
+    for size, color in zip(
+        payload["sizes"],
+        (navy, orange),
+        strict=True,
+    ):
+        twin.plot(
+            g_values,
+            np.full_like(g_values, size["minimum_external_gap"]),
+            ":",
+            color=color,
+            lw=1.1,
+            alpha=0.75,
+        )
+    twin.set_ylabel("external gap $\\Delta$", color=grey)
+    twin.tick_params(axis="y", colors=grey)
+    axis.legend(frameon=False, loc="center left")
+    axis.text(
+        0.98,
+        0.08,
+        "$H_g=\\mathcal{U}_g H_0\\mathcal{U}_g^\\dagger$",
+        transform=axis.transAxes,
+        ha="right",
+        color=grey,
+        fontsize=7.2,
+    )
+
+    axis = axes[0, 1]
+    _panel_label(axis, "(b)")
+    axis.plot(
+        transverse,
+        base_flow,
+        color=navy,
+        lw=1.65,
+        label="$g=0$",
+    )
+    axis.plot(
+        transverse,
+        final_flow,
+        color=orange,
+        lw=1.65,
+        label="$g=1$",
+    )
+    axis.axhline(10.0, color=grey, lw=0.7, ls=":")
+    axis.set_xlabel("transverse twist $\\theta_y/2\\pi$")
+    axis.set_ylabel(
+        "$\\frac{1}{2\\pi}\\sum_{y'<y}\\Phi_{\\det}(y')$"
+    )
+    axis.set_title("$N=4$: fixed winding, deformed flow", pad=5)
+    axis.legend(frameon=False, loc="upper left")
+    axis.grid(alpha=0.18, lw=0.55)
+    axis.text(
+        0.97,
+        0.10,
+        "both endpoints: $C_1=10$",
+        transform=axis.transAxes,
+        ha="right",
+        color=orange,
+        fontsize=7.2,
+    )
+
+    axis = axes[1, 0]
+    _panel_label(axis, "(c)")
+    for index, (color, pale, marker) in enumerate(
+        zip(
+            (navy, orange),
+            (pale_navy, pale_orange),
+            ("o", "s"),
+            strict=True,
+        )
+    ):
+        seed_interval = np.quantile(
+            gap_mean[index],
+            [0.025, 0.5, 0.975],
+            axis=0,
+        )
+        axis.fill_between(
+            g_values,
+            seed_interval[0],
+            seed_interval[2],
+            color=pale,
+            alpha=0.9,
+            zorder=1,
+        )
+        axis.plot(
+            g_values,
+            seed_interval[1],
+            marker=marker,
+            color=color,
+            lw=1.5,
+            ms=3.7,
+            label=rf"$N={payload['sizes'][index]['N']}$",
+            zorder=3,
+        )
+        cue_interval = np.quantile(
+            cue_gap[index],
+            [0.025, 0.5, 0.975],
+        )
+        axis.axhline(
+            cue_interval[1],
+            color=color,
+            lw=0.9,
+            ls=":",
+            alpha=0.9,
+        )
+    axis.plot(
+        g_values,
+        commuting_gap[1],
+        "D--",
+        color=grey,
+        lw=1.15,
+        ms=3.2,
+        label="$N=4$ commuting control",
+    )
+    axis.axhspan(
+        min(np.quantile(values, 0.025) for values in cue_gap),
+        max(np.quantile(values, 0.975) for values in cue_gap),
+        color="#ececef",
+        alpha=0.75,
+        zorder=0,
+        label="CUE 95% range",
+    )
+    axis.set_xlabel("isospectral deformation $g$")
+    axis.set_ylabel("Wilson circular gap ratio $\\langle r_W\\rangle$")
+    axis.set_ylim(0.25, 0.77)
+    axis.set_title("Holonomy changes, but remains non-CUE", pad=5)
+    axis.legend(frameon=False, loc="upper left", ncol=2)
+    axis.grid(alpha=0.18, lw=0.55)
+
+    axis = axes[1, 1]
+    _panel_label(axis, "(d)")
+    size_index = 1
+    rank = int(payload["sizes"][size_index]["rank"])
+    stop = int(payload["sizes"][size_index]["cue_nonplateau_stop"])
+    k_values = np.arange(1, stop + 1)
+    base_form = form_mean[size_index][0, 0, :stop]
+    final_form = np.median(
+        form_mean[size_index][:, -1, :stop],
+        axis=0,
+    )
+    control_form = commuting_form[size_index][-1, :stop]
+    cue_mean = np.mean(cue_form[size_index][:, :stop], axis=0)
+    lower = np.maximum(cue_lower[size_index][:stop], 1e-3)
+    upper = cue_upper[size_index][:stop]
+    axis.fill_between(
+        k_values,
+        lower,
+        upper,
+        color="#e5e5e8",
+        alpha=0.9,
+        label="CUE simultaneous band",
+    )
+    axis.plot(
+        k_values,
+        cue_mean,
+        color="black",
+        lw=1.0,
+        label="CUE mean",
+    )
+    axis.plot(
+        k_values,
+        base_form,
+        "o-",
+        color=navy,
+        lw=1.25,
+        ms=3.2,
+        label="$g=0$",
+    )
+    axis.plot(
+        k_values,
+        final_form,
+        "s-",
+        color=orange,
+        lw=1.35,
+        ms=3.2,
+        label="$g=1$ median",
+    )
+    axis.plot(
+        k_values,
+        control_form,
+        "D--",
+        color=teal,
+        lw=1.05,
+        ms=2.8,
+        label="commuting $g=1$",
+    )
+    axis.set_yscale("log")
+    axis.set_xlabel("Wilson power $k$")
+    axis.set_ylabel("$K_W(k)=|\\mathrm{Tr}\\,W^k|^2/D$")
+    axis.set_title(rf"$N=4$, $D={rank}$: structured Wilson SFF", pad=5)
+    axis.legend(frameon=False, loc="upper left", ncol=2)
+    axis.grid(alpha=0.18, lw=0.55, which="both")
+
+    figure.savefig(FIGURE_PDF)
+    figure.savefig(FIGURE_PNG, dpi=300)
+    plt.close(figure)
+    manifest = (
+        json.loads(MANIFEST.read_text(encoding="utf-8"))
+        if MANIFEST.exists()
+        else {}
+    )
+    manifest["figure_7_topological_holonomy_v3"] = {
+        "source_json": str(SOURCE_JSON.relative_to(SCRIPT_ROOT)),
+        "source_json_sha256": _sha256(SOURCE_JSON),
+        "source_npz": str(SOURCE_NPZ.relative_to(SCRIPT_ROOT)),
+        "source_npz_sha256": _sha256(SOURCE_NPZ),
+        "checkpoint_hashes": checkpoint_hashes,
+        "pdf": str(FIGURE_PDF.relative_to(SCRIPT_ROOT)),
+        "pdf_sha256": _sha256(FIGURE_PDF),
+        "png": str(FIGURE_PNG.relative_to(SCRIPT_ROOT)),
+        "png_sha256": _sha256(FIGURE_PNG),
+        "width_inches": 7.0,
+        "png_width_pixels": 2100,
+        "result_branch": payload["result_branch"],
+        "panels": [
+            "fixed_chern_and_gap",
+            "determinant_winding",
+            "wilson_gap_ratio",
+            "wilson_form_factor",
+        ],
+    }
+    _atomic_json(MANIFEST, manifest)
+    return manifest["figure_7_topological_holonomy_v3"]
+
+
+def main() -> None:
+    print(json.dumps(make_figure(), indent=2, sort_keys=True))
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/citation_audit_v1.json b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/citation_audit_v1.json
new file mode 100644
index 000000000..3068ede90
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/citation_audit_v1.json
@@ -0,0 +1,1266 @@
+{
+  "all_checks_pass": true,
+  "article": "From Local Repulsion to Global Geometry: Large-Scale Tests of Geometric ETH",
+  "bibliography": "overleaf_sync/geometric_eth_large_scale/references.bib",
+  "bibliography_records": 35,
+  "errors": [],
+  "missing_bibliography_keys": [],
+  "records": [
+    {
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+      "key": "berry1984",
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+          "Michael Berry"
+        ],
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+        "metadata_source": "OpenAlex DOI resolution",
+        "title": "Quantal phase factors accompanying adiabatic changes",
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+          "Frank Wilczek",
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+        ],
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+        "title": "Appearance of Gauge Structure in Simple Dynamical Systems",
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+      },
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+        "year": 1980
+      },
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+        "Colin-Ellerin",
+        "Mamroud",
+        "Papadodimas"
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+          "Yiming Chen",
+          "Sean Colin-Ellerin",
+          "Ohad Mamroud",
+          "Kyriakos Papadodimas"
+        ],
+        "identifier": "https://arxiv.org/abs/2604.23287",
+        "metadata_source": "arXiv Atom API",
+        "title": "Chaos of Berry curvature for BPS microstates",
+        "year": 2026
+      },
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+      "title": "Chaos of Berry curvature for BPS microstates",
+      "title_similarity": 1.0,
+      "verified": true,
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+    {
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+          "B. Andrei Bernevig",
+          "F. D. M. Haldane"
+        ],
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+        "metadata_source": "OpenAlex DOI resolution",
+        "title": "Model Fractional Quantum Hall States and Jack Polynomials",
+        "year": 2008
+      },
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+          "Li Chen",
+          "Alexander Seidel"
+        ],
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+        "metadata_source": "OpenAlex DOI resolution",
+        "title": "Algebraic approach to the study of zero modes of Haldane pseudopotentials",
+        "year": 2015
+      },
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+          "Gregory Moore",
+          "Nicholas Read"
+        ],
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+        "metadata_source": "OpenAlex DOI resolution",
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+        "metadata_source": "OpenAlex DOI resolution",
+        "title": "Beyond paired quantum Hall states: Parafermions and incompressible states in the first excited Landau level",
+        "year": 1999
+      },
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+        "Matheus Schossler",
+        "Seidel",
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+      },
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+      "key": "zhang2023",
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+          "Fanmao Zhang",
+          "Matheus Schossler",
+          "Alexander Seidel",
+          "Li Chen"
+        ],
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+        "metadata_source": "OpenAlex DOI resolution",
+        "title": "From frustration-free parent Hamiltonians to off-diagonal long-range order: Moore-Read and related states in second quantization",
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+          "Tahereh Mazaheri",
+          "Gerardo Ort\u00edz",
+          "Zohar Nussinov",
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+        ],
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+        "metadata_source": "OpenAlex DOI resolution",
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+          "Eliot Kapit",
+          "Erich J. Mueller"
+        ],
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+        "metadata_source": "OpenAlex DOI resolution",
+        "title": "Exact Parent Hamiltonian for the Quantum Hall States in a Lattice",
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+      },
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+      "key": "leeqi2014",
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+          "Ching Hua Lee",
+          "Xiao-Liang Qi"
+        ],
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+        "metadata_source": "OpenAlex DOI resolution",
+        "title": "Lattice construction of pseudopotential Hamiltonians for fractional Chern insulators",
+        "year": 2014
+      },
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+      "title": "Lattice construction of pseudopotential Hamiltonians for fractional Chern insulators",
+      "title_similarity": 1.0,
+      "verified": true,
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+    },
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+      },
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+          "Titus Neupert",
+          "Luiz H. Santos",
+          "Claudio Chamon",
+          "Christopher Mudry"
+        ],
+        "identifier": "https://doi.org/10.1103/physrevlett.106.236804",
+        "metadata_source": "OpenAlex DOI resolution",
+        "title": "Fractional Quantum Hall States at Zero Magnetic Field",
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+          "Matthew B. Hastings",
+          "Spyridon Michalakis"
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+        "metadata_source": "OpenAlex DOI resolution",
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+      "key": "bachmann2011",
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+          "Sven Bachmann",
+          "Spyridon Michalakis",
+          "Bruno Nachtergaele",
+          "Robert Sims"
+        ],
+        "identifier": "https://doi.org/10.1007/s00220-011-1380-0",
+        "metadata_source": "OpenAlex DOI resolution",
+        "title": "Automorphic Equivalence within Gapped Phases of Quantum Lattice Systems",
+        "year": 2011
+      },
+      "section": "gapped-phase transport",
+      "title": "Automorphic equivalence within gapped phases of quantum lattice systems",
+      "title_similarity": 1.0,
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+    },
+    {
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+      },
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+        "Schuch",
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+      ],
+      "checks": {
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+      },
+      "doi": "10.1103/PhysRevB.84.165139",
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+          "Norbert Schuch",
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+        ],
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+        "title": "Classifying quantum phases using matrix product states and projected entangled pair states",
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diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/figure_1_spectral_silence_v2.pdf b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/figure_1_spectral_silence_v2.pdf
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diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/figure_2_falsification_triangle_v2.pdf b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/figure_2_falsification_triangle_v2.pdf
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diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/figure_2_scale_hierarchy_v1.pdf b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/figure_2_scale_hierarchy_v1.pdf
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diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/figure_3_atom_crossover_v1.pdf b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/figure_3_atom_crossover_v1.pdf
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diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/figure_3_independent_channels_v2.pdf b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/figure_3_independent_channels_v2.pdf
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diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/figure_4_geometric_hierarchy_v2.pdf b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/figure_4_geometric_hierarchy_v2.pdf
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diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/figure_5_covariance_mechanism_v1.pdf b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/figure_5_covariance_mechanism_v1.pdf
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diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/figure_5_jacobi_atoms_v2.pdf b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/figure_5_jacobi_atoms_v2.pdf
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diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/figure_6_wick_factorization_v3.pdf b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/figure_6_wick_factorization_v3.pdf
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new file mode 100644
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--- /dev/null
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diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/generated_numbers_v1.tex b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/generated_numbers_v1.tex
new file mode 100644
index 000000000..7edcf9088
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/generated_numbers_v1.tex
@@ -0,0 +1,30 @@
+\newcommand{\PhysicalMatrices}{20000}
+\newcommand{\PhysicalTestMatrices}{4000}
+\newcommand{\PhysicalRank}{50}
+\newcommand{\PhysicalChannels}{170}
+\newcommand{\TrainingRows}{1024}
+\newcommand{\HaarMatrices}{10000}
+\newcommand{\DeformedMatrices}{10000}
+\newcommand{\SelectedCovFloor}{0.050}
+\newcommand{\DensityHaarLone}{0.2910}
+\newcommand{\DensityCovLone}{0.1237}
+\newcommand{\DensityImprovementPercent}{57.5\%}
+\newcommand{\PhysicalGapRatio}{0.599806}
+\newcommand{\HaarGapRatio}{0.599395}
+\newcommand{\DeformedGapRatio}{0.599200}
+\newcommand{\LargestRank}{800}
+\newcommand{\LargestChannels}{680}
+\newcommand{\LargestAtomMultiplicity}{120}
+\newcommand{\LargestAtomWeightPercent}{30.0\%}
+\newcommand{\LargestInteriorDensityLone}{0.0523}
+\newcommand{\DensityFitExponent}{0.593}
+\newcommand{\BootstrapReplicates}{10000}
+\newcommand{\RootMatricesTotal}{8750}
+\newcommand{\CovarianceAnisotropy}{0.867}
+\newcommand{\PhysicalParticipation}{0.625}
+\newcommand{\NumberVariancePhysEight}{0.696}
+\newcommand{\NumberVarianceHaarEight}{0.570}
+\newcommand{\NumberVarianceCovEight}{0.570}
+\newcommand{\FormFactorPhysHalf}{0.502}
+\newcommand{\FormFactorHaarHalf}{0.495}
+\newcommand{\FormFactorCovHalf}{0.502}
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/generated_numbers_v2.tex b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/generated_numbers_v2.tex
new file mode 100644
index 000000000..5f3b57ce1
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/generated_numbers_v2.tex
@@ -0,0 +1,22 @@
+\newcommand{\EnergyRawSFF}{50}
+\newcommand{\EnergyConnectedSFF}{0}
+\newcommand{\StructuredFormHalf}{4.476}
+\newcommand{\PhysicalFormHalf}{0.502}
+\newcommand{\JacobiFormHalf}{0.501}
+\newcommand{\GeometricTauOnset}{0.25}
+\newcommand{\GeometricLocalOnset}{0.20}
+\newcommand{\GeometricRampOnset}{0.40}
+\newcommand{\NumberVarianceExtent}{1.0}
+\newcommand{\NumberResidualEight}{0.12582}
+\newcommand{\NumberResidualEightLower}{0.11428}
+\newcommand{\NumberResidualEightUpper}{0.13736}
+\newcommand{\PoissonEndpointRatio}{0.385645}
+\newcommand{\GUEEndpointRatio}{0.598677}
+\newcommand{\StructuredMomenta}{24}
+\newcommand{\StructuredOrbits}{12}
+\newcommand{\GeometricSamplesPerPoint}{4000}
+\newcommand{\SpectralSamplesPerPoint}{4000}
+\newcommand{\BootstrapReplicatesVTwo}{10000}
+\newcommand{\LargestRankVTwo}{800}
+\newcommand{\LargestAtomEachVTwo}{120}
+\newcommand{\LargestConnectedPlateau}{0.7}
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/generated_numbers_v3.tex b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/generated_numbers_v3.tex
new file mode 100644
index 000000000..b3c34e8c3
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/generated_numbers_v3.tex
@@ -0,0 +1,30 @@
+% Generated from audited v3 artifacts by the release pipeline.
+\newcommand{\MatrixElementBranch}{deformed\_geometric\_eth}
+\newcommand{\MatrixElementBranchText}{The four-channel residual decreases along the genuine many-body sequence and retains a resolved connected component at the largest size.}
+\newcommand{\LargestManyBodyN}{5}
+\newcommand{\LargestManyBodyRank}{36}
+\newcommand{\LargestManyBodyDimension}{4368}
+\newcommand{\LargestNRFour}{0.20906}
+\newcommand{\LargestGaussianRFour}{0.12723}
+\newcommand{\LargestGaussianRFourLow}{0.12657}
+\newcommand{\LargestGaussianRFourHigh}{0.12797}
+\newcommand{\LargestRFourExcess}{0.08183}
+\newcommand{\TopologyBranch}{fixed\_chern\_deformed\_holonomy}
+\newcommand{\TopologyBranchText}{The Chern class and complete spectrum remain fixed while Wilson statistics change significantly and occupy a structured class distinct from the circular-unitary reference.}
+\newcommand{\TopologyPrimaryMesh}{16}
+\newcommand{\TopologyConvergenceMesh}{20}
+\newcommand{\TopologyNThreeChern}{6}
+\newcommand{\TopologyNFourChern}{10}
+\newcommand{\TopologyNThreeGap}{0.051741}
+\newcommand{\TopologyNFourGap}{0.094695}
+\newcommand{\TopologyNThreeGapChangeLow}{0.02777}
+\newcommand{\TopologyNThreeGapChangeHigh}{0.05068}
+\newcommand{\TopologyNFourGapChangeLow}{0.01805}
+\newcommand{\TopologyNFourGapChangeHigh}{0.02835}
+\newcommand{\TopologyNThreeFinalGapRatio}{0.32115}
+\newcommand{\TopologyNFourFinalGapRatio}{0.33175}
+\newcommand{\TopologyNThreeCUERatio}{0.60153}
+\newcommand{\TopologyNFourCUERatio}{0.60079}
+\newcommand{\TopologyMinimumBranchMargin}{1.17980}
+\newcommand{\TopologyMinimumOverlap}{0.83693}
+\newcommand{\TopologyGaugeError}{6.85e-15}
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/generated_tables_v1.tex b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/generated_tables_v1.tex
new file mode 100644
index 000000000..0c6cc0d80
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/generated_tables_v1.tex
@@ -0,0 +1,13 @@
+\begin{tabular}{rrrrrr}
+\hline\hline
+$D$ & $M$ & samples & atoms/edge & $\Delta\langle r\rangle$ & $L^1_{\rm int}$ \\
+\hline
+16 & 80 & 2000 & 0 & 0.03023 & 0.43375 \\
+50 & 140 & 2000 & 0 & 0.00767 & 0.22916 \\
+112 & 216 & 2000 & 0 & 0.00403 & 0.14094 \\
+210 & 308 & 1000 & 0 & 0.00173 & 0.09624 \\
+352 & 416 & 1000 & 0 & 0.00290 & 0.06866 \\
+546 & 540 & 500 & 6 & 0.00024 & 0.05149 \\
+800 & 680 & 250 & 120 & 0.00423 & 0.05226 \\
+\hline\hline
+\end{tabular}
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/generated_tables_v2.tex b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/generated_tables_v2.tex
new file mode 100644
index 000000000..9e38a3fb2
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/generated_tables_v2.tex
@@ -0,0 +1,13 @@
+\begin{tabular}{rrrr}
+\hline\hline
+$g$ & $\langle r_F\rangle$ & lower & upper \\
+\hline
+0.02 & 0.577596 & 0.575437 & 0.579755 \\
+0.05 & 0.590540 & 0.589162 & 0.591919 \\
+0.10 & 0.594497 & 0.592683 & 0.596310 \\
+0.20 & 0.598927 & 0.597464 & 0.600390 \\
+0.40 & 0.599034 & 0.597900 & 0.600167 \\
+0.70 & 0.599670 & 0.597824 & 0.601517 \\
+1.00 & 0.600307 & 0.598866 & 0.601749 \\
+\hline\hline
+\end{tabular}
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/generated_tables_v3.tex b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/generated_tables_v3.tex
new file mode 100644
index 000000000..aad5da441
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/generated_tables_v3.tex
@@ -0,0 +1,10 @@
+% Generated from audited v3 artifacts by the release pipeline.
+\newcommand{\MatrixElementResultRows}{%
+3 & 8 & 16 & 120 & 0.055872 & 0.37093 & 0.21708 & 0.15385 \\
+4 & 10 & 25 & 715 & 0.103502 & 0.24715 & 0.14638 & 0.10078 \\
+5 & 12 & 36 & 4368 & 0.093593 & 0.20906 & 0.12723 & 0.08183 \\
+}
+\newcommand{\TopologyResultRows}{%
+3 & 16 & 6 & 0.051741 & 2.06643 & 0.85325 & 0.32115 & 0.60153 \\
+4 & 25 & 10 & 0.094695 & 1.17980 & 0.83693 & 0.33175 & 0.60079 \\
+}
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/geometric_eth_topology_assets_v3.json b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/geometric_eth_topology_assets_v3.json
new file mode 100644
index 000000000..adca74dc2
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/geometric_eth_topology_assets_v3.json
@@ -0,0 +1,24 @@
+{
+  "generated_utc": "2026-07-30T11:23:45.133228+00:00",
+  "git_commit": "854fe38e71d93c24fa02ec3db3f8363db27067d6",
+  "input_hashes": {
+    "output/figure_6_wick_factorization_v3.pdf": "214191d7b885e6638758df3d6d245efada7b67e17dddf9362b89aa6f16639ade",
+    "output/figure_7_topological_holonomy_v3.pdf": "11e101309d975a61a3efedb1025c2552149c7f1a6f72433594f4adb1c0a16258",
+    "output/matrix_element_delivery_audit_v3.json": "64974e1b3db8bc15dccd16041ce06912c076281cba2234c557868ef72bbf4769",
+    "output/matrix_element_geometric_eth_v3.json": "bbacad6f795559f417c1e39c034a6fe51669fd509a983099c10965fb68ee34a3",
+    "output/topological_holonomy_delivery_audit_v3.json": "224d546389ccd4cec53343c6db789d449b988eda88f8b8efee84628b8892f42b",
+    "output/topological_holonomy_v3.json": "ff15e7cd2f947b43da5a5973bb82c50319b164877883d187c7c46b2a073823c6"
+  },
+  "matrix_branch": "deformed_geometric_eth",
+  "output_hashes": {
+    "output/generated_numbers_v3.tex": "c2be6699d9f461342c2b320aa647628dd28ddde05cc7d41b15e74d5cd135e5dd",
+    "output/generated_tables_v3.tex": "de39deac3dcac0b9bcc84f51b46d94dbfcf47f094ad457cdf3c4835ae940e6c8"
+  },
+  "overleaf_hashes": {
+    "overleaf_sync/geometric_eth_large_scale/generated/generated_numbers_v3.tex": "c2be6699d9f461342c2b320aa647628dd28ddde05cc7d41b15e74d5cd135e5dd",
+    "overleaf_sync/geometric_eth_large_scale/generated/generated_tables_v3.tex": "de39deac3dcac0b9bcc84f51b46d94dbfcf47f094ad457cdf3c4835ae940e6c8"
+  },
+  "source_sha256": "0eeeba6cafe8bee7b706e29c707170503be13beb200809afc4b2c0bc482c9824",
+  "topology_branch": "fixed_chern_deformed_holonomy",
+  "version": "v3"
+}
\ No newline at end of file
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/geometric_eth_topology_delivery_audit_v3.json b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/geometric_eth_topology_delivery_audit_v3.json
new file mode 100644
index 000000000..fd68eb262
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/geometric_eth_topology_delivery_audit_v3.json
@@ -0,0 +1,191 @@
+{
+  "archived_pdf_sha256": "a75377f76acd78eb3354e186a57933abdf11abbbe5e9a8abd43482ca8c4e05ad",
+  "checks": {
+    "affiliations_visible": true,
+    "all_pages_rendered_180dpi": true,
+    "asset_branches_exact": true,
+    "citation_audit_passes": true,
+    "code_and_data_availability_visible": true,
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diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/large_scale_delivery_audit_v1.json b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/large_scale_delivery_audit_v1.json
new file mode 100644
index 000000000..114fff03c
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+  "checks": {
+    "channel_support": true,
+    "external_gap": true,
+    "gauge_invariance": true,
+    "kernel_count": true,
+    "n2_excluded_before_production": true,
+    "reference_reproducibility": true,
+    "resolvent_residual": true
+  },
+  "configuration": {
+    "case_indices": [
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+      2
+    ],
+    "gaussian_samples": 2000,
+    "panel_size": 8,
+    "panels": 24,
+    "production": true,
+    "relative_shifts": [
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+    "seed": 20260728320
+  },
+  "descriptive_slope_per_particle": -0.08093438144112026,
+  "environment": {
+    "numpy": "2.3.5",
+    "platform": "macOS-15.6-arm64-arm-64bit",
+    "python": "3.12.11"
+  },
+  "excluded_small_case": {
+    "N": 2,
+    "accepted": false,
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+    "n_flux": 6,
+    "observed_rank": 12
+  },
+  "generated_utc": "2026-07-28T15:42:01.770489+00:00",
+  "npz_sha256": "c817a758fd03710483883840758a28ba2d5d9c74270a8f30ad71874a6336262c",
+  "result_branch": "deformed_geometric_eth",
+  "runtime_seconds": 267.24987595900166,
+  "version": "v3"
+}
\ No newline at end of file
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/matrix_element_geometric_eth_v3.npz b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/matrix_element_geometric_eth_v3.npz
new file mode 100644
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HcmV?d00001

diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/matrix_element_topology_theory_v3.json b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/matrix_element_topology_theory_v3.json
new file mode 100644
index 000000000..7f8ba3b95
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/matrix_element_topology_theory_v3.json
@@ -0,0 +1,30 @@
+{
+  "checks": {
+    "chern_branch": true,
+    "chern_isomorphism": true,
+    "gauge_R4": true,
+    "gauge_tensor": true,
+    "gram_reduction": true,
+    "wick_monte_carlo": true
+  },
+  "gauge_and_gram": {
+    "R4_error": 1.1102230246251565e-16,
+    "gram_spectrum_error": 6.661338147750939e-16,
+    "tensor_error": 3.3306690738754696e-15
+  },
+  "generated_utc": "2026-07-28T17:54:45.183871+00:00",
+  "passed": true,
+  "topology": {
+    "chern_after": -0.9999999999999991,
+    "chern_before": -0.9999999999999994,
+    "chern_error": 3.3306690738754696e-16,
+    "minimum_branch_margin": 3.0518857391907717
+  },
+  "version": "v3",
+  "wick": {
+    "A_left": 1.0850661625708886,
+    "B_right": 0.6469893742621016,
+    "maximum_absolute_error": 0.00937106043678515,
+    "relative_error": 0.007298791405822385
+  }
+}
\ No newline at end of file
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/physical_ensemble_v1.json b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/physical_ensemble_v1.json
new file mode 100644
index 000000000..4fbd4088f
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/physical_ensemble_v1.json
@@ -0,0 +1,49 @@
+{
+  "schema_version": 1,
+  "version": "v1",
+  "generated_utc": "2026-07-28T08:33:44.010905+00:00",
+  "physical_case": {
+    "N": 3,
+    "n": 10,
+    "D": 50,
+    "M": 170
+  },
+  "sample_count": 20000,
+  "seed": 20260728110,
+  "seed_blocks": 8,
+  "split": {
+    "train": 12000,
+    "validation": 4000,
+    "test": 4000,
+    "split_seed": 20260728111
+  },
+  "parent": {
+    "kernel_bandwidth": 5.782554623436307e-16,
+    "external_gap": 0.10667223401027637
+  },
+  "jacobi_parameters": {
+    "interior_dimension": 50,
+    "exponent": 120,
+    "plus_atoms": 0,
+    "minus_atoms": 0
+  },
+  "observed_exact_atoms": 0,
+  "checks": {
+    "registered_rank_is_50": true,
+    "parent_kernel_exact": true,
+    "parent_gap_open": true,
+    "all_active_ranks_are_full": true,
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index 000000000..877921d81
--- /dev/null
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@@ -0,0 +1,2 @@
+..............                                                           [100%]
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diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/pytest_v2.txt b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/pytest_v2.txt
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+..................................                                       [100%]
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diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/rank_scaling_v1.json b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/rank_scaling_v1.json
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+    },
+    {
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+      "role": "main_figure",
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+      "size_bytes": 332956
+    },
+    {
+      "path": "01_task_folder/task_05/script/output/figure_6_wick_factorization_v3.png",
+      "role": "main_figure",
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+      "size_bytes": 346911
+    },
+    {
+      "path": "01_task_folder/task_05/script/output/figure_7_topological_holonomy_v3.png",
+      "role": "main_figure",
+      "sha256": "4c19bc37413ea4cdbece1ef84023b505d3d279264e2107601907cb72d2d731ff",
+      "size_bytes": 289213
+    }
+  ],
+  "generated_utc": "2026-07-30T06:31:04.730833+00:00",
+  "headline": "Exact degeneracy turns quantum geometry into the signal.",
+  "paper": {
+    "page_count": 17,
+    "path": "01_task_folder/task_05/script/output/spectral_silence_and_geometric_chaos_v3.pdf",
+    "sha256": "a75377f76acd78eb3354e186a57933abdf11abbbe5e9a8abd43482ca8c4e05ad",
+    "size_bytes": 672204,
+    "title": "Spectral Silence and Geometric Chaos in an Exactly Degenerate Topological Manifold"
+  },
+  "release_id": "task05-geometric-chaos-v1",
+  "result_branches": {
+    "matrix_element": "deformed_geometric_eth",
+    "topology": "fixed_chern_deformed_holonomy"
+  },
+  "schema_version": 1,
+  "scientific_scope": [
+    "exact-degeneracy projector geometry",
+    "finite-rank local Jacobi universality",
+    "structured matrix-element and Wilson correlations"
+  ],
+  "verification": {
+    "article": "bash run_geometric_eth_topology_article_v3.sh",
+    "full": "bash run_full_recompute_v1.sh",
+    "quick": "bash run_quick_verify_v1.sh"
+  }
+}
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/spectral_silence_and_geometric_chaos_v2.pdf b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/spectral_silence_and_geometric_chaos_v2.pdf
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diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/spectral_silence_and_geometric_chaos_v3.pdf b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/spectral_silence_and_geometric_chaos_v3.pdf
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diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/spectral_silence_v2.json b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/spectral_silence_v2.json
new file mode 100644
index 000000000..505d729fd
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/spectral_silence_v2.json
@@ -0,0 +1,103 @@
+{
+  "schema_version": 2,
+  "version": "v2",
+  "generated_utc": "2026-07-28T11:27:53.666915+00:00",
+  "registered_seed": 20260728210,
+  "sample_counts": {
+    "structured_momenta": 24,
+    "structured_orbits": 12,
+    "per_positive_g": 4000,
+    "fixed_projector_per_alpha": 4000,
+    "rank_form_factor_requested": 500,
+    "rank_form_factor_actual": [
+      500,
+      500,
+      500,
+      500,
+      500,
+      500,
+      250
+    ],
+    "physical_test": 4000,
+    "haar_reference": 10000
+  },
+  "grids": {
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+      0.0,
+      0.02,
+      0.05,
+      0.1,
+      0.2,
+      0.4,
+      0.7,
+      1.0
+    ],
+    "alpha": [
+      0.0,
+      0.1,
+      0.2,
+      0.35,
+      0.5,
+      0.7,
+      0.85,
+      1.0
+    ],
+    "times": {
+      "minimum": 0.0,
+      "maximum": 3.0,
+      "points": 121
+    }
+  },
+  "physical_case": {
+    "N": 3,
+    "n": 10,
+    "D": 50,
+    "M": 170,
+    "kernel_bandwidth": 5.782554623436307e-16,
+    "external_gap": 0.10667223401027637
+  },
+  "structured_control": {
+    "minimum_active_rank": 50,
+    "maximum_distinct_eigenvalues": 10
+  },
+  "fixed_projector_control": {
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+    "gue_endpoint_gap_ratio": 0.598677371645903,
+    "maximum_projector_distance": 1.1483897216095898e-14,
+    "maximum_curvature_spectrum_error": 0.0
+  },
+  "finite_jacobi": {
+    "quadrature_order": 512,
+    "mass_error": 4.192202140984591e-13,
+    "orthogonality_error": 4.177769241664464e-13,
+    "atom_relation_error": 0.0,
+    "raw_atom_closure_error": 1.1368683772161603e-13
+  },
+  "inputs": {
+    "output/physical_ensemble_v1.npz": "cf44e830188f6a7252ff692c0db33ea3f2cd3ce604a37e31b49a80d37ad70652",
+    "output/physical_ensemble_v1.json": "f0f0c97483f66800b8da208fd3dad7259fc30a7650b7360060499f9326ad4000",
+    "output/covariance_model_v1.npz": "7581adc06ceeb6afb3d5bb5f58f1ca91a1ae9398e45dc09869751989f86a4836",
+    "output/covariance_model_v1.json": "7183934946be50deb9973755dc189360b9f8aaabcdbd7107860980b15ae859a0",
+    "output/rank_scaling_v1.npz": "0373a6b0ddef31ea0208f0acc3d6feee0bda372058eb2a0d689b0eed92cd4338",
+    "output/rank_scaling_v1.json": "46be556194eac79ff29017c9b969146e32b6e0a08a1407a6cfe4e2a924cf77e7"
+  },
+  "checks": {
+    "input_v1_artifacts_pass": true,
+    "exact_energy_silence": true,
+    "structured_control_full_rank": true,
+    "structured_control_multiplets": true,
+    "geometry_axis_full_rank": true,
+    "geometry_axis_exact_parent": true,
+    "fixed_projector_invariance": true,
+    "spectral_axis_resolved": true,
+    "finite_jacobi_mass_and_basis": true,
+    "atom_plateau_theorem": true
+  },
+  "all_checks_pass": true,
+  "runtime_seconds": 342.8376511250008,
+  "environment": {
+    "python": "3.12.11",
+    "numpy": "2.3.5",
+    "platform": "macOS-15.6-arm64-arm-64bit"
+  }
+}
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/statistical_analysis_v1.json b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/statistical_analysis_v1.json
new file mode 100644
index 000000000..1abe3e033
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/statistical_analysis_v1.json
@@ -0,0 +1,399 @@
+{
+  "schema_version": 1,
+  "version": "v1",
+  "generated_utc": "2026-07-28T08:35:27.297185+00:00",
+  "sources": {
+    "physical": "output/physical_ensemble_v1.npz",
+    "covariance": "output/covariance_model_v1.npz",
+    "scaling_json": "output/rank_scaling_v1.json",
+    "scaling_npz": "output/rank_scaling_v1.npz"
+  },
+  "bootstrap_replicates": 10000,
+  "kde_bandwidth": 0.025,
+  "bulk_fraction": 0.7,
+  "unfolding": "ensemble_cdf",
+  "physical_test_matrices": 4000,
+  "haar_matrices": 10000,
+  "deformed_matrices": 10000,
+  "ensemble_inference": {
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+        "units": 8,
+        "replicates": 10000,
+        "critical_value": 3.20338214267544
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+        "replicates": 10000,
+        "critical_value": 2.0712875866961724
+      }
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+    "deformed": {
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diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/statistical_analysis_v1.npz b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/statistical_analysis_v1.npz
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diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/topological_holonomy_delivery_audit_v3.json b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/topological_holonomy_delivery_audit_v3.json
new file mode 100644
index 000000000..19f498cbb
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/topological_holonomy_delivery_audit_v3.json
@@ -0,0 +1,72 @@
+{
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+    "checkpoint:output/topology_v3_checkpoints/N3_mesh20_twist_bundle_v3.npz": true,
+    "checkpoint:output/topology_v3_checkpoints/N4_mesh16_twist_bundle_v3.json": true,
+    "checkpoint:output/topology_v3_checkpoints/N4_mesh16_twist_bundle_v3.npz": true,
+    "checkpoint:output/topology_v3_checkpoints/N4_mesh20_twist_bundle_v3.json": true,
+    "checkpoint:output/topology_v3_checkpoints/N4_mesh20_twist_bundle_v3.npz": true,
+    "chern_fixed": true,
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+    "figure_png_hash": true,
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+    "registered_generator_seeds": true,
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+    "registered_sizes": true,
+    "result_npz_hash": true,
+    "runner_checks": true,
+    "size_0_commuting_control": true,
+    "size_0_cue_count": true,
+    "size_0_loop_shapes": true,
+    "size_0_seed_shapes": true,
+    "size_1_commuting_control": true,
+    "size_1_cue_count": true,
+    "size_1_loop_shapes": true,
+    "size_1_seed_shapes": true,
+    "supported_branch": true
+  },
+  "figure": {
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+    "pdf_sha256": "11e101309d975a61a3efedb1025c2552149c7f1a6f72433594f4adb1c0a16258",
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+  "passed": true,
+  "registered_meshes": [
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+    20
+  ],
+  "registered_sizes": [
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+  "result_branch": "fixed_chern_deformed_holonomy",
+  "result_sha256": "ff15e7cd2f947b43da5a5973bb82c50319b164877883d187c7c46b2a073823c6",
+  "version": "v3"
+}
\ No newline at end of file
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/topological_holonomy_mesh12_alias_audit_v3.json b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/topological_holonomy_mesh12_alias_audit_v3.json
new file mode 100644
index 000000000..c8f7745b8
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/topological_holonomy_mesh12_alias_audit_v3.json
@@ -0,0 +1,309 @@
+{
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+  "runtime_seconds": 478.42586700000174,
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+}
\ No newline at end of file
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/topological_holonomy_v3.json b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/topological_holonomy_v3.json
new file mode 100644
index 000000000..f57fe74e7
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/topological_holonomy_v3.json
@@ -0,0 +1,332 @@
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+      "primary_mesh": 16,
+      "rank": 25
+    }
+  ],
+  "version": "v3"
+}
\ No newline at end of file
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/topological_holonomy_v3.npz b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/topological_holonomy_v3.npz
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diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/requirements.txt b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/requirements.txt
new file mode 100644
index 000000000..261b165e5
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/requirements.txt
@@ -0,0 +1,7 @@
+numpy==2.3.5
+scipy==1.16.3
+matplotlib==3.10.8
+Pillow==12.0.0
+pypdf==6.7.0
+pytest==9.0.2
+PyYAML==6.0.3
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/run_covariance_model_v1.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/run_covariance_model_v1.py
new file mode 100644
index 000000000..615afb2c1
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/run_covariance_model_v1.py
@@ -0,0 +1,458 @@
+#!/usr/bin/env python3
+"""Fit and test a held-out covariance-deformed Geometric-ETH model."""
+
+from __future__ import annotations
+
+import argparse
+import json
+import platform
+import time
+from datetime import datetime, timezone
+from pathlib import Path
+from typing import Any
+
+import numpy as np
+
+from lgeth.grassmann import (
+    coordinate_participation,
+    covariance_deformed_rows,
+    frame_overlap,
+    haar_frame_overlap_mean,
+    polarization_imbalance,
+    principal_angles,
+    regularize_covariance,
+)
+from lgeth.jacobi import (
+    canonical_channel_form,
+    normalized_curvature,
+    sample_jacobi_compression,
+)
+from lgeth.statistics import bulk_gap_ratio_per_spectrum, histogram_l1
+
+
+VERSION = "v1"
+REGISTERED_DIAGNOSTIC_ROWS = 1_024
+REGISTERED_MODEL_SAMPLES = 10_000
+CANDIDATE_FLOORS = (0.002, 0.005, 0.01, 0.02, 0.05)
+HISTOGRAM_EDGES = np.linspace(-1.0, 1.0, 161)
+
+
+def _channel(
+    coefficients: np.ndarray,
+    channel_basis: np.ndarray,
+    tangent_gram: np.ndarray,
+) -> np.ndarray:
+    norm_squared = float(coefficients @ tangent_gram @ coefficients)
+    if norm_squared <= 0.0:
+        raise RuntimeError("cached tangent has zero many-body norm")
+    return (
+        np.tensordot(coefficients, channel_basis, axes=(0, 0))
+        / np.sqrt(norm_squared)
+    )
+
+
+def _physical_rows(
+    arrays: Any,
+    indices: np.ndarray,
+):
+    channel_basis = arrays["channel_basis"]
+    tangent_gram = arrays["tangent_gram"]
+    coefficients_v = arrays["tangent_coefficients_v"]
+    coefficients_w = arrays["tangent_coefficients_w"]
+    for raw_index in indices:
+        index = int(raw_index)
+        channel_v = _channel(
+            coefficients_v[index], channel_basis, tangent_gram
+        )
+        channel_w = _channel(
+            coefficients_w[index], channel_basis, tangent_gram
+        )
+        yield normalized_curvature(
+            channel_v,
+            channel_w,
+            rtol=1e-10,
+        ).Y
+
+
+def _training_geometry(
+    arrays: Any,
+    indices: np.ndarray,
+) -> tuple[np.ndarray, dict[str, np.ndarray | float]]:
+    dimension = int(arrays["channel_basis"].shape[2] * 2)
+    rank = int(arrays["normalized_spectra"].shape[1])
+    mean_projector = np.zeros((dimension, dimension), dtype=complex)
+    per_block = np.zeros((8, dimension, dimension), dtype=complex)
+    block_count = np.zeros(8, dtype=int)
+    participation = np.empty(indices.size, dtype=float)
+    polarization = np.empty(indices.size, dtype=float)
+    frame_overlaps = np.empty(indices.size // 2, dtype=float)
+    angles: list[np.ndarray] = []
+    previous = None
+    pair = 0
+    second_sum = 0.0
+    fourth_sum = 0.0
+    entry_count = 0
+    for position, (index, rows) in enumerate(
+        zip(indices, _physical_rows(arrays, indices), strict=True)
+    ):
+        projector = rows.conj().T @ rows
+        mean_projector += projector
+        block = int(arrays["seed_block"][int(index)])
+        per_block[block] += projector
+        block_count[block] += 1
+        participation[position] = coordinate_participation(rows)["fraction"]
+        polarization[position] = polarization_imbalance(rows)
+        squared = np.abs(rows).ravel() ** 2
+        second_sum += float(np.sum(squared))
+        fourth_sum += float(np.sum(squared * squared))
+        entry_count += squared.size
+        if position % 2 == 0:
+            previous = rows
+        elif previous is not None:
+            frame_overlaps[pair] = frame_overlap(previous, rows)
+            angles.append(principal_angles(previous, rows))
+            previous = None
+            pair += 1
+    mean_projector /= indices.size
+    for block in range(8):
+        if block_count[block]:
+            per_block[block] /= block_count[block]
+    isotropic = (rank / dimension) * np.eye(dimension)
+    anisotropy = float(
+        np.linalg.norm(mean_projector - isotropic)
+        / np.linalg.norm(isotropic)
+    )
+    principal = np.concatenate(angles) if angles else np.empty(0)
+    second = second_sum / entry_count
+    fourth_ratio = (fourth_sum / entry_count) / (second * second)
+    diagnostics: dict[str, np.ndarray | float] = {
+        "mean_projector_by_seed_block": per_block,
+        "seed_block_counts": block_count,
+        "participation": participation,
+        "polarization": polarization,
+        "frame_overlaps": frame_overlaps,
+        "principal_angles": principal,
+        "relative_frobenius_anisotropy": anisotropy,
+        "entry_fourth_ratio": fourth_ratio,
+    }
+    return mean_projector, diagnostics
+
+
+def _spectra_from_deformed(
+    rank: int,
+    covariance: np.ndarray,
+    floor: float,
+    samples: int,
+    seed: int,
+    progress_label: str | None = None,
+) -> np.ndarray:
+    dimension = covariance.shape[0]
+    form = canonical_channel_form(dimension // 2)
+    spectra = np.empty((samples, rank), dtype=np.float32)
+    rng = np.random.default_rng(seed)
+    for index, rows in enumerate(
+        covariance_deformed_rows(
+            rank,
+            covariance,
+            samples,
+            rng,
+            floor_fraction=floor,
+        )
+    ):
+        omega = rows @ form @ rows.conj().T
+        spectra[index] = np.linalg.eigvalsh(
+            0.5 * (omega + omega.conj().T)
+        )
+        if (
+            progress_label is not None
+            and (index + 1) % max(1, samples // 4) == 0
+        ):
+            print(
+                f"{progress_label}: {index + 1}/{samples}",
+                flush=True,
+            )
+    return spectra
+
+
+def _comparison(
+    physical: np.ndarray,
+    haar: np.ndarray,
+    deformed: np.ndarray,
+) -> dict[str, Any]:
+    haar_l1 = histogram_l1(physical, haar, HISTOGRAM_EDGES)
+    deformed_l1 = histogram_l1(physical, deformed, HISTOGRAM_EDGES)
+    physical_gap = bulk_gap_ratio_per_spectrum(physical)
+    haar_gap = bulk_gap_ratio_per_spectrum(haar)
+    deformed_gap = bulk_gap_ratio_per_spectrum(deformed)
+    moments = {}
+    for order in (2, 4, 6, 8):
+        moments[str(order)] = {
+            "physical": float(np.mean(physical.astype(float) ** order)),
+            "haar": float(np.mean(haar.astype(float) ** order)),
+            "deformed": float(np.mean(deformed.astype(float) ** order)),
+        }
+    improvement = (haar_l1 - deformed_l1) / haar_l1
+    gap_difference = abs(
+        float(np.mean(physical_gap)) - float(np.mean(deformed_gap))
+    )
+    if improvement >= 0.25 and gap_difference < 0.025:
+        branch = "leading_covariance_capture"
+    elif improvement > 0.05:
+        branch = "partial_capture"
+    else:
+        branch = "no_held_out_improvement"
+    return {
+        "density_l1": {
+            "physical_vs_haar": haar_l1,
+            "physical_vs_deformed": deformed_l1,
+            "relative_improvement": improvement,
+        },
+        "mean_gap_ratio": {
+            "physical": float(np.mean(physical_gap)),
+            "haar": float(np.mean(haar_gap)),
+            "deformed": float(np.mean(deformed_gap)),
+            "physical_deformed_absolute_difference": gap_difference,
+        },
+        "moments": moments,
+        "result_branch": branch,
+    }
+
+
+def run(
+    physical_npz: Path,
+    output_json: Path,
+    output_npz: Path,
+    diagnostic_rows: int = REGISTERED_DIAGNOSTIC_ROWS,
+    model_samples: int = REGISTERED_MODEL_SAMPLES,
+) -> dict[str, Any]:
+    """Fit on train, choose the floor on validation, and report only test."""
+
+    started = time.perf_counter()
+    row_count = int(diagnostic_rows)
+    sample_count = int(model_samples)
+    if row_count < 16 or sample_count < 16:
+        raise ValueError("require at least 16 diagnostic rows and spectra")
+    with np.load(physical_npz) as arrays:
+        train_all = arrays["train_indices"]
+        validation_indices = arrays["validation_indices"]
+        test_indices = arrays["test_indices"]
+        if row_count > train_all.size:
+            raise ValueError("diagnostic_rows exceeds the training split")
+        diagnostic_indices = train_all[:row_count]
+        mean_projector, geometry = _training_geometry(
+            arrays,
+            diagnostic_indices,
+        )
+        rank = int(arrays["normalized_spectra"].shape[1])
+        dimension = int(mean_projector.shape[0])
+        physical_validation = arrays["normalized_spectra"][
+            validation_indices
+        ].astype(float)
+        physical_test = arrays["normalized_spectra"][test_indices].astype(
+            float
+        )
+    validation_samples = min(max(32, sample_count // 20), 512)
+    validation_scores: dict[str, dict[str, float]] = {}
+    validation_spectra = np.empty(
+        (len(CANDIDATE_FLOORS), validation_samples, rank),
+        dtype=np.float32,
+    )
+    for floor_index, floor in enumerate(CANDIDATE_FLOORS):
+        candidate = _spectra_from_deformed(
+            rank,
+            mean_projector,
+            floor,
+            validation_samples,
+            seed=20260728200,
+        )
+        validation_spectra[floor_index] = candidate
+        density_l1 = histogram_l1(
+            physical_validation,
+            candidate,
+            HISTOGRAM_EDGES,
+        )
+        physical_gap = float(
+            np.mean(bulk_gap_ratio_per_spectrum(physical_validation))
+        )
+        candidate_gap = float(
+            np.mean(bulk_gap_ratio_per_spectrum(candidate))
+        )
+        gap_difference = abs(physical_gap - candidate_gap)
+        validation_scores[str(floor)] = {
+            "density_l1": density_l1,
+            "gap_ratio_difference": gap_difference,
+            "selection_score": density_l1 + 0.5 * gap_difference,
+        }
+    selected_floor = min(
+        CANDIDATE_FLOORS,
+        key=lambda floor: validation_scores[str(floor)][
+            "selection_score"
+        ],
+    )
+    haar_spectra = sample_jacobi_compression(
+        rank,
+        dimension // 2,
+        sample_count,
+        seed=20260728210,
+    ).astype(np.float32)
+    print(f"Haar reference: {sample_count}/{sample_count}", flush=True)
+    deformed_spectra = _spectra_from_deformed(
+        rank,
+        mean_projector,
+        selected_floor,
+        sample_count,
+        seed=20260728220,
+        progress_label="deformed model",
+    )
+    comparison = _comparison(
+        physical_test,
+        haar_spectra,
+        deformed_spectra,
+    )
+    regularized = regularize_covariance(
+        mean_projector,
+        floor_fraction=selected_floor,
+    )
+    covariance_eigenvalues = np.linalg.eigvalsh(regularized)
+    frame_baseline = haar_frame_overlap_mean(rank, dimension)
+    geometry_summary = {
+        "relative_frobenius_anisotropy": float(
+            geometry["relative_frobenius_anisotropy"]
+        ),
+        "mean_participation_fraction": float(
+            np.mean(geometry["participation"])
+        ),
+        "mean_absolute_polarization": float(
+            np.mean(np.abs(geometry["polarization"]))
+        ),
+        "mean_frame_overlap": float(np.mean(geometry["frame_overlaps"])),
+        "haar_frame_overlap": frame_baseline,
+        "mean_principal_angle": float(
+            np.mean(geometry["principal_angles"])
+        ),
+        "entry_fourth_ratio": float(geometry["entry_fourth_ratio"]),
+    }
+    checks = {
+        "train_validation_test_disjoint": bool(
+            np.intersect1d(diagnostic_indices, validation_indices).size == 0
+            and np.intersect1d(diagnostic_indices, test_indices).size == 0
+            and np.intersect1d(validation_indices, test_indices).size == 0
+        ),
+        "covariance_fit_uses_requested_training_rows": (
+            diagnostic_indices.size == row_count
+        ),
+        "all_candidate_floors_scored": (
+            len(validation_scores) == len(CANDIDATE_FLOORS)
+        ),
+        "selected_floor_is_registered": selected_floor in CANDIDATE_FLOORS,
+        "model_shapes_match": bool(
+            haar_spectra.shape == (sample_count, rank)
+            and deformed_spectra.shape == (sample_count, rank)
+        ),
+        "all_spectra_bounded": bool(
+            np.max(np.abs(haar_spectra)) <= 1.0 + 2e-7
+            and np.max(np.abs(deformed_spectra)) <= 1.0 + 2e-7
+        ),
+        "branch_registered": comparison["result_branch"]
+        in {
+            "leading_covariance_capture",
+            "partial_capture",
+            "no_held_out_improvement",
+        },
+    }
+    result = {
+        "schema_version": 1,
+        "version": VERSION,
+        "generated_utc": datetime.now(timezone.utc).isoformat(),
+        "physical_source": str(physical_npz),
+        "rank": rank,
+        "ambient_channel_dimension": dimension,
+        "diagnostic_training_rows": row_count,
+        "validation_model_samples_per_floor": validation_samples,
+        "haar_samples": sample_count,
+        "deformed_samples": sample_count,
+        "candidate_floors": list(CANDIDATE_FLOORS),
+        "validation_scores": validation_scores,
+        "selected_floor": selected_floor,
+        "training_geometry": geometry_summary,
+        "held_out_test": comparison,
+        "checks": checks,
+        "all_checks_pass": bool(all(checks.values())),
+        "runtime_seconds": time.perf_counter() - started,
+        "environment": {
+            "python": platform.python_version(),
+            "numpy": np.__version__,
+            "platform": platform.platform(),
+        },
+    }
+    output_json.parent.mkdir(parents=True, exist_ok=True)
+    output_npz.parent.mkdir(parents=True, exist_ok=True)
+    output_json.write_text(
+        json.dumps(result, indent=2) + "\n",
+        encoding="utf-8",
+    )
+    np.savez_compressed(
+        output_npz,
+        mean_projector=mean_projector,
+        covariance_eigenvalues=covariance_eigenvalues,
+        diagnostic_indices=diagnostic_indices,
+        validation_indices=validation_indices,
+        test_indices=test_indices,
+        validation_spectra=validation_spectra,
+        candidate_floors=np.asarray(CANDIDATE_FLOORS),
+        haar_spectra=haar_spectra,
+        deformed_spectra=deformed_spectra,
+        mean_projector_by_seed_block=geometry[
+            "mean_projector_by_seed_block"
+        ],
+        seed_block_counts=geometry["seed_block_counts"],
+        physical_participation=geometry["participation"],
+        physical_polarization=geometry["polarization"],
+        physical_frame_overlaps=geometry["frame_overlaps"],
+        physical_principal_angles=geometry["principal_angles"],
+    )
+    return result
+
+
+def main() -> None:
+    parser = argparse.ArgumentParser()
+    parser.add_argument(
+        "--physical-npz",
+        type=Path,
+        default=Path("output/physical_ensemble_v1.npz"),
+    )
+    parser.add_argument(
+        "--output-json",
+        type=Path,
+        default=Path("output/covariance_model_v1.json"),
+    )
+    parser.add_argument(
+        "--output-npz",
+        type=Path,
+        default=Path("output/covariance_model_v1.npz"),
+    )
+    parser.add_argument(
+        "--diagnostic-rows",
+        type=int,
+        default=REGISTERED_DIAGNOSTIC_ROWS,
+    )
+    parser.add_argument(
+        "--model-samples",
+        type=int,
+        default=REGISTERED_MODEL_SAMPLES,
+    )
+    args = parser.parse_args()
+    result = run(
+        args.physical_npz,
+        args.output_json,
+        args.output_npz,
+        diagnostic_rows=args.diagnostic_rows,
+        model_samples=args.model_samples,
+    )
+    print(json.dumps(result, indent=2))
+    if not result["all_checks_pass"]:
+        raise SystemExit("covariance-model audit failed")
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/run_full_recompute_v1.sh b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/run_full_recompute_v1.sh
new file mode 100755
index 000000000..5d730d47d
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/run_full_recompute_v1.sh
@@ -0,0 +1,11 @@
+#!/usr/bin/env bash
+set -euo pipefail
+
+SCRIPT_DIR="$(cd "$(dirname "${BASH_SOURCE[0]}")" && pwd)"
+cd "${SCRIPT_DIR}"
+
+bash run_large_scale_article_v1.sh
+bash run_spectral_silence_article_v2.sh
+FULL_RECOMPUTE=1 bash run_geometric_eth_topology_article_v3.sh
+python make_release_manifest_v1.py
+python verify_release_contract_v1.py
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/run_geometric_eth_topology_article_v3.sh b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/run_geometric_eth_topology_article_v3.sh
new file mode 100755
index 000000000..a91bb88a6
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/run_geometric_eth_topology_article_v3.sh
@@ -0,0 +1,41 @@
+#!/usr/bin/env bash
+set -euo pipefail
+
+SCRIPT_DIR="$(cd "$(dirname "${BASH_SOURCE[0]}")" && pwd)"
+REPO_ROOT="$(cd "${SCRIPT_DIR}/../../.." && pwd)"
+ARTICLE_DIR="${REPO_ROOT}/overleaf_sync/geometric_eth_large_scale"
+export SOURCE_DATE_EPOCH="${SOURCE_DATE_EPOCH:-1785283200}"
+
+cd "${SCRIPT_DIR}"
+
+if [[ "${FULL_RECOMPUTE:-0}" == "1" ]]; then
+  python run_matrix_element_geometric_eth_v3.py
+  python run_topological_holonomy_v3.py --workers "${TOPOLOGY_WORKERS:-4}"
+  python make_matrix_element_geometric_eth_figure_v3.py
+  python verify_matrix_element_geometric_eth_v3.py
+  python make_topological_holonomy_figure_v3.py
+  python verify_topological_holonomy_v3.py
+  python make_geometric_eth_topology_assets_v3.py
+  python verify_matrix_element_topology_theory_v3.py
+fi
+
+if [[ "${VALIDATE_CITATIONS:-0}" == "1" ]]; then
+  python validate_citations_v1.py
+fi
+cp output/figure_6_wick_factorization_v3.pdf \
+  "${ARTICLE_DIR}/figures/figure_6_wick_factorization_v3.pdf"
+cp output/figure_7_topological_holonomy_v3.pdf \
+  "${ARTICLE_DIR}/figures/figure_7_topological_holonomy_v3.pdf"
+
+cd "${ARTICLE_DIR}"
+latexmk -C main.tex
+latexmk -pdf -interaction=nonstopmode -halt-on-error main.tex
+
+cd "${SCRIPT_DIR}"
+python verify_geometric_eth_topology_article_v3.py
+PYTHONPATH="${SCRIPT_DIR}${PYTHONPATH:+:${PYTHONPATH}}" python -m pytest -q \
+  tests/test_geometric_eth_topology_assets_v3.py \
+  tests/test_matrix_element_topology_theory_v3.py \
+  tests/test_geometric_eth_topology_article_v3.py
+python make_release_manifest_v1.py
+python verify_release_contract_v1.py
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/run_large_scale_article_v1.sh b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/run_large_scale_article_v1.sh
new file mode 100755
index 000000000..879ca3175
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/run_large_scale_article_v1.sh
@@ -0,0 +1,38 @@
+#!/usr/bin/env bash
+set -euo pipefail
+
+SCRIPT_DIR="$(cd "$(dirname "${BASH_SOURCE[0]}")" && pwd)"
+REPO_ROOT="$(cd "$SCRIPT_DIR/../../.." && pwd)"
+ARTICLE_DIR="$REPO_ROOT/overleaf_sync/geometric_eth_large_scale"
+OUTPUT_DIR="$SCRIPT_DIR/output"
+
+cd "$SCRIPT_DIR"
+python run_physical_ensemble_v1.py
+python run_covariance_model_v1.py
+python run_rank_scaling_v1.py
+python run_statistical_analysis_v1.py
+python make_large_scale_figures_v1.py
+python validate_citations_v1.py
+
+for stem in \
+  figure_1_physical_law_v1 \
+  figure_2_scale_hierarchy_v1 \
+  figure_3_atom_crossover_v1 \
+  figure_4_finite_size_v1 \
+  figure_5_covariance_mechanism_v1
+do
+  cp "$OUTPUT_DIR/$stem.pdf" "$ARTICLE_DIR/figures/$stem.pdf"
+done
+cp "$OUTPUT_DIR/generated_numbers_v1.tex" \
+  "$ARTICLE_DIR/generated/generated_numbers_v1.tex"
+cp "$OUTPUT_DIR/generated_tables_v1.tex" \
+  "$ARTICLE_DIR/generated/generated_tables_v1.tex"
+
+cd "$ARTICLE_DIR"
+latexmk -pdf -interaction=nonstopmode -halt-on-error main.tex
+cp main.pdf \
+  "$OUTPUT_DIR/from_local_repulsion_to_global_geometry_v1.pdf"
+
+cd "$SCRIPT_DIR"
+python -m pytest -q tests | tee "$OUTPUT_DIR/pytest_v1.txt"
+python verify_large_scale_article_v1.py
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/run_matrix_element_geometric_eth_v3.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/run_matrix_element_geometric_eth_v3.py
new file mode 100644
index 000000000..2850f4737
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/run_matrix_element_geometric_eth_v3.py
@@ -0,0 +1,575 @@
+#!/usr/bin/env python3
+"""Run gauge-invariant four-channel tests on a genuine many-body sequence."""
+
+from __future__ import annotations
+
+import argparse
+import hashlib
+import json
+import platform
+import time
+from dataclasses import asdict
+from datetime import datetime, timezone
+from pathlib import Path
+from typing import Any
+
+import numpy as np
+
+from lgeth.lattice import build_kapit_laughlin_parent
+from lgeth.manybody_response import (
+    SiteResponseCache,
+    audit_unregistered_small_case,
+    build_site_response_cache,
+    registered_fixed_two_qh_cases,
+    solve_kernel_frame,
+)
+from lgeth.wick_channels import (
+    assemble_channels,
+    covariance_matched_wick,
+    fourier_density_panel,
+    gaussian_r4_reference,
+    local_density_panels,
+)
+
+
+VERSION = "v3"
+SCRIPT_ROOT = Path(__file__).resolve().parent
+OUTPUT_ROOT = SCRIPT_ROOT / "output"
+OUTPUT_JSON = OUTPUT_ROOT / "matrix_element_geometric_eth_v3.json"
+OUTPUT_NPZ = OUTPUT_ROOT / "matrix_element_geometric_eth_v3.npz"
+CHECKPOINT_ROOT = OUTPUT_ROOT / "matrix_element_v3_checkpoints"
+REGISTERED_PANELS = 24
+REGISTERED_PANEL_SIZE = 8
+REGISTERED_GAUSSIAN_SAMPLES = 2_000
+REGISTERED_SEED = 20260728320
+RELATIVE_SHIFTS = (1e-3, 5e-4)
+
+
+def _sha256_file(path: Path) -> str:
+    digest = hashlib.sha256()
+    with path.open("rb") as handle:
+        for chunk in iter(lambda: handle.read(1 << 20), b""):
+            digest.update(chunk)
+    return digest.hexdigest()
+
+
+def _json_hash(payload: dict[str, Any]) -> str:
+    encoded = json.dumps(
+        payload,
+        sort_keys=True,
+        separators=(",", ":"),
+    ).encode("utf-8")
+    return hashlib.sha256(encoded).hexdigest()
+
+
+def _atomic_json(path: Path, payload: dict[str, Any]) -> None:
+    path.parent.mkdir(parents=True, exist_ok=True)
+    temporary = path.with_suffix(path.suffix + ".tmp")
+    temporary.write_text(
+        json.dumps(payload, indent=2, sort_keys=True),
+        encoding="utf-8",
+    )
+    temporary.replace(path)
+
+
+def _atomic_npz(path: Path, **arrays: np.ndarray) -> None:
+    path.parent.mkdir(parents=True, exist_ok=True)
+    temporary = path.with_suffix(path.suffix + ".tmp")
+    with temporary.open("wb") as handle:
+        np.savez_compressed(handle, **arrays)
+    temporary.replace(path)
+
+
+def _checkpoint_identity(case) -> dict[str, Any]:
+    sources = (
+        SCRIPT_ROOT / "lgeth" / "manybody_response.py",
+        SCRIPT_ROOT / "lgeth" / "lattice.py",
+        SCRIPT_ROOT / "lgeth" / "combinatorics.py",
+    )
+    return {
+        "version": VERSION,
+        "case": asdict(case),
+        "relative_shifts": list(RELATIVE_SHIFTS),
+        "sources": {
+            str(path.relative_to(SCRIPT_ROOT)): _sha256_file(path)
+            for path in sources
+        },
+        "numpy": np.__version__,
+    }
+
+
+def _checkpoint_paths(
+    checkpoint_dir: Path,
+    N: int,
+) -> tuple[Path, Path]:
+    stem = checkpoint_dir / f"N{int(N)}_site_response_v3"
+    return stem.with_suffix(".json"), stem.with_suffix(".npz")
+
+
+def _load_checkpoint(
+    checkpoint_dir: Path,
+    case,
+) -> tuple[SiteResponseCache, dict[str, Any]] | None:
+    metadata_path, arrays_path = _checkpoint_paths(checkpoint_dir, case.N)
+    if not metadata_path.exists() or not arrays_path.exists():
+        return None
+    metadata = json.loads(metadata_path.read_text(encoding="utf-8"))
+    identity = _checkpoint_identity(case)
+    if metadata.get("identity_hash") != _json_hash(identity):
+        return None
+    if metadata.get("identity") != identity:
+        return None
+    if not all(metadata.get("checks", {}).values()):
+        return None
+    with np.load(arrays_path, allow_pickle=False) as arrays:
+        cache = SiteResponseCache(
+            case=case,
+            site_indices=tuple(
+                int(value) for value in arrays["site_indices"]
+            ),
+            solutions=np.asarray(arrays["solutions"], dtype=complex),
+            tangent_gram=np.asarray(arrays["tangent_gram"]),
+            external_gap=float(metadata["external_gap"]),
+            shift_values=tuple(
+                float(value) for value in metadata["shift_values"]
+            ),
+            maximum_relative_residual=float(
+                metadata["maximum_relative_residual"]
+            ),
+            maximum_shift_difference=float(
+                metadata["maximum_shift_difference"]
+            ),
+            maximum_kernel_leakage=float(
+                metadata["maximum_kernel_leakage"]
+            ),
+        )
+    return cache, metadata
+
+
+def _build_checkpoint(
+    checkpoint_dir: Path,
+    case,
+    seed: int,
+) -> tuple[SiteResponseCache, dict[str, Any]]:
+    started = time.perf_counter()
+    system = build_kapit_laughlin_parent(
+        case.N,
+        case.n_flux,
+        case.theta_x,
+        case.theta_y,
+    )
+    kernel = solve_kernel_frame(system, case, seed=seed)
+    cache = build_site_response_cache(
+        system,
+        kernel,
+        relative_shifts=RELATIVE_SHIFTS,
+    )
+    checks = {
+        "kernel_count": kernel.observed_rank == case.expected_rank,
+        "external_gap": kernel.external_gap > 1e-8,
+        "kernel_residual": kernel.residual_norm
+        < (1e-8 if kernel.method == "dense" else 5e-7),
+        "kernel_orthonormality": kernel.orthonormality_error < 1e-9,
+        "resolvent_residual": cache.maximum_relative_residual < 2e-3,
+        "resolvent_shift_stability": cache.maximum_shift_difference < 5e-2,
+        "kernel_leakage": cache.maximum_kernel_leakage < 1e-7,
+    }
+    identity = _checkpoint_identity(case)
+    metadata = {
+        "identity": identity,
+        "identity_hash": _json_hash(identity),
+        "case": asdict(case),
+        "basis_dimension": system.basis.dimension,
+        "physical_sites": system.orbitals.shape[0],
+        "lattice_length": system.length,
+        "kernel_method": kernel.method,
+        "observed_rank": kernel.observed_rank,
+        "external_gap": kernel.external_gap,
+        "kernel_residual_norm": kernel.residual_norm,
+        "kernel_orthonormality_error": kernel.orthonormality_error,
+        "shift_values": list(cache.shift_values),
+        "maximum_relative_residual": cache.maximum_relative_residual,
+        "maximum_shift_difference": cache.maximum_shift_difference,
+        "maximum_kernel_leakage": cache.maximum_kernel_leakage,
+        "runtime_seconds": time.perf_counter() - started,
+        "checks": checks,
+    }
+    if not all(checks.values()):
+        raise RuntimeError(
+            f"many-body response checkpoint failed for N={case.N}: {checks}"
+        )
+    metadata_path, arrays_path = _checkpoint_paths(
+        checkpoint_dir,
+        case.N,
+    )
+    _atomic_npz(
+        arrays_path,
+        site_indices=np.asarray(cache.site_indices, dtype=np.int16),
+        solutions=cache.solutions,
+        tangent_gram=cache.tangent_gram,
+    )
+    metadata["arrays_sha256"] = _sha256_file(arrays_path)
+    _atomic_json(metadata_path, metadata)
+    return cache, metadata
+
+
+def _seeded_unitary(dimension: int, seed: int) -> np.ndarray:
+    rng = np.random.default_rng(int(seed))
+    matrix = rng.normal(size=(dimension, dimension))
+    matrix = matrix + 1j * rng.normal(size=matrix.shape)
+    unitary, _ = np.linalg.qr(matrix)
+    return unitary
+
+
+def _gauge_invariance_error(
+    channels: np.ndarray,
+    seed: int,
+) -> float:
+    values = np.asarray(channels, dtype=complex)
+    reference = covariance_matched_wick(values).R4
+    label = _seeded_unitary(values.shape[0], seed)
+    target = _seeded_unitary(values.shape[2], seed + 1)
+    rng = np.random.default_rng(seed + 2)
+    external_phases = np.exp(
+        2j * np.pi * rng.random(values.shape[1])
+    )
+    transformed = np.einsum(
+        "mn,a,naj,jk->mak",
+        label,
+        external_phases,
+        values,
+        target,
+        optimize=True,
+    )
+    observed = covariance_matched_wick(transformed).R4
+    return abs(observed - reference)
+
+
+def _pooled_spectrum(spectra: list[np.ndarray]) -> np.ndarray:
+    if not spectra:
+        raise ValueError("cannot pool an empty covariance spectrum")
+    maximum = max(values.size for values in spectra)
+    padded = np.zeros((len(spectra), maximum), dtype=float)
+    for index, values in enumerate(spectra):
+        normalized = np.asarray(values, dtype=float)
+        normalized = normalized / np.sum(normalized)
+        padded[index, -normalized.size :] = normalized
+    pooled = np.mean(padded, axis=0)
+    return pooled[pooled > 1e-14 * np.max(pooled)]
+
+
+def _case_statistics(
+    cache: SiteResponseCache,
+    metadata: dict[str, Any],
+    panels: int,
+    gaussian_samples: int,
+    seed: int,
+) -> tuple[dict[str, Any], dict[str, np.ndarray]]:
+    length = int(metadata["lattice_length"])
+    panel_coefficients = local_density_panels(
+        length=length,
+        panel_size=REGISTERED_PANEL_SIZE,
+        panels=panels,
+        seed=seed,
+    )
+    physical_R4 = np.empty(panels, dtype=float)
+    A_left = np.empty(panels, dtype=float)
+    B_right = np.empty(panels, dtype=float)
+    condition = np.empty(panels, dtype=float)
+    left_spectra: list[np.ndarray] = []
+    right_spectra: list[np.ndarray] = []
+    first_channels: np.ndarray | None = None
+    for panel in range(panels):
+        channels = assemble_channels(cache, panel_coefficients[panel])
+        if first_channels is None:
+            first_channels = channels
+        result = covariance_matched_wick(channels)
+        physical_R4[panel] = result.R4
+        A_left[panel] = result.A_left
+        B_right[panel] = result.B_right
+        condition[panel] = (
+            result.channel_covariance_eigenvalues[-1]
+            / result.channel_covariance_eigenvalues[0]
+        )
+        left_spectra.append(result.left_eigenvalues)
+        right_spectra.append(result.right_eigenvalues)
+    if first_channels is None:
+        raise RuntimeError("no physical operator panels were evaluated")
+    structured_channels = assemble_channels(
+        cache,
+        fourier_density_panel(length, REGISTERED_PANEL_SIZE),
+    )
+    structured = covariance_matched_wick(structured_channels)
+    pooled_left = _pooled_spectrum(left_spectra)
+    pooled_right = _pooled_spectrum(right_spectra)
+    reproducibility_first = gaussian_r4_reference(
+        pooled_left,
+        pooled_right,
+        REGISTERED_PANEL_SIZE,
+        samples=min(16, gaussian_samples),
+        seed=seed + 100,
+    )
+    reproducibility_second = gaussian_r4_reference(
+        pooled_left,
+        pooled_right,
+        REGISTERED_PANEL_SIZE,
+        samples=min(16, gaussian_samples),
+        seed=seed + 100,
+    )
+    reference = gaussian_r4_reference(
+        pooled_left,
+        pooled_right,
+        REGISTERED_PANEL_SIZE,
+        samples=gaussian_samples,
+        seed=seed + 200,
+    )
+    quantiles = np.quantile(reference, [0.025, 0.5, 0.975])
+    case_checks = dict(metadata["checks"])
+    case_checks.update(
+        {
+            "channel_support": bool(np.all(np.isfinite(condition))),
+            "gauge_invariance": _gauge_invariance_error(
+                first_channels,
+                seed + 300,
+            )
+            < 2e-9,
+            "reference_reproducibility": bool(
+                np.array_equal(
+                    reproducibility_first,
+                    reproducibility_second,
+                )
+            ),
+        }
+    )
+    summary = {
+        "N": cache.case.N,
+        "n_flux": cache.case.n_flux,
+        "rank": cache.case.expected_rank,
+        "basis_dimension": metadata["basis_dimension"],
+        "physical_sites": metadata["physical_sites"],
+        "lattice_length": length,
+        "kernel_method": metadata["kernel_method"],
+        "external_gap": metadata["external_gap"],
+        "kernel_residual_norm": metadata["kernel_residual_norm"],
+        "kernel_orthonormality_error": metadata[
+            "kernel_orthonormality_error"
+        ],
+        "maximum_relative_residual": metadata[
+            "maximum_relative_residual"
+        ],
+        "maximum_shift_difference": metadata[
+            "maximum_shift_difference"
+        ],
+        "maximum_kernel_leakage": metadata[
+            "maximum_kernel_leakage"
+        ],
+        "physical_R4": physical_R4.tolist(),
+        "physical_R4_median": float(np.median(physical_R4)),
+        "physical_R4_interval": np.quantile(
+            physical_R4,
+            [0.025, 0.975],
+        ).tolist(),
+        "structured_R4": structured.R4,
+        "gaussian_R4_interval": quantiles.tolist(),
+        "physical_excess": float(np.median(physical_R4) - quantiles[1]),
+        "A_left_median": float(np.median(A_left)),
+        "B_right_median": float(np.median(B_right)),
+        "channel_condition_maximum": float(np.max(condition)),
+        "gauge_invariance_error": _gauge_invariance_error(
+            first_channels,
+            seed + 300,
+        ),
+        "checks": case_checks,
+    }
+    arrays = {
+        "physical_R4": physical_R4,
+        "A_left": A_left,
+        "B_right": B_right,
+        "channel_condition": condition,
+        "gaussian_R4": reference,
+        "pooled_left_eigenvalues": pooled_left,
+        "pooled_right_eigenvalues": pooled_right,
+        "structured_R4": np.asarray(structured.R4),
+    }
+    return summary, arrays
+
+
+def select_result_branch(payload: dict[str, Any]) -> str:
+    """Select the preregistered matrix-element result branch."""
+
+    cases = payload.get("cases", [])
+    checks = payload.get("checks", {})
+    if len(cases) != 3 or not all(checks.values()):
+        return "manybody_sequence_incomplete"
+    medians = np.asarray(
+        [case["physical_R4_median"] for case in cases],
+        dtype=float,
+    )
+    upper = np.asarray(
+        [case["gaussian_R4_interval"][2] for case in cases],
+        dtype=float,
+    )
+    slope = float(np.polyfit([3.0, 4.0, 5.0], medians, 1)[0])
+    if medians[-1] <= upper[-1] and slope < 0.0:
+        return "wick_compatible_trend"
+    if medians[-1] > upper[-1] and np.count_nonzero(medians > upper) >= 2:
+        return "deformed_geometric_eth"
+    return "no_matrix_element_eth_trend"
+
+
+def run(
+    output_json: Path = OUTPUT_JSON,
+    output_npz: Path = OUTPUT_NPZ,
+    checkpoint_dir: Path = CHECKPOINT_ROOT,
+    case_indices: tuple[int, ...] = (0, 1, 2),
+    panels: int = REGISTERED_PANELS,
+    gaussian_samples: int = REGISTERED_GAUSSIAN_SAMPLES,
+    production: bool = True,
+    seed: int = REGISTERED_SEED,
+) -> dict[str, Any]:
+    """Run the registered or reduced matrix-element calculation."""
+
+    started = time.perf_counter()
+    panel_count = int(panels)
+    reference_count = int(gaussian_samples)
+    if panel_count < 2 or reference_count < 8:
+        raise ValueError("require at least two panels and eight references")
+    registered = registered_fixed_two_qh_cases()
+    selected = tuple(registered[int(index)] for index in case_indices)
+    if not selected:
+        raise ValueError("at least one many-body case is required")
+    excluded = audit_unregistered_small_case(2, 6, 0.17, 0.29)
+    case_summaries: list[dict[str, Any]] = []
+    case_arrays: list[dict[str, np.ndarray]] = []
+    for offset, case in enumerate(selected):
+        loaded = _load_checkpoint(checkpoint_dir, case)
+        reused = loaded is not None
+        if loaded is None:
+            cache, metadata = _build_checkpoint(
+                checkpoint_dir,
+                case,
+                seed=seed + 10 * offset,
+            )
+        else:
+            cache, metadata = loaded
+        summary, arrays = _case_statistics(
+            cache,
+            metadata,
+            panels=panel_count,
+            gaussian_samples=reference_count,
+            seed=seed + 1_000 * offset,
+        )
+        summary["checkpoint_reused"] = reused
+        summary["checkpoint_identity_hash"] = metadata["identity_hash"]
+        case_summaries.append(summary)
+        case_arrays.append(arrays)
+    all_case_checks = {
+        key: all(case["checks"].get(key, False) for case in case_summaries)
+        for key in {
+            key
+            for case in case_summaries
+            for key in case["checks"]
+        }
+    }
+    checks = {
+        "kernel_count": all_case_checks.get("kernel_count", False),
+        "external_gap": all_case_checks.get("external_gap", False),
+        "resolvent_residual": all_case_checks.get(
+            "resolvent_residual",
+            False,
+        ),
+        "channel_support": all_case_checks.get("channel_support", False),
+        "gauge_invariance": all_case_checks.get("gauge_invariance", False),
+        "reference_reproducibility": all_case_checks.get(
+            "reference_reproducibility",
+            False,
+        ),
+        "n2_excluded_before_production": (
+            excluded.expected_rank == 9
+            and excluded.observed_rank == 12
+            and not excluded.accepted
+        ),
+    }
+    payload: dict[str, Any] = {
+        "version": VERSION,
+        "generated_utc": datetime.now(timezone.utc).isoformat(),
+        "configuration": {
+            "case_indices": list(case_indices),
+            "panel_size": REGISTERED_PANEL_SIZE,
+            "panels": panel_count,
+            "gaussian_samples": reference_count,
+            "seed": int(seed),
+            "relative_shifts": list(RELATIVE_SHIFTS),
+            "production": bool(production),
+        },
+        "excluded_small_case": asdict(excluded),
+        "cases": case_summaries,
+        "checks": checks,
+        "runtime_seconds": time.perf_counter() - started,
+        "environment": {
+            "python": platform.python_version(),
+            "numpy": np.__version__,
+            "platform": platform.platform(),
+        },
+    }
+    if len(case_summaries) == 3:
+        medians = np.asarray(
+            [case["physical_R4_median"] for case in case_summaries]
+        )
+        payload["descriptive_slope_per_particle"] = float(
+            np.polyfit([3.0, 4.0, 5.0], medians, 1)[0]
+        )
+    else:
+        payload["descriptive_slope_per_particle"] = None
+    payload["result_branch"] = select_result_branch(payload)
+    output_arrays: dict[str, np.ndarray] = {
+        "N": np.asarray([case["N"] for case in case_summaries]),
+        "rank": np.asarray([case["rank"] for case in case_summaries]),
+        "external_gap": np.asarray(
+            [case["external_gap"] for case in case_summaries]
+        ),
+    }
+    for index, arrays in enumerate(case_arrays):
+        for key, values in arrays.items():
+            output_arrays[f"case_{index}_{key}"] = np.asarray(values)
+    _atomic_npz(output_npz, **output_arrays)
+    payload["npz_sha256"] = _sha256_file(output_npz)
+    _atomic_json(output_json, payload)
+    if production and (
+        len(case_summaries) != 3
+        or not all(checks.values())
+    ):
+        raise RuntimeError("production matrix-element gates failed")
+    return payload
+
+
+def main() -> None:
+    parser = argparse.ArgumentParser()
+    parser.add_argument(
+        "--reduced",
+        action="store_true",
+        help="run the N=3 smoke configuration",
+    )
+    arguments = parser.parse_args()
+    if arguments.reduced:
+        payload = run(
+            case_indices=(0,),
+            panels=3,
+            gaussian_samples=32,
+            production=False,
+        )
+    else:
+        payload = run()
+    print(json.dumps(
+        {
+            "result_branch": payload["result_branch"],
+            "checks": payload["checks"],
+            "runtime_seconds": payload["runtime_seconds"],
+        },
+        indent=2,
+        sort_keys=True,
+    ))
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/run_physical_ensemble_v1.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/run_physical_ensemble_v1.py
new file mode 100644
index 000000000..1c70a1f7a
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/run_physical_ensemble_v1.py
@@ -0,0 +1,235 @@
+#!/usr/bin/env python3
+"""Generate the high-statistics physical Berry-curvature ensemble."""
+
+from __future__ import annotations
+
+import argparse
+import json
+import platform
+import time
+from datetime import datetime, timezone
+from pathlib import Path
+from typing import Any
+
+import numpy as np
+
+from lgeth.channels import (
+    build_physical_channel_cache,
+    cached_channel,
+    curvature_from_channels,
+    normalized_potential,
+)
+from lgeth.jacobi import jacobi_parameters, normalized_curvature
+
+
+VERSION = "v1"
+REGISTERED_SAMPLES = 20_000
+REGISTERED_SEED_BLOCKS = 8
+REGISTERED_SEED = 20260728110
+
+
+def _split_indices(count: int, seed: int) -> tuple[np.ndarray, ...]:
+    if count == REGISTERED_SAMPLES:
+        sizes = (12_000, 4_000, 4_000)
+    else:
+        train = int(round(0.625 * count))
+        validation = (count - train) // 2
+        sizes = (train, validation, count - train - validation)
+    permutation = np.random.default_rng(seed).permutation(count)
+    first = sizes[0]
+    second = first + sizes[1]
+    return (
+        np.sort(permutation[:first]),
+        np.sort(permutation[first:second]),
+        np.sort(permutation[second:]),
+    )
+
+
+def run(
+    output_json: Path,
+    output_npz: Path,
+    samples: int = REGISTERED_SAMPLES,
+    seed_blocks: int = REGISTERED_SEED_BLOCKS,
+    seed: int = REGISTERED_SEED,
+) -> dict[str, Any]:
+    """Generate physical spectra and fixed train/validation/test indices."""
+
+    started = time.perf_counter()
+    count = int(samples)
+    blocks = int(seed_blocks)
+    if count < 64 or blocks < 2 or count < blocks:
+        raise ValueError("require samples>=64 and 2<=seed_blocks<=samples")
+    cache = build_physical_channel_cache()
+    D = cache.rank
+    M = cache.external_dimension
+    parameters = jacobi_parameters(D, M)
+    if parameters.plus_atoms or parameters.minus_atoms:
+        raise RuntimeError("the registered physical ensemble must be atom free")
+    sites = cache.channel_basis.shape[0]
+    raw_spectra = np.empty((count, D), dtype=np.float32)
+    normalized_spectra = np.empty((count, D), dtype=np.float32)
+    coefficients_v = np.empty((count, sites), dtype=np.float32)
+    coefficients_w = np.empty_like(coefficients_v)
+    active_ranks = np.empty(count, dtype=np.int16)
+    curvature_ranks = np.empty(count, dtype=np.int16)
+    seed_block = np.empty(count, dtype=np.int16)
+    block_indices = np.array_split(np.arange(count), blocks)
+    child_sequences = np.random.SeedSequence(seed).spawn(blocks)
+    for block, indices in enumerate(block_indices):
+        rng = np.random.default_rng(child_sequences[block])
+        for sample in indices:
+            potential_v = normalized_potential(rng, sites)
+            potential_w = normalized_potential(rng, sites)
+            channel_v = cached_channel(potential_v, cache)
+            channel_w = cached_channel(potential_w, cache)
+            raw = np.linalg.eigvalsh(
+                curvature_from_channels(channel_v, channel_w)
+            )
+            normalized = normalized_curvature(
+                channel_v,
+                channel_w,
+                rtol=1e-10,
+            )
+            normalized_values = np.linalg.eigvalsh(normalized.omega)
+            raw_spectra[sample] = raw
+            normalized_spectra[sample] = normalized_values
+            coefficients_v[sample] = potential_v
+            coefficients_w[sample] = potential_w
+            active_ranks[sample] = normalized.rank
+            cutoff = 1e-10 * float(np.max(np.abs(raw)))
+            curvature_ranks[sample] = np.count_nonzero(np.abs(raw) > cutoff)
+            seed_block[sample] = block
+        print(
+            f"physical block {block + 1}/{blocks}: "
+            f"{indices[-1] + 1}/{count} samples",
+            flush=True,
+        )
+    train_indices, validation_indices, test_indices = _split_indices(
+        count,
+        seed + 1,
+    )
+    observed_atoms = int(
+        np.count_nonzero(
+            np.isclose(
+                np.abs(normalized_spectra),
+                1.0,
+                atol=2e-7,
+                rtol=0.0,
+            )
+        )
+    )
+    checks = {
+        "registered_rank_is_50": D == 50,
+        "parent_kernel_exact": cache.kernel_bandwidth < 1e-10,
+        "parent_gap_open": cache.external_gap > 1e-3,
+        "all_active_ranks_are_full": bool(np.all(active_ranks == D)),
+        "all_curvature_ranks_are_full": bool(np.all(curvature_ranks == D)),
+        "normalized_spectra_bounded": bool(
+            np.max(np.abs(normalized_spectra)) <= 1.0 + 2e-7
+        ),
+        "no_exact_atoms": observed_atoms == 0,
+        "split_complete_and_disjoint": bool(
+            np.array_equal(
+                np.sort(
+                    np.concatenate(
+                        [train_indices, validation_indices, test_indices]
+                    )
+                ),
+                np.arange(count),
+            )
+            and np.intersect1d(train_indices, validation_indices).size == 0
+            and np.intersect1d(train_indices, test_indices).size == 0
+            and np.intersect1d(validation_indices, test_indices).size == 0
+        ),
+        "all_seed_blocks_nonempty": bool(
+            np.array_equal(np.unique(seed_block), np.arange(blocks))
+        ),
+    }
+    result = {
+        "schema_version": 1,
+        "version": VERSION,
+        "generated_utc": datetime.now(timezone.utc).isoformat(),
+        "physical_case": {"N": cache.N, "n": cache.n_flux, "D": D, "M": M},
+        "sample_count": count,
+        "seed": int(seed),
+        "seed_blocks": blocks,
+        "split": {
+            "train": int(train_indices.size),
+            "validation": int(validation_indices.size),
+            "test": int(test_indices.size),
+            "split_seed": int(seed + 1),
+        },
+        "parent": {
+            "kernel_bandwidth": cache.kernel_bandwidth,
+            "external_gap": cache.external_gap,
+        },
+        "jacobi_parameters": {
+            "interior_dimension": parameters.interior_dimension,
+            "exponent": parameters.exponent,
+            "plus_atoms": parameters.plus_atoms,
+            "minus_atoms": parameters.minus_atoms,
+        },
+        "observed_exact_atoms": observed_atoms,
+        "checks": checks,
+        "all_checks_pass": bool(all(checks.values())),
+        "runtime_seconds": time.perf_counter() - started,
+        "environment": {
+            "python": platform.python_version(),
+            "numpy": np.__version__,
+            "platform": platform.platform(),
+        },
+    }
+    output_json.parent.mkdir(parents=True, exist_ok=True)
+    output_npz.parent.mkdir(parents=True, exist_ok=True)
+    output_json.write_text(
+        json.dumps(result, indent=2) + "\n",
+        encoding="utf-8",
+    )
+    np.savez_compressed(
+        output_npz,
+        normalized_spectra=normalized_spectra,
+        raw_spectra=raw_spectra,
+        tangent_coefficients_v=coefficients_v,
+        tangent_coefficients_w=coefficients_w,
+        train_indices=train_indices.astype(np.int32),
+        validation_indices=validation_indices.astype(np.int32),
+        test_indices=test_indices.astype(np.int32),
+        seed_block=seed_block,
+        active_ranks=active_ranks,
+        curvature_ranks=curvature_ranks,
+        channel_basis=cache.channel_basis,
+        tangent_gram=cache.tangent_gram,
+    )
+    return result
+
+
+def main() -> None:
+    parser = argparse.ArgumentParser()
+    parser.add_argument(
+        "--output-json",
+        type=Path,
+        default=Path("output/physical_ensemble_v1.json"),
+    )
+    parser.add_argument(
+        "--output-npz",
+        type=Path,
+        default=Path("output/physical_ensemble_v1.npz"),
+    )
+    parser.add_argument("--samples", type=int, default=REGISTERED_SAMPLES)
+    parser.add_argument(
+        "--seed-blocks", type=int, default=REGISTERED_SEED_BLOCKS
+    )
+    args = parser.parse_args()
+    result = run(
+        args.output_json,
+        args.output_npz,
+        samples=args.samples,
+        seed_blocks=args.seed_blocks,
+    )
+    print(json.dumps(result, indent=2))
+    if not result["all_checks_pass"]:
+        raise SystemExit("physical-ensemble audit failed")
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/run_quick_verify_v1.sh b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/run_quick_verify_v1.sh
new file mode 100755
index 000000000..6409b1de5
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/run_quick_verify_v1.sh
@@ -0,0 +1,15 @@
+#!/usr/bin/env bash
+set -euo pipefail
+
+SCRIPT_DIR="$(cd "$(dirname "${BASH_SOURCE[0]}")" && pwd)"
+cd "${SCRIPT_DIR}"
+
+python verify_release_contract_v1.py
+PYTHONPATH="${SCRIPT_DIR}${PYTHONPATH:+:${PYTHONPATH}}" python -m pytest -q \
+  tests/test_independent_core.py \
+  tests/test_form_factors_v2.py \
+  tests/test_controls_v2.py \
+  tests/test_holonomy_v3.py \
+  tests/test_wick_channels_v3.py \
+  tests/test_matrix_element_topology_theory_v3.py \
+  tests/test_release_contract_v1.py
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/run_rank_scaling_v1.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/run_rank_scaling_v1.py
new file mode 100644
index 000000000..7006daddb
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/run_rank_scaling_v1.py
@@ -0,0 +1,472 @@
+#!/usr/bin/env python3
+"""Compute the root-response Jacobi crossover through active rank 800."""
+
+from __future__ import annotations
+
+import argparse
+import json
+import platform
+import time
+from dataclasses import dataclass
+from datetime import datetime, timezone
+from pathlib import Path
+from typing import Any
+
+import numpy as np
+
+from lgeth.channels import root_response_partition
+from lgeth.jacobi import jacobi_parameters, sample_jacobi_wishart
+from lgeth.statistics import bulk_gap_ratio_per_spectrum, histogram_l1
+
+
+VERSION = "v1"
+ALGORITHM_VERSION = 1
+REGISTERED_CASES = (
+    (8, 2_000),
+    (10, 2_000),
+    (12, 2_000),
+    (14, 1_000),
+    (16, 1_000),
+    (18, 500),
+    (20, 250),
+)
+RESPONSE_ENTRY_CEILING = 1_200_000
+
+
+@dataclass(frozen=True)
+class ResponseAssembler:
+    """Sparse lookup for a root-space one-body response block."""
+
+    D: int
+    M: int
+    row: np.ndarray
+    column: np.ndarray
+    destination: np.ndarray
+    source: np.ndarray
+    population: np.ndarray
+
+    def channel(self, tangent: np.ndarray) -> np.ndarray:
+        values = self.population * tangent[self.destination, self.source]
+        matrix = np.zeros((self.D, self.M), dtype=float)
+        np.add.at(matrix, (self.row, self.column), values)
+        return matrix
+
+
+def build_response_assembler(partition) -> ResponseAssembler:
+    """Precompute the nonzero one-body representation map."""
+
+    target_column = {
+        int(basis_index): column
+        for column, basis_index in enumerate(
+            partition.descendant_external
+        )
+    }
+    state_index = {
+        state: index for index, state in enumerate(partition.states)
+    }
+    rows: list[int] = []
+    columns: list[int] = []
+    destinations: list[int] = []
+    sources: list[int] = []
+    populations: list[int] = []
+    for row, basis_index in enumerate(partition.zero_modes):
+        state = partition.states[int(basis_index)]
+        for source, population in enumerate(state):
+            if population == 0:
+                continue
+            for destination in range(len(state)):
+                if destination == source:
+                    continue
+                updated = list(state)
+                updated[source] -= 1
+                updated[destination] += 1
+                target_index = state_index[tuple(updated)]
+                column = target_column.get(target_index)
+                if column is not None:
+                    rows.append(row)
+                    columns.append(column)
+                    destinations.append(destination)
+                    sources.append(source)
+                    populations.append(population)
+    return ResponseAssembler(
+        D=len(partition.zero_modes),
+        M=len(partition.descendant_external),
+        row=np.asarray(rows, dtype=np.int32),
+        column=np.asarray(columns, dtype=np.int32),
+        destination=np.asarray(destinations, dtype=np.int16),
+        source=np.asarray(sources, dtype=np.int16),
+        population=np.asarray(populations, dtype=float),
+    )
+
+
+def _random_symmetric_tangent(
+    rng: np.random.Generator,
+    orbitals: int,
+) -> np.ndarray:
+    upper = rng.integers(
+        -16,
+        17,
+        size=(orbitals, orbitals),
+        dtype=np.int64,
+    )
+    tangent = np.triu(upper, 1)
+    tangent += tangent.T
+    np.fill_diagonal(
+        tangent,
+        rng.integers(-16, 17, size=orbitals, dtype=np.int64),
+    )
+    return tangent.astype(float)
+
+
+def qr_normalized_curvature(
+    channel_v: np.ndarray,
+    channel_w: np.ndarray,
+) -> tuple[np.ndarray, np.ndarray, float]:
+    """Return row isometry and normalized-curvature spectrum by thin QR."""
+
+    doubled = np.concatenate([channel_v, channel_w], axis=1)
+    q, triangular = np.linalg.qr(doubled.T, mode="reduced")
+    diagonal = np.abs(np.diag(triangular))
+    condition_indicator = float(np.min(diagonal) / np.max(diagonal))
+    if condition_indicator <= 1e-12:
+        raise RuntimeError("root-response channel lost active rank")
+    rows = q.T
+    M = channel_v.shape[1]
+    plus = rows[:, :M]
+    minus = rows[:, M:]
+    omega = 1j * (
+        plus @ minus.T - minus @ plus.T
+    )
+    spectrum = np.linalg.eigvalsh(
+        0.5 * (omega + omega.conj().T)
+    )
+    return rows, spectrum, condition_indicator
+
+
+def _row_diagnostics(rows: np.ndarray, M: int) -> tuple[float, float]:
+    weights = np.sum(rows * rows, axis=0)
+    rank = float(rows.shape[0])
+    effective = rank * rank / float(np.sum(weights * weights))
+    participation = effective / rows.shape[1]
+    polarization = abs(
+        float(np.sum(weights[:M]) - np.sum(weights[M:])) / rank
+    )
+    return participation, polarization
+
+
+def _strip_atoms(
+    spectra: np.ndarray,
+    plus_atoms: int,
+    minus_atoms: int,
+) -> tuple[np.ndarray, np.ndarray, float]:
+    labels = np.zeros_like(spectra, dtype=bool)
+    maximum_residual = 0.0
+    if minus_atoms:
+        labels[:, :minus_atoms] = True
+        labels[:, -plus_atoms:] = True
+        maximum_residual = max(
+            float(np.max(np.abs(spectra[:, :minus_atoms] + 1.0))),
+            float(np.max(np.abs(spectra[:, -plus_atoms:] - 1.0))),
+        )
+    interior = spectra[~labels].reshape(
+        spectra.shape[0],
+        spectra.shape[1] - plus_atoms - minus_atoms,
+    )
+    return interior, labels, maximum_residual
+
+
+def _checkpoint_paths(directory: Path, n: int) -> tuple[Path, Path]:
+    return directory / f"n{n}_v1.json", directory / f"n{n}_v1.npz"
+
+
+def _computed_case(
+    n: int,
+    samples: int,
+    checkpoint_dir: Path,
+) -> tuple[dict[str, Any], dict[str, np.ndarray]]:
+    json_path, npz_path = _checkpoint_paths(checkpoint_dir, n)
+    if json_path.exists() and npz_path.exists():
+        result = json.loads(json_path.read_text(encoding="utf-8"))
+        if (
+            result.get("algorithm_version") == ALGORITHM_VERSION
+            and result.get("samples") == samples
+            and result.get("status") == "computed"
+        ):
+            with np.load(npz_path) as arrays:
+                return result, {key: arrays[key] for key in arrays.files}
+    started = time.perf_counter()
+    partition = root_response_partition(3, n)
+    assembler = build_response_assembler(partition)
+    D, M = assembler.D, assembler.M
+    parameters = jacobi_parameters(D, M)
+    count = int(samples)
+    spectra = np.empty((count, D), dtype=np.float32)
+    participation = np.empty(count, dtype=np.float32)
+    polarization = np.empty(count, dtype=np.float32)
+    condition_indicator = np.empty(count, dtype=np.float32)
+    seed_block = np.empty(count, dtype=np.int16)
+    frame_pair_count = min(count // 2, 64 if D <= 352 else 24)
+    frame_overlaps = np.empty(frame_pair_count, dtype=np.float32)
+    previous = None
+    pair = 0
+    blocks = min(8, count)
+    child_sequences = np.random.SeedSequence(
+        20260728300 + n
+    ).spawn(blocks)
+    index_blocks = np.array_split(np.arange(count), blocks)
+    for block, indices in enumerate(index_blocks):
+        rng = np.random.default_rng(child_sequences[block])
+        for sample in indices:
+            tangent_v = _random_symmetric_tangent(rng, n)
+            tangent_w = _random_symmetric_tangent(rng, n)
+            channel_v = assembler.channel(tangent_v)
+            channel_w = assembler.channel(tangent_w)
+            rows, values, indicator = qr_normalized_curvature(
+                channel_v,
+                channel_w,
+            )
+            spectra[sample] = values
+            condition_indicator[sample] = indicator
+            participation[sample], polarization[sample] = _row_diagnostics(
+                rows,
+                M,
+            )
+            seed_block[sample] = block
+            if pair < frame_pair_count:
+                if sample % 2 == 0:
+                    previous = rows
+                elif previous is not None:
+                    frame_overlaps[pair] = np.linalg.norm(
+                        previous @ rows.T
+                    ) ** 2
+                    pair += 1
+                    previous = None
+        print(
+            f"root n={n}, D={D}, block {block + 1}/{blocks}: "
+            f"{indices[-1] + 1}/{count}",
+            flush=True,
+        )
+    interior, atom_labels, atom_residual = _strip_atoms(
+        spectra,
+        parameters.plus_atoms,
+        parameters.minus_atoms,
+    )
+    reference_full, reference_interior, reference_atom_labels = (
+        sample_jacobi_wishart(
+            D,
+            M,
+            count,
+            seed=20260728400 + n,
+        )
+    )
+    physical_ratios = bulk_gap_ratio_per_spectrum(interior)
+    reference_ratios = bulk_gap_ratio_per_spectrum(reference_interior)
+    density_l1 = histogram_l1(
+        interior,
+        reference_interior,
+        np.linspace(-1.0, 1.0, 161),
+    )
+    arrays = {
+        "full_spectra": spectra,
+        "interior_spectra": interior.astype(np.float32),
+        "atom_labels": atom_labels,
+        "reference_full_spectra": reference_full.astype(np.float32),
+        "reference_interior_spectra": reference_interior.astype(
+            np.float32
+        ),
+        "reference_atom_labels": reference_atom_labels,
+        "gap_ratios": physical_ratios.astype(np.float32),
+        "reference_gap_ratios": reference_ratios.astype(np.float32),
+        "seed_block": seed_block,
+        "participation": participation,
+        "polarization": polarization,
+        "frame_overlaps": frame_overlaps,
+        "condition_indicator": condition_indicator,
+    }
+    result = {
+        "algorithm_version": ALGORITHM_VERSION,
+        "status": "computed",
+        "N": 3,
+        "n": n,
+        "D": D,
+        "M": M,
+        "samples": count,
+        "ambient_hilbert_dimension": len(partition.states),
+        "response_entries": D * 2 * M,
+        "response_nonzero_terms": int(assembler.row.size),
+        "interior_dimension": parameters.interior_dimension,
+        "plus_atoms_per_matrix": parameters.plus_atoms,
+        "minus_atoms_per_matrix": parameters.minus_atoms,
+        "observed_plus_atoms_per_matrix": int(
+            np.mean(np.sum(atom_labels[:, -parameters.plus_atoms :], axis=1))
+        )
+        if parameters.plus_atoms
+        else 0,
+        "observed_minus_atoms_per_matrix": int(
+            np.mean(np.sum(atom_labels[:, : parameters.minus_atoms], axis=1))
+        )
+        if parameters.minus_atoms
+        else 0,
+        "maximum_atom_residual": atom_residual,
+        "mean_gap_ratio": float(np.mean(physical_ratios)),
+        "reference_mean_gap_ratio": float(np.mean(reference_ratios)),
+        "gap_ratio_difference": abs(
+            float(np.mean(physical_ratios))
+            - float(np.mean(reference_ratios))
+        ),
+        "interior_density_l1": density_l1,
+        "mean_participation": float(np.mean(participation)),
+        "mean_polarization": float(np.mean(polarization)),
+        "mean_frame_overlap": float(np.mean(frame_overlaps)),
+        "minimum_condition_indicator": float(
+            np.min(condition_indicator)
+        ),
+        "seed_blocks": blocks,
+        "frame_pairs": frame_pair_count,
+        "runtime_seconds": time.perf_counter() - started,
+    }
+    checkpoint_dir.mkdir(parents=True, exist_ok=True)
+    json_path.write_text(
+        json.dumps(result, indent=2) + "\n",
+        encoding="utf-8",
+    )
+    np.savez_compressed(npz_path, **arrays)
+    return result, arrays
+
+
+def run(
+    output_json: Path,
+    output_npz: Path,
+    cases: tuple[tuple[int, int], ...] = REGISTERED_CASES,
+    response_entry_ceiling: int = RESPONSE_ENTRY_CEILING,
+) -> dict[str, Any]:
+    """Run registered cases with per-size resumable checkpoints."""
+
+    started = time.perf_counter()
+    checkpoint_dir = (
+        output_npz.parent / f"{output_npz.stem}_checkpoints"
+    )
+    case_results: list[dict[str, Any]] = []
+    saved_arrays: dict[str, np.ndarray] = {}
+    for n, samples in cases:
+        partition = root_response_partition(3, n)
+        D = len(partition.zero_modes)
+        M = len(partition.descendant_external)
+        entries = D * 2 * M
+        if entries > int(response_entry_ceiling):
+            result = {
+                "status": "resource_rejected",
+                "N": 3,
+                "n": n,
+                "D": D,
+                "M": M,
+                "samples": int(samples),
+                "response_entries": entries,
+                "response_entry_ceiling": int(response_entry_ceiling),
+            }
+            arrays = {}
+        else:
+            result, arrays = _computed_case(
+                n,
+                int(samples),
+                checkpoint_dir,
+            )
+        case_results.append(result)
+        for key, value in arrays.items():
+            saved_arrays[f"n{n}_{key}"] = value
+    computed = [case for case in case_results if case["status"] == "computed"]
+    registered = tuple(cases) == REGISTERED_CASES
+    checks = {
+        "registered_dimensions_match": all(
+            (case["D"], case["M"])
+            == {
+                8: (16, 80),
+                10: (50, 140),
+                12: (112, 216),
+                14: (210, 308),
+                16: (352, 416),
+                18: (546, 540),
+                20: (800, 680),
+            }[case["n"]]
+            for case in case_results
+        ),
+        "statuses_explicit": all(
+            case["status"] in {"computed", "resource_rejected"}
+            for case in case_results
+        ),
+        "registered_run_has_no_rejections": (
+            not registered
+            or all(case["status"] == "computed" for case in case_results)
+        ),
+        "registered_sample_counts_unchanged": (
+            not registered
+            or all(
+                case["samples"] == samples
+                for case, (_, samples) in zip(
+                    case_results,
+                    REGISTERED_CASES,
+                    strict=True,
+                )
+            )
+        ),
+        "atom_counts_match_intersection_theorem": all(
+            case["observed_plus_atoms_per_matrix"]
+            == max(case["D"] - case["M"], 0)
+            and case["observed_minus_atoms_per_matrix"]
+            == max(case["D"] - case["M"], 0)
+            for case in computed
+        ),
+        "atom_residual_below_tolerance": all(
+            case["maximum_atom_residual"] < 2e-5 for case in computed
+        ),
+    }
+    result = {
+        "schema_version": 1,
+        "version": VERSION,
+        "generated_utc": datetime.now(timezone.utc).isoformat(),
+        "registered_cases": [
+            {"n": n, "samples": samples}
+            for n, samples in REGISTERED_CASES
+        ],
+        "response_entry_ceiling": int(response_entry_ceiling),
+        "cases": case_results,
+        "checks": checks,
+        "all_checks_pass": bool(all(checks.values())),
+        "runtime_seconds": time.perf_counter() - started,
+        "environment": {
+            "python": platform.python_version(),
+            "numpy": np.__version__,
+            "platform": platform.platform(),
+        },
+    }
+    output_json.parent.mkdir(parents=True, exist_ok=True)
+    output_npz.parent.mkdir(parents=True, exist_ok=True)
+    output_json.write_text(
+        json.dumps(result, indent=2) + "\n",
+        encoding="utf-8",
+    )
+    np.savez_compressed(output_npz, **saved_arrays)
+    return result
+
+
+def main() -> None:
+    parser = argparse.ArgumentParser()
+    parser.add_argument(
+        "--output-json",
+        type=Path,
+        default=Path("output/rank_scaling_v1.json"),
+    )
+    parser.add_argument(
+        "--output-npz",
+        type=Path,
+        default=Path("output/rank_scaling_v1.npz"),
+    )
+    args = parser.parse_args()
+    result = run(args.output_json, args.output_npz)
+    print(json.dumps(result, indent=2))
+    if not result["all_checks_pass"]:
+        raise SystemExit("rank-scaling audit failed")
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/run_spectral_silence_article_v2.sh b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/run_spectral_silence_article_v2.sh
new file mode 100755
index 000000000..09e504324
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/run_spectral_silence_article_v2.sh
@@ -0,0 +1,23 @@
+#!/usr/bin/env bash
+set -euo pipefail
+
+SCRIPT_DIR="$(cd "$(dirname "${BASH_SOURCE[0]}")" && pwd)"
+REPO_ROOT="$(cd "$SCRIPT_DIR/../../.." && pwd)"
+ARTICLE_DIR="$REPO_ROOT/overleaf_sync/geometric_eth_large_scale"
+OUTPUT_DIR="$SCRIPT_DIR/output"
+PYTHON_BIN="/Users/thomasjwang/miniforge3/bin/python3.12"
+
+cd "$SCRIPT_DIR"
+"$PYTHON_BIN" run_spectral_silence_v2.py
+"$PYTHON_BIN" run_spectral_silence_statistics_v2.py
+"$PYTHON_BIN" make_spectral_silence_figures_v2.py
+
+cd "$ARTICLE_DIR"
+latexmk -pdf -interaction=nonstopmode -halt-on-error main.tex
+cp main.pdf \
+  "$OUTPUT_DIR/spectral_silence_and_geometric_chaos_v2.pdf"
+
+cd "$SCRIPT_DIR"
+"$PYTHON_BIN" -m pytest -q tests \
+  | tee "$OUTPUT_DIR/pytest_v2.txt"
+"$PYTHON_BIN" verify_spectral_silence_article_v2.py
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/run_spectral_silence_statistics_v2.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/run_spectral_silence_statistics_v2.py
new file mode 100644
index 000000000..bae4a633d
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/run_spectral_silence_statistics_v2.py
@@ -0,0 +1,721 @@
+#!/usr/bin/env python3
+"""Simultaneous-band inference for spectral silence and geometric chaos."""
+
+from __future__ import annotations
+
+import argparse
+import hashlib
+import json
+import platform
+import time
+from datetime import datetime, timezone
+from pathlib import Path
+from typing import Any
+
+import numpy as np
+
+from lgeth.statistics import (
+    CurveBand,
+    matrix_bootstrap_band,
+    number_variance_matrix_curves,
+    unfold_spectra,
+)
+
+
+VERSION = "v2"
+REGISTERED_BOOTSTRAP_REPLICATES = 10_000
+REGISTERED_SEED = 20260728220
+RATIO_EDGES = np.linspace(0.0, 1.0, 61)
+LENGTHS = np.linspace(0.25, 8.0, 32)
+TAU_MIN = 0.25
+TAU_MAX = 1.50
+
+
+def _default_output(name: str) -> Path:
+    return Path(__file__).resolve().parent / "output" / name
+
+
+def _sha256(path: Path) -> str:
+    digest = hashlib.sha256()
+    with path.open("rb") as handle:
+        for block in iter(lambda: handle.read(1024 * 1024), b""):
+            digest.update(block)
+    return digest.hexdigest()
+
+
+def registered_compatibility_onset(
+    grid: np.ndarray,
+    lower: np.ndarray,
+    upper: np.ndarray,
+    minimum: float,
+    maximum: float,
+) -> float | None:
+    """Return the first point after which all registered bands contain zero."""
+
+    values = np.asarray(grid, dtype=float)
+    low = np.asarray(lower, dtype=float)
+    high = np.asarray(upper, dtype=float)
+    if values.ndim != 1 or low.shape != values.shape or high.shape != values.shape:
+        raise ValueError("grid and confidence bounds must be matching vectors")
+    if np.any(low > high):
+        raise ValueError("lower confidence bound exceeds upper bound")
+    indices = np.flatnonzero(
+        (values >= float(minimum)) & (values <= float(maximum))
+    )
+    if indices.size == 0:
+        raise ValueError("registered interval contains no grid points")
+    compatible = (low[indices] <= 0.0) & (high[indices] >= 0.0)
+    for offset, index in enumerate(indices):
+        if bool(np.all(compatible[offset:])):
+            return float(values[index])
+    return None
+
+
+def registered_compatibility_extent(
+    grid: np.ndarray,
+    lower: np.ndarray,
+    upper: np.ndarray,
+    minimum: float,
+    maximum: float,
+) -> float | None:
+    """Return the largest initial scale with uninterrupted compatibility."""
+
+    values = np.asarray(grid, dtype=float)
+    low = np.asarray(lower, dtype=float)
+    high = np.asarray(upper, dtype=float)
+    if values.ndim != 1 or low.shape != values.shape or high.shape != values.shape:
+        raise ValueError("grid and confidence bounds must be matching vectors")
+    indices = np.flatnonzero(
+        (values >= float(minimum)) & (values <= float(maximum))
+    )
+    if indices.size == 0:
+        raise ValueError("registered interval contains no grid points")
+    compatible = (low[indices] <= 0.0) & (high[indices] >= 0.0)
+    if not bool(compatible[0]):
+        return None
+    stop = 0
+    while stop + 1 < compatible.size and bool(compatible[stop + 1]):
+        stop += 1
+    return float(values[indices[stop]])
+
+
+def _partition_matrix_curves(
+    spectra: np.ndarray,
+    times: np.ndarray,
+) -> np.ndarray:
+    values = np.asarray(spectra, dtype=float)
+    grid = np.asarray(times, dtype=float)
+    if values.ndim != 2 or values.shape[1] < 2:
+        raise ValueError("spectra must be a matrix with at least two levels")
+    partition = np.empty(
+        (values.shape[0], grid.size),
+        dtype=np.complex128,
+    )
+    for start in range(0, values.shape[0], 512):
+        stop = min(start + 512, values.shape[0])
+        phases = np.exp(
+            -2j
+            * np.pi
+            * values[start:stop, :, None]
+            * grid[None, None, :]
+        )
+        partition[start:stop] = np.sum(phases, axis=1)
+    mean_partition = np.mean(partition, axis=0)
+    return (
+        np.abs(partition) ** 2
+        - np.abs(mean_partition)[None, :] ** 2
+    ) / values.shape[1]
+
+
+def _ratio_values(spectrum: np.ndarray) -> np.ndarray:
+    ordered = np.sort(np.asarray(spectrum, dtype=float))
+    trim = int(np.floor(0.15 * ordered.size))
+    bulk = ordered[trim : ordered.size - trim if trim else ordered.size]
+    gaps = np.diff(bulk)
+    left = gaps[:-1]
+    right = gaps[1:]
+    denominator = np.maximum(left, right)
+    scale = max(float(np.ptp(bulk)), 1.0)
+    tolerance = 1e-11 * scale
+    ratios = np.zeros_like(denominator)
+    keep = denominator > tolerance
+    ratios[keep] = (
+        np.minimum(left[keep], right[keep]) / denominator[keep]
+    )
+    return ratios
+
+
+def _ratio_matrix_curves(
+    spectra: np.ndarray,
+) -> tuple[np.ndarray, np.ndarray]:
+    values = np.asarray(spectra, dtype=float)
+    width = np.diff(RATIO_EDGES)
+    curves = np.empty(
+        (values.shape[0], RATIO_EDGES.size - 1),
+        dtype=np.float32,
+    )
+    means = np.empty(values.shape[0], dtype=float)
+    for matrix, spectrum in enumerate(values):
+        ratios = _ratio_values(spectrum)
+        counts, _ = np.histogram(ratios, bins=RATIO_EDGES)
+        curves[matrix] = counts / (np.sum(counts) * width)
+        means[matrix] = float(np.mean(ratios))
+    return curves, means
+
+
+def _curve_sets(
+    spectra: np.ndarray,
+    times: np.ndarray,
+    include_number: bool,
+) -> dict[str, np.ndarray]:
+    unfolded = unfold_spectra(spectra, "ensemble_cdf")
+    ratio, ratio_mean = _ratio_matrix_curves(spectra)
+    result = {
+        "form": _partition_matrix_curves(unfolded, times),
+        "ratio": ratio,
+        "ratio_mean": ratio_mean[:, None],
+    }
+    if include_number:
+        result["number"] = number_variance_matrix_curves(
+            unfolded,
+            LENGTHS,
+        )
+    return result
+
+
+def _reduced_units(
+    curves: np.ndarray,
+    groups: np.ndarray | None,
+) -> np.ndarray:
+    values = np.asarray(curves, dtype=float)
+    if groups is None:
+        return values
+    labels = np.asarray(groups)
+    if labels.shape != (values.shape[0],):
+        raise ValueError("groups must provide one label per curve")
+    return np.asarray(
+        [
+            np.mean(values[labels == label], axis=0)
+            for label in np.unique(labels)
+        ]
+    )
+
+
+def _independent_difference_band(
+    first_curves: np.ndarray,
+    second_curves: np.ndarray,
+    replicates: int,
+    seed: int,
+    first_groups: np.ndarray | None = None,
+    second_groups: np.ndarray | None = None,
+) -> CurveBand:
+    first = _reduced_units(first_curves, first_groups)
+    second = _reduced_units(second_curves, second_groups)
+    if first.shape[1] != second.shape[1]:
+        raise ValueError("difference curves must share one grid")
+    if first.shape[0] < 2 or second.shape[0] < 2:
+        raise ValueError("each difference ensemble needs two units")
+    first_mean = np.mean(first, axis=0)
+    second_mean = np.mean(second, axis=0)
+    mean = first_mean - second_mean
+    first_centered = first - first_mean
+    second_centered = second - second_mean
+    covariance = (
+        first_centered.T @ first_centered
+        / (first.shape[0] * (first.shape[0] - 1))
+        + second_centered.T @ second_centered
+        / (second.shape[0] * (second.shape[0] - 1))
+    )
+    covariance = 0.5 * (covariance + covariance.T)
+    eigenvalues, eigenvectors = np.linalg.eigh(covariance)
+    cutoff = max(float(eigenvalues[-1]) * 1e-13, 0.0)
+    keep = eigenvalues > cutoff
+    factor = (
+        eigenvectors[:, keep] * np.sqrt(eigenvalues[keep])[None, :]
+    )
+    rng = np.random.default_rng(int(seed))
+    draws = mean + rng.normal(
+        size=(int(replicates), int(np.count_nonzero(keep)))
+    ) @ factor.T
+    pointwise_lower, pointwise_upper = np.quantile(
+        draws,
+        (0.025, 0.975),
+        axis=0,
+    )
+    standard_error = np.std(draws, axis=0, ddof=1)
+    safe = np.maximum(standard_error, 1e-15)
+    maximum = np.max(np.abs((draws - mean) / safe), axis=1)
+    critical = float(np.quantile(maximum, 0.95))
+    return CurveBand(
+        mean=mean,
+        lower=mean - critical * standard_error,
+        upper=mean + critical * standard_error,
+        pointwise_lower=pointwise_lower,
+        pointwise_upper=pointwise_upper,
+        standard_error=standard_error,
+        critical_value=critical,
+        replicates=int(replicates),
+        units=int(first.shape[0] + second.shape[0]),
+        method="independent_unit_gaussian_multiplier",
+    )
+
+
+def _store_band(
+    prefix: str,
+    band: CurveBand,
+    output: dict[str, np.ndarray],
+) -> None:
+    output[f"{prefix}_mean"] = band.mean.astype(np.float32)
+    output[f"{prefix}_lower"] = band.lower.astype(np.float32)
+    output[f"{prefix}_upper"] = band.upper.astype(np.float32)
+    output[f"{prefix}_pointwise_lower"] = (
+        band.pointwise_lower.astype(np.float32)
+    )
+    output[f"{prefix}_pointwise_upper"] = (
+        band.pointwise_upper.astype(np.float32)
+    )
+    output[f"{prefix}_standard_error"] = (
+        band.standard_error.astype(np.float32)
+    )
+
+
+def run(
+    output_json: Path,
+    output_npz: Path,
+    bootstrap_replicates: int = REGISTERED_BOOTSTRAP_REPLICATES,
+) -> dict[str, Any]:
+    """Run simultaneous-band inference for every v2 control."""
+
+    started = time.perf_counter()
+    draws = int(bootstrap_replicates)
+    if draws < 500:
+        raise ValueError("bootstrap_replicates must be at least 500")
+    script_dir = Path(__file__).resolve().parent
+    source_json_path = script_dir / "output" / "spectral_silence_v2.json"
+    source_npz_path = script_dir / "output" / "spectral_silence_v2.npz"
+    source_json = json.loads(
+        source_json_path.read_text(encoding="utf-8")
+    )
+    source = np.load(source_npz_path, allow_pickle=False)
+    if not source_json["all_checks_pass"]:
+        raise RuntimeError("spectral-silence source audit failed")
+    times = np.asarray(source["times"], dtype=float)
+    analytic = np.asarray(source["jacobi_connected_D50"], dtype=float)
+    structured_sets = _curve_sets(
+        source["structured_spectra"],
+        times,
+        include_number=True,
+    )
+    physical_sets = _curve_sets(
+        source["physical_test_spectra"],
+        times,
+        include_number=True,
+    )
+    haar_sets = _curve_sets(
+        source["haar_spectra"],
+        times,
+        include_number=True,
+    )
+    output: dict[str, np.ndarray] = {
+        "times": times.astype(np.float32),
+        "ratio_centers": (
+            0.5 * (RATIO_EDGES[:-1] + RATIO_EDGES[1:])
+        ).astype(np.float32),
+        "lengths": LENGTHS.astype(np.float32),
+        "jacobi_connected_D50": analytic.astype(np.float32),
+    }
+    base_specs = (
+        (
+            "structured",
+            structured_sets,
+            source["structured_orbit_id"],
+            0,
+        ),
+        (
+            "physical",
+            physical_sets,
+            source["physical_seed_block"],
+            20,
+        ),
+        ("haar", haar_sets, None, 40),
+    )
+    band_metadata: dict[str, Any] = {}
+    base_bands: dict[str, dict[str, CurveBand]] = {}
+    for label, sets, groups, offset in base_specs:
+        base_bands[label] = {}
+        band_metadata[label] = {}
+        for curve_index, curve_name in enumerate(
+            ("form", "ratio", "ratio_mean", "number")
+        ):
+            band = matrix_bootstrap_band(
+                sets[curve_name],
+                replicates=draws,
+                seed=REGISTERED_SEED + offset + curve_index,
+                groups=groups,
+            )
+            base_bands[label][curve_name] = band
+            _store_band(f"{label}_{curve_name}", band, output)
+            band_metadata[label][curve_name] = {
+                "units": band.units,
+                "method": band.method,
+                "critical_value": band.critical_value,
+            }
+    physical_residual = CurveBand(
+        mean=base_bands["physical"]["form"].mean - analytic,
+        lower=base_bands["physical"]["form"].lower - analytic,
+        upper=base_bands["physical"]["form"].upper - analytic,
+        pointwise_lower=(
+            base_bands["physical"]["form"].pointwise_lower - analytic
+        ),
+        pointwise_upper=(
+            base_bands["physical"]["form"].pointwise_upper - analytic
+        ),
+        standard_error=base_bands["physical"]["form"].standard_error,
+        critical_value=base_bands["physical"]["form"].critical_value,
+        replicates=draws,
+        units=base_bands["physical"]["form"].units,
+        method="physical_minus_exact_finite_jacobi",
+    )
+    structured_residual = CurveBand(
+        mean=base_bands["structured"]["form"].mean - analytic,
+        lower=base_bands["structured"]["form"].lower - analytic,
+        upper=base_bands["structured"]["form"].upper - analytic,
+        pointwise_lower=(
+            base_bands["structured"]["form"].pointwise_lower - analytic
+        ),
+        pointwise_upper=(
+            base_bands["structured"]["form"].pointwise_upper - analytic
+        ),
+        standard_error=base_bands["structured"]["form"].standard_error,
+        critical_value=base_bands["structured"]["form"].critical_value,
+        replicates=draws,
+        units=base_bands["structured"]["form"].units,
+        method="structured_minus_exact_finite_jacobi",
+    )
+    _store_band("physical_form_residual", physical_residual, output)
+    _store_band("structured_form_residual", structured_residual, output)
+    number_residual = _independent_difference_band(
+        physical_sets["number"],
+        haar_sets["number"],
+        replicates=draws,
+        seed=REGISTERED_SEED + 60,
+        first_groups=source["physical_seed_block"],
+    )
+    _store_band("physical_haar_number_residual", number_residual, output)
+    tau_onset = registered_compatibility_onset(
+        times,
+        physical_residual.lower,
+        physical_residual.upper,
+        minimum=TAU_MIN,
+        maximum=TAU_MAX,
+    )
+    length_extent = registered_compatibility_extent(
+        LENGTHS,
+        number_residual.lower,
+        number_residual.upper,
+        minimum=float(LENGTHS[0]),
+        maximum=float(LENGTHS[-1]),
+    )
+    g_values = np.asarray(source["g_values"], dtype=float)
+    g_count = g_values.size
+    g_form_arrays = {
+        name: np.empty((g_count, times.size), dtype=np.float32)
+        for name in ("mean", "lower", "upper", "standard_error")
+    }
+    g_ratio_arrays = {
+        name: np.empty(
+            (g_count, RATIO_EDGES.size - 1),
+            dtype=np.float32,
+        )
+        for name in ("mean", "lower", "upper", "standard_error")
+    }
+    g_ratio_scalar = {
+        name: np.empty(g_count, dtype=np.float32)
+        for name in ("mean", "lower", "upper")
+    }
+    g_tau_onset: list[float | None] = []
+    for index, g in enumerate(g_values):
+        sets = _curve_sets(
+            source["g_spectra"][index],
+            times,
+            include_number=False,
+        )
+        groups = source["g_seed_block"][index]
+        form_band = matrix_bootstrap_band(
+            sets["form"],
+            replicates=draws,
+            seed=REGISTERED_SEED + 100 + 4 * index,
+            groups=groups,
+        )
+        ratio_band = matrix_bootstrap_band(
+            sets["ratio"],
+            replicates=draws,
+            seed=REGISTERED_SEED + 101 + 4 * index,
+            groups=groups,
+        )
+        scalar_band = matrix_bootstrap_band(
+            sets["ratio_mean"],
+            replicates=draws,
+            seed=REGISTERED_SEED + 102 + 4 * index,
+            groups=groups,
+        )
+        for name in ("mean", "lower", "upper", "standard_error"):
+            g_form_arrays[name][index] = getattr(form_band, name)
+            g_ratio_arrays[name][index] = getattr(ratio_band, name)
+        for name in ("mean", "lower", "upper"):
+            g_ratio_scalar[name][index] = float(
+                getattr(scalar_band, name)[0]
+            )
+        g_tau_onset.append(
+            registered_compatibility_onset(
+                times,
+                form_band.lower - analytic,
+                form_band.upper - analytic,
+                minimum=TAU_MIN,
+                maximum=TAU_MAX,
+            )
+        )
+    for name, values in g_form_arrays.items():
+        output[f"g_form_{name}"] = values
+    for name, values in g_ratio_arrays.items():
+        output[f"g_ratio_{name}"] = values
+    for name, values in g_ratio_scalar.items():
+        output[f"g_ratio_scalar_{name}"] = values
+    output["g_values"] = g_values.astype(np.float32)
+    alpha_values = np.asarray(source["alpha_values"], dtype=float)
+    alpha_count = alpha_values.size
+    energy_gap = {
+        name: np.empty(alpha_count, dtype=np.float32)
+        for name in ("mean", "lower", "upper")
+    }
+    energy_form = {
+        name: np.empty((alpha_count, times.size), dtype=np.float32)
+        for name in ("mean", "lower", "upper", "standard_error")
+    }
+    for index, alpha in enumerate(alpha_values):
+        sets = _curve_sets(
+            source["energy_spectra_alpha"][index],
+            times,
+            include_number=False,
+        )
+        gap_band = matrix_bootstrap_band(
+            sets["ratio_mean"],
+            replicates=draws,
+            seed=REGISTERED_SEED + 200 + 3 * index,
+        )
+        form_band = matrix_bootstrap_band(
+            sets["form"],
+            replicates=draws,
+            seed=REGISTERED_SEED + 201 + 3 * index,
+        )
+        for name in ("mean", "lower", "upper"):
+            energy_gap[name][index] = float(getattr(gap_band, name)[0])
+        for name in ("mean", "lower", "upper", "standard_error"):
+            energy_form[name][index] = getattr(form_band, name)
+    for name, values in energy_gap.items():
+        output[f"energy_gap_ratio_{name}"] = values
+    for name, values in energy_form.items():
+        output[f"energy_form_{name}"] = values
+    output["alpha_values"] = alpha_values.astype(np.float32)
+    output["projector_distance_alpha"] = source[
+        "projector_distance_alpha"
+    ]
+    output["curvature_error_alpha"] = source["curvature_error_alpha"]
+    output["rank_D"] = source["rank_D"]
+    output["rank_interior"] = source["rank_interior"]
+    output["rank_atom_each"] = source["rank_atom_each"]
+    output["rank_physical_connected_full"] = source[
+        "rank_physical_connected_full"
+    ]
+    output["rank_reference_connected_full"] = source[
+        "rank_reference_connected_full"
+    ]
+    compatible_g_indices = [
+        index
+        for index, onset in enumerate(g_tau_onset)
+        if onset is not None
+        and np.count_nonzero(
+            (times >= onset) & (times <= TAU_MAX)
+        )
+        >= 8
+    ]
+    first_compatible_g = (
+        float(g_values[compatible_g_indices[0]])
+        if compatible_g_indices
+        else None
+    )
+    haar_ratio_lower = float(
+        base_bands["haar"]["ratio_mean"].lower[0]
+    )
+    haar_ratio_upper = float(
+        base_bands["haar"]["ratio_mean"].upper[0]
+    )
+    local_compatible_indices = [
+        index
+        for index in range(g_count)
+        if float(g_ratio_scalar["upper"][index]) >= haar_ratio_lower
+        and float(g_ratio_scalar["lower"][index]) <= haar_ratio_upper
+    ]
+    first_local_g = (
+        float(g_values[local_compatible_indices[0]])
+        if local_compatible_indices
+        else None
+    )
+    tau_index = int(np.argmin(np.abs(times - 0.5)))
+    length_index = -1
+    structured_rejects = bool(
+        structured_residual.lower[tau_index] > 0.0
+        or structured_residual.upper[tau_index] < 0.0
+    )
+    physical_window = bool(
+        tau_onset is not None
+        and np.count_nonzero(
+            (times >= tau_onset) & (times <= TAU_MAX)
+        )
+        >= 8
+    )
+    long_range_resolved = bool(
+        number_residual.lower[length_index] > 0.0
+        or number_residual.upper[length_index] < 0.0
+    )
+    spectral_separated = bool(
+        energy_gap["upper"][0] < energy_gap["lower"][-1]
+    )
+    checks = {
+        "source_artifact_passes": bool(source_json["all_checks_pass"]),
+        "structured_control_rejects_jacobi": structured_rejects,
+        "physical_has_registered_jacobi_window": physical_window,
+        "geometry_axis_crossover_resolved": (
+            first_compatible_g is not None
+        ),
+        "local_to_ramp_hierarchy_resolved": bool(
+            first_local_g is not None
+            and first_compatible_g is not None
+            and first_local_g < first_compatible_g
+        ),
+        "spectral_axis_confidence_separated": spectral_separated,
+        "fixed_projector_invariance_retained": bool(
+            np.max(source["projector_distance_alpha"]) < 1e-12
+            and np.max(source["curvature_error_alpha"]) < 1e-12
+        ),
+        "long_range_memory_resolved": long_range_resolved,
+        "atom_plateau_data_retained": bool(
+            int(source["rank_atom_each"][-1]) == 120
+            and abs(
+                float(
+                    source["rank_interior"][-1]
+                    / source["rank_D"][-1]
+                )
+                - 0.7
+            )
+            < 1e-12
+        ),
+    }
+    result = {
+        "schema_version": 2,
+        "version": VERSION,
+        "generated_utc": datetime.now(timezone.utc).isoformat(),
+        "source_sha256": {
+            "json": _sha256(source_json_path),
+            "npz": _sha256(source_npz_path),
+        },
+        "bootstrap_replicates": draws,
+        "registered_windows": {
+            "tau_minimum": TAU_MIN,
+            "tau_maximum": TAU_MAX,
+            "number_minimum": float(LENGTHS[0]),
+            "number_maximum": float(LENGTHS[-1]),
+        },
+        "outcomes": {
+            "physical_tau_compatibility_onset": tau_onset,
+            "number_variance_compatibility_extent": length_extent,
+            "g_tau_compatibility_onsets": g_tau_onset,
+            "first_g_with_registered_jacobi_window": first_compatible_g,
+            "first_g_with_haar_gap_ratio_interval": first_local_g,
+            "haar_gap_ratio_interval": {
+                "mean": float(
+                    base_bands["haar"]["ratio_mean"].mean[0]
+                ),
+                "lower": haar_ratio_lower,
+                "upper": haar_ratio_upper,
+            },
+            "tau_0p5": {
+                "structured": float(
+                    base_bands["structured"]["form"].mean[tau_index]
+                ),
+                "physical": float(
+                    base_bands["physical"]["form"].mean[tau_index]
+                ),
+                "haar": float(
+                    base_bands["haar"]["form"].mean[tau_index]
+                ),
+                "analytic_jacobi": float(analytic[tau_index]),
+            },
+            "number_variance_L8_residual": {
+                "mean": float(number_residual.mean[length_index]),
+                "lower": float(number_residual.lower[length_index]),
+                "upper": float(number_residual.upper[length_index]),
+            },
+            "energy_gap_ratio_endpoints": {
+                "poisson": float(energy_gap["mean"][0]),
+                "poisson_lower": float(energy_gap["lower"][0]),
+                "poisson_upper": float(energy_gap["upper"][0]),
+                "gue": float(energy_gap["mean"][-1]),
+                "gue_lower": float(energy_gap["lower"][-1]),
+                "gue_upper": float(energy_gap["upper"][-1]),
+            },
+        },
+        "band_metadata": band_metadata,
+        "checks": checks,
+        "all_checks_pass": bool(all(checks.values())),
+        "runtime_seconds": time.perf_counter() - started,
+        "environment": {
+            "python": platform.python_version(),
+            "numpy": np.__version__,
+            "platform": platform.platform(),
+        },
+    }
+    output_json.parent.mkdir(parents=True, exist_ok=True)
+    output_npz.parent.mkdir(parents=True, exist_ok=True)
+    output_json.write_text(
+        json.dumps(result, indent=2) + "\n",
+        encoding="utf-8",
+    )
+    np.savez_compressed(output_npz, **output)
+    return result
+
+
+def main() -> None:
+    parser = argparse.ArgumentParser()
+    parser.add_argument(
+        "--output-json",
+        type=Path,
+        default=_default_output(
+            "spectral_silence_statistics_v2.json"
+        ),
+    )
+    parser.add_argument(
+        "--output-npz",
+        type=Path,
+        default=_default_output(
+            "spectral_silence_statistics_v2.npz"
+        ),
+    )
+    parser.add_argument(
+        "--bootstrap-replicates",
+        type=int,
+        default=REGISTERED_BOOTSTRAP_REPLICATES,
+    )
+    args = parser.parse_args()
+    result = run(
+        args.output_json,
+        args.output_npz,
+        bootstrap_replicates=args.bootstrap_replicates,
+    )
+    print(json.dumps(result, indent=2))
+    if not result["all_checks_pass"]:
+        raise SystemExit("spectral-silence statistical audit failed")
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/run_spectral_silence_v2.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/run_spectral_silence_v2.py
new file mode 100644
index 000000000..c19ab15c1
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/run_spectral_silence_v2.py
@@ -0,0 +1,684 @@
+#!/usr/bin/env python3
+"""Generate the spectral-silence and independent-chaos control artifact."""
+
+from __future__ import annotations
+
+import argparse
+import hashlib
+import json
+import platform
+import time
+from datetime import datetime, timezone
+from pathlib import Path
+from typing import Any
+
+import numpy as np
+
+from lgeth.channels import (
+    build_physical_channel_cache,
+    cached_channel,
+)
+from lgeth.controls import (
+    fixed_projector_spectral_ensemble,
+    fourier_tangent_pairs,
+    scrambled_tangent_pair,
+)
+from lgeth.form_factors import (
+    atom_raw_decomposition,
+    degenerate_energy_form_factor,
+    finite_jacobi_form_factor,
+    form_factor_parts,
+)
+from lgeth.jacobi import normalized_curvature
+from lgeth.statistics import unfold_spectra
+
+
+VERSION = "v2"
+REGISTERED_SEED = 20260728210
+G_VALUES = np.asarray(
+    [0.0, 0.02, 0.05, 0.10, 0.20, 0.40, 0.70, 1.0],
+    dtype=float,
+)
+ALPHA_VALUES = np.asarray(
+    [0.0, 0.10, 0.20, 0.35, 0.50, 0.70, 0.85, 1.0],
+    dtype=float,
+)
+TIMES = np.linspace(0.0, 3.0, 121)
+REGISTERED_SAMPLES_PER_G = 4000
+REGISTERED_SPECTRAL_SAMPLES = 4000
+REGISTERED_QUADRATURE_ORDER = 512
+REGISTERED_RANK_FORM_FACTOR_SAMPLES = 500
+RANK_LABELS = ("n8", "n10", "n12", "n14", "n16", "n18", "n20")
+
+
+def _sha256(path: Path) -> str:
+    digest = hashlib.sha256()
+    with path.open("rb") as handle:
+        for block in iter(lambda: handle.read(1024 * 1024), b""):
+            digest.update(block)
+    return digest.hexdigest()
+
+
+def _default_output(name: str) -> Path:
+    return Path(__file__).resolve().parent / "output" / name
+
+
+def _connected_parts(spectra: np.ndarray) -> tuple[np.ndarray, ...]:
+    unfolded = unfold_spectra(spectra, "ensemble_cdf")
+    parts = form_factor_parts(unfolded, TIMES)
+    return parts.raw, parts.disconnected, parts.connected
+
+
+def _structured_control(
+    cache,
+) -> dict[str, np.ndarray]:
+    pairs = fourier_tangent_pairs(5)
+    spectra = np.empty((len(pairs), cache.rank), dtype=np.float32)
+    active_ranks = np.empty(len(pairs), dtype=np.int16)
+    unique_counts = np.empty(len(pairs), dtype=np.int16)
+    momenta = np.empty((len(pairs), 2), dtype=np.int16)
+    orbit_keys = np.empty((len(pairs), 2), dtype=np.int16)
+    orbit_lookup = {
+        key: index
+        for index, key in enumerate(
+            sorted({pair.orbit_key for pair in pairs})
+        )
+    }
+    orbit_id = np.empty(len(pairs), dtype=np.int16)
+    for index, pair in enumerate(pairs):
+        channel_v = cached_channel(pair.v, cache)
+        channel_w = cached_channel(pair.w, cache)
+        normalized = normalized_curvature(
+            channel_v,
+            channel_w,
+            rtol=1e-10,
+        )
+        spectrum = np.linalg.eigvalsh(normalized.omega)
+        spectra[index] = spectrum
+        active_ranks[index] = normalized.rank
+        unique_counts[index] = np.unique(
+            np.round(spectrum, 10)
+        ).size
+        momenta[index] = (pair.kx, pair.ky)
+        orbit_keys[index] = pair.orbit_key
+        orbit_id[index] = orbit_lookup[pair.orbit_key]
+    raw, disconnected, connected = _connected_parts(spectra)
+    return {
+        "spectra": spectra,
+        "active_ranks": active_ranks,
+        "unique_counts": unique_counts,
+        "momenta": momenta,
+        "orbit_keys": orbit_keys,
+        "orbit_id": orbit_id,
+        "raw": raw,
+        "disconnected": disconnected,
+        "connected": connected,
+    }
+
+
+def _geometry_axis(
+    cache,
+    samples_per_g: int,
+    seed: int,
+) -> dict[str, np.ndarray]:
+    count = int(samples_per_g)
+    if count < 24:
+        raise ValueError("samples_per_g must be at least 24")
+    positive_g = G_VALUES[1:]
+    pairs = fourier_tangent_pairs(5)
+    spectra = np.empty(
+        (positive_g.size, count, cache.rank),
+        dtype=np.float32,
+    )
+    active_ranks = np.empty(
+        (positive_g.size, count),
+        dtype=np.int16,
+    )
+    unique_counts = np.empty_like(active_ranks)
+    momentum_index = np.empty_like(active_ranks)
+    seed_block = np.empty_like(active_ranks)
+    child_sequences = np.random.SeedSequence(seed).spawn(
+        positive_g.size
+    )
+    for g_index, (g, child) in enumerate(
+        zip(positive_g, child_sequences, strict=True)
+    ):
+        rng = np.random.default_rng(child)
+        blocks = np.array_split(np.arange(count), 8)
+        for block, indices in enumerate(blocks):
+            for sample in indices:
+                pair_index = int(sample % len(pairs))
+                pair = pairs[pair_index]
+                random_v = rng.normal(size=pair.v.size)
+                random_w = rng.normal(size=pair.w.size)
+                coefficients_v, coefficients_w = scrambled_tangent_pair(
+                    pair,
+                    random_v,
+                    random_w,
+                    float(g),
+                    cache.tangent_gram,
+                )
+                channel_v = cached_channel(coefficients_v, cache)
+                channel_w = cached_channel(coefficients_w, cache)
+                normalized = normalized_curvature(
+                    channel_v,
+                    channel_w,
+                    rtol=1e-10,
+                )
+                spectrum = np.linalg.eigvalsh(normalized.omega)
+                spectra[g_index, sample] = spectrum
+                active_ranks[g_index, sample] = normalized.rank
+                unique_counts[g_index, sample] = np.unique(
+                    np.round(spectrum, 10)
+                ).size
+                momentum_index[g_index, sample] = pair_index
+                seed_block[g_index, sample] = block
+        print(
+            f"geometry axis g={g:.2f}: {count} spectra",
+            flush=True,
+        )
+    raw = np.empty((positive_g.size, TIMES.size), dtype=float)
+    disconnected = np.empty_like(raw)
+    connected = np.empty_like(raw)
+    for index in range(positive_g.size):
+        raw[index], disconnected[index], connected[index] = (
+            _connected_parts(spectra[index])
+        )
+    return {
+        "g_values": positive_g,
+        "spectra": spectra,
+        "active_ranks": active_ranks,
+        "unique_counts": unique_counts,
+        "momentum_index": momentum_index,
+        "seed_block": seed_block,
+        "raw": raw,
+        "disconnected": disconnected,
+        "connected": connected,
+    }
+
+
+def _rank_form_factors(
+    scaling: np.lib.npyio.NpzFile,
+    scaling_metadata: dict[str, Any],
+    requested_samples: int,
+) -> dict[str, np.ndarray]:
+    cases = scaling_metadata["cases"]
+    rank_count = len(cases)
+    physical_continuous = np.empty(
+        (rank_count, TIMES.size),
+        dtype=float,
+    )
+    physical_full = np.empty_like(physical_continuous)
+    reference_continuous = np.empty_like(physical_continuous)
+    reference_full = np.empty_like(physical_continuous)
+    raw_full = np.empty_like(physical_continuous)
+    raw_atom_atom = np.empty_like(physical_continuous)
+    raw_atom_continuum = np.empty_like(physical_continuous)
+    raw_continuum_continuum = np.empty_like(physical_continuous)
+    dimensions = np.empty(rank_count, dtype=np.int16)
+    channels = np.empty(rank_count, dtype=np.int16)
+    interiors = np.empty(rank_count, dtype=np.int16)
+    atoms = np.empty(rank_count, dtype=np.int16)
+    sample_counts = np.empty(rank_count, dtype=np.int32)
+    for index, (label, case) in enumerate(
+        zip(RANK_LABELS, cases, strict=True)
+    ):
+        physical = scaling[f"{label}_interior_spectra"]
+        reference = scaling[f"{label}_reference_interior_spectra"]
+        count = min(
+            int(requested_samples),
+            int(physical.shape[0]),
+        )
+        indices = np.linspace(
+            0,
+            physical.shape[0] - 1,
+            count,
+            dtype=int,
+        )
+        physical_sample = np.asarray(physical[indices], dtype=float)
+        reference_sample = np.asarray(reference[indices], dtype=float)
+        physical_parts = form_factor_parts(
+            unfold_spectra(physical_sample, "ensemble_cdf"),
+            TIMES,
+        )
+        reference_parts = form_factor_parts(
+            unfold_spectra(reference_sample, "ensemble_cdf"),
+            TIMES,
+        )
+        D = int(case["D"])
+        M = int(case["M"])
+        k = int(case["interior_dimension"])
+        atom_each = int(case["plus_atoms_per_matrix"])
+        physical_continuous[index] = physical_parts.connected
+        reference_continuous[index] = reference_parts.connected
+        physical_full[index] = (k / D) * physical_parts.connected
+        reference_full[index] = (k / D) * reference_parts.connected
+        decomposition = atom_raw_decomposition(
+            reference_sample,
+            minus_atoms=atom_each,
+            plus_atoms=atom_each,
+            times=TIMES,
+        )
+        raw_full[index] = decomposition["full"]
+        raw_atom_atom[index] = decomposition["atom_atom"]
+        raw_atom_continuum[index] = decomposition["atom_continuum"]
+        raw_continuum_continuum[index] = decomposition[
+            "continuum_continuum"
+        ]
+        dimensions[index] = D
+        channels[index] = M
+        interiors[index] = k
+        atoms[index] = atom_each
+        sample_counts[index] = count
+    return {
+        "D": dimensions,
+        "M": channels,
+        "interior": interiors,
+        "atom_each": atoms,
+        "sample_count": sample_counts,
+        "physical_connected_continuous": physical_continuous,
+        "physical_connected_full": physical_full,
+        "reference_connected_continuous": reference_continuous,
+        "reference_connected_full": reference_full,
+        "reference_raw_full": raw_full,
+        "reference_raw_atom_atom": raw_atom_atom,
+        "reference_raw_atom_continuum": raw_atom_continuum,
+        "reference_raw_continuum_continuum": (
+            raw_continuum_continuum
+        ),
+    }
+
+
+def run(
+    output_json: Path,
+    output_npz: Path,
+    samples_per_g: int = REGISTERED_SAMPLES_PER_G,
+    spectral_samples: int = REGISTERED_SPECTRAL_SAMPLES,
+    quadrature_order: int = REGISTERED_QUADRATURE_ORDER,
+    rank_form_factor_samples: int = (
+        REGISTERED_RANK_FORM_FACTOR_SAMPLES
+    ),
+) -> dict[str, Any]:
+    """Generate all A+B control and finite-Jacobi data."""
+
+    started = time.perf_counter()
+    script_dir = Path(__file__).resolve().parent
+    physical_path = script_dir / "output" / "physical_ensemble_v1.npz"
+    physical_json_path = (
+        script_dir / "output" / "physical_ensemble_v1.json"
+    )
+    covariance_path = script_dir / "output" / "covariance_model_v1.npz"
+    covariance_json_path = (
+        script_dir / "output" / "covariance_model_v1.json"
+    )
+    scaling_path = script_dir / "output" / "rank_scaling_v1.npz"
+    scaling_json_path = script_dir / "output" / "rank_scaling_v1.json"
+    input_paths = (
+        physical_path,
+        physical_json_path,
+        covariance_path,
+        covariance_json_path,
+        scaling_path,
+        scaling_json_path,
+    )
+    for path in input_paths:
+        if not path.is_file():
+            raise FileNotFoundError(path)
+    physical_metadata = json.loads(
+        physical_json_path.read_text(encoding="utf-8")
+    )
+    covariance_metadata = json.loads(
+        covariance_json_path.read_text(encoding="utf-8")
+    )
+    scaling_metadata = json.loads(
+        scaling_json_path.read_text(encoding="utf-8")
+    )
+    physical = np.load(physical_path, allow_pickle=False)
+    covariance = np.load(covariance_path, allow_pickle=False)
+    scaling = np.load(scaling_path, allow_pickle=False)
+    cache = build_physical_channel_cache()
+    structured = _structured_control(cache)
+    geometry = _geometry_axis(
+        cache,
+        samples_per_g=int(samples_per_g),
+        seed=REGISTERED_SEED,
+    )
+    test_indices = physical["test_indices"]
+    physical_test_spectra = np.asarray(
+        physical["normalized_spectra"][test_indices],
+        dtype=np.float32,
+    )
+    physical_raw, physical_disconnected, physical_connected = (
+        _connected_parts(physical_test_spectra)
+    )
+    haar_spectra = np.asarray(
+        covariance["haar_spectra"],
+        dtype=np.float32,
+    )
+    haar_raw, haar_disconnected, haar_connected = _connected_parts(
+        haar_spectra
+    )
+    exact_energy = degenerate_energy_form_factor(cache.rank, TIMES)
+    analytic_jacobi = finite_jacobi_form_factor(
+        cache.rank,
+        cache.external_dimension,
+        TIMES,
+        quadrature_order=int(quadrature_order),
+    )
+    fixed = fixed_projector_spectral_ensemble(
+        dimension=cache.rank,
+        samples=int(spectral_samples),
+        alphas=ALPHA_VALUES,
+        seed=REGISTERED_SEED + 1,
+        reference_curvature_spectrum=physical_test_spectra[0],
+        times=TIMES,
+    )
+    rank = _rank_form_factors(
+        scaling,
+        scaling_metadata,
+        requested_samples=int(rank_form_factor_samples),
+    )
+    atom_relation_error = float(
+        np.max(
+            np.abs(
+                rank["reference_connected_full"]
+                - (
+                    rank["interior"] / rank["D"]
+                )[:, None]
+                * rank["reference_connected_continuous"]
+            )
+        )
+    )
+    raw_closure_error = float(
+        np.max(
+            np.abs(
+                rank["reference_raw_full"]
+                - rank["reference_raw_atom_atom"]
+                - rank["reference_raw_atom_continuum"]
+                - rank["reference_raw_continuum_continuum"]
+            )
+        )
+    )
+    checks = {
+        "input_v1_artifacts_pass": bool(
+            physical_metadata["all_checks_pass"]
+            and covariance_metadata["all_checks_pass"]
+            and scaling_metadata["all_checks_pass"]
+        ),
+        "exact_energy_silence": bool(
+            np.max(
+                np.abs(exact_energy.raw - cache.rank)
+            )
+            < 1e-12
+            and np.max(np.abs(exact_energy.connected)) < 1e-12
+        ),
+        "structured_control_full_rank": bool(
+            np.all(structured["active_ranks"] == cache.rank)
+        ),
+        "structured_control_multiplets": bool(
+            np.max(structured["unique_counts"]) <= 10
+        ),
+        "geometry_axis_full_rank": bool(
+            np.all(geometry["active_ranks"] == cache.rank)
+        ),
+        "geometry_axis_exact_parent": bool(
+            cache.kernel_bandwidth < 1e-10
+            and cache.external_gap > 1e-3
+            and abs(
+                cache.kernel_bandwidth
+                - physical_metadata["parent"]["kernel_bandwidth"]
+            )
+            < 1e-12
+            and abs(
+                cache.external_gap
+                - physical_metadata["parent"]["external_gap"]
+            )
+            < 1e-12
+        ),
+        "fixed_projector_invariance": bool(
+            np.max(fixed.projector_distance) < 1e-12
+            and np.max(fixed.curvature_spectrum_error) < 1e-12
+        ),
+        "spectral_axis_resolved": bool(
+            fixed.mean_gap_ratio[-1]
+            > fixed.mean_gap_ratio[0] + 0.12
+        ),
+        "finite_jacobi_mass_and_basis": bool(
+            analytic_jacobi.mass_error < 2e-8
+            and analytic_jacobi.orthogonality_error < 2e-8
+            and abs(analytic_jacobi.connected_continuous[0]) < 1e-9
+        ),
+        "atom_plateau_theorem": bool(
+            atom_relation_error < 1e-12
+            and raw_closure_error < 1e-12
+        ),
+    }
+    result = {
+        "schema_version": 2,
+        "version": VERSION,
+        "generated_utc": datetime.now(timezone.utc).isoformat(),
+        "registered_seed": REGISTERED_SEED,
+        "sample_counts": {
+            "structured_momenta": int(
+                structured["spectra"].shape[0]
+            ),
+            "structured_orbits": int(
+                np.unique(structured["orbit_id"]).size
+            ),
+            "per_positive_g": int(samples_per_g),
+            "fixed_projector_per_alpha": int(spectral_samples),
+            "rank_form_factor_requested": int(
+                rank_form_factor_samples
+            ),
+            "rank_form_factor_actual": (
+                rank["sample_count"].astype(int).tolist()
+            ),
+            "physical_test": int(physical_test_spectra.shape[0]),
+            "haar_reference": int(haar_spectra.shape[0]),
+        },
+        "grids": {
+            "g": G_VALUES.tolist(),
+            "alpha": ALPHA_VALUES.tolist(),
+            "times": {
+                "minimum": float(TIMES[0]),
+                "maximum": float(TIMES[-1]),
+                "points": int(TIMES.size),
+            },
+        },
+        "physical_case": {
+            "N": cache.N,
+            "n": cache.n_flux,
+            "D": cache.rank,
+            "M": cache.external_dimension,
+            "kernel_bandwidth": cache.kernel_bandwidth,
+            "external_gap": cache.external_gap,
+        },
+        "structured_control": {
+            "minimum_active_rank": int(
+                np.min(structured["active_ranks"])
+            ),
+            "maximum_distinct_eigenvalues": int(
+                np.max(structured["unique_counts"])
+            ),
+        },
+        "fixed_projector_control": {
+            "poisson_endpoint_gap_ratio": float(
+                fixed.mean_gap_ratio[0]
+            ),
+            "gue_endpoint_gap_ratio": float(
+                fixed.mean_gap_ratio[-1]
+            ),
+            "maximum_projector_distance": float(
+                np.max(fixed.projector_distance)
+            ),
+            "maximum_curvature_spectrum_error": float(
+                np.max(fixed.curvature_spectrum_error)
+            ),
+        },
+        "finite_jacobi": {
+            "quadrature_order": int(quadrature_order),
+            "mass_error": analytic_jacobi.mass_error,
+            "orthogonality_error": (
+                analytic_jacobi.orthogonality_error
+            ),
+            "atom_relation_error": atom_relation_error,
+            "raw_atom_closure_error": raw_closure_error,
+        },
+        "inputs": {
+            str(path.relative_to(script_dir)): _sha256(path)
+            for path in input_paths
+        },
+        "checks": checks,
+        "all_checks_pass": bool(all(checks.values())),
+        "runtime_seconds": time.perf_counter() - started,
+        "environment": {
+            "python": platform.python_version(),
+            "numpy": np.__version__,
+            "platform": platform.platform(),
+        },
+    }
+    output_json.parent.mkdir(parents=True, exist_ok=True)
+    output_npz.parent.mkdir(parents=True, exist_ok=True)
+    output_json.write_text(
+        json.dumps(result, indent=2) + "\n",
+        encoding="utf-8",
+    )
+    np.savez_compressed(
+        output_npz,
+        times=TIMES.astype(np.float32),
+        energy_raw=exact_energy.raw.astype(np.float32),
+        energy_disconnected=exact_energy.disconnected.astype(np.float32),
+        energy_connected=exact_energy.connected.astype(np.float32),
+        jacobi_connected_D50=(
+            analytic_jacobi.connected_continuous.astype(np.float32)
+        ),
+        structured_spectra=structured["spectra"],
+        structured_active_ranks=structured["active_ranks"],
+        structured_unique_counts=structured["unique_counts"],
+        structured_momenta=structured["momenta"],
+        structured_orbit_keys=structured["orbit_keys"],
+        structured_orbit_id=structured["orbit_id"],
+        structured_raw=structured["raw"].astype(np.float32),
+        structured_disconnected=(
+            structured["disconnected"].astype(np.float32)
+        ),
+        structured_connected=structured["connected"].astype(
+            np.float32
+        ),
+        physical_test_spectra=physical_test_spectra,
+        physical_raw=physical_raw.astype(np.float32),
+        physical_disconnected=physical_disconnected.astype(np.float32),
+        physical_connected=physical_connected.astype(np.float32),
+        physical_seed_block=physical["seed_block"][test_indices],
+        haar_spectra=haar_spectra,
+        haar_raw=haar_raw.astype(np.float32),
+        haar_disconnected=haar_disconnected.astype(np.float32),
+        haar_connected=haar_connected.astype(np.float32),
+        g_values=geometry["g_values"].astype(np.float32),
+        g_spectra=geometry["spectra"],
+        g_active_ranks=geometry["active_ranks"],
+        g_unique_counts=geometry["unique_counts"],
+        g_momentum_index=geometry["momentum_index"],
+        g_seed_block=geometry["seed_block"],
+        g_raw=geometry["raw"].astype(np.float32),
+        g_disconnected=geometry["disconnected"].astype(np.float32),
+        g_connected=geometry["connected"].astype(np.float32),
+        alpha_values=fixed.alphas.astype(np.float32),
+        energy_spectra_alpha=fixed.energy_spectra,
+        energy_gap_ratio_alpha=fixed.mean_gap_ratio.astype(np.float32),
+        energy_raw_alpha=fixed.energy_raw.astype(np.float32),
+        energy_disconnected_alpha=(
+            fixed.energy_disconnected.astype(np.float32)
+        ),
+        energy_connected_alpha=fixed.energy_connected.astype(
+            np.float32
+        ),
+        projector_distance_alpha=fixed.projector_distance.astype(
+            np.float64
+        ),
+        curvature_error_alpha=(
+            fixed.curvature_spectrum_error.astype(np.float64)
+        ),
+        rank_D=rank["D"],
+        rank_M=rank["M"],
+        rank_interior=rank["interior"],
+        rank_atom_each=rank["atom_each"],
+        rank_form_factor_sample_count=rank["sample_count"],
+        rank_physical_connected_continuous=(
+            rank["physical_connected_continuous"].astype(np.float32)
+        ),
+        rank_physical_connected_full=(
+            rank["physical_connected_full"].astype(np.float32)
+        ),
+        rank_reference_connected_continuous=(
+            rank["reference_connected_continuous"].astype(np.float32)
+        ),
+        rank_reference_connected_full=(
+            rank["reference_connected_full"].astype(np.float32)
+        ),
+        rank_reference_raw_full=(
+            rank["reference_raw_full"].astype(np.float32)
+        ),
+        rank_reference_raw_atom_atom=(
+            rank["reference_raw_atom_atom"].astype(np.float32)
+        ),
+        rank_reference_raw_atom_continuum=(
+            rank["reference_raw_atom_continuum"].astype(np.float32)
+        ),
+        rank_reference_raw_continuum_continuum=(
+            rank["reference_raw_continuum_continuum"].astype(
+                np.float32
+            )
+        ),
+    )
+    return result
+
+
+def main() -> None:
+    parser = argparse.ArgumentParser()
+    parser.add_argument(
+        "--output-json",
+        type=Path,
+        default=_default_output("spectral_silence_v2.json"),
+    )
+    parser.add_argument(
+        "--output-npz",
+        type=Path,
+        default=_default_output("spectral_silence_v2.npz"),
+    )
+    parser.add_argument(
+        "--samples-per-g",
+        type=int,
+        default=REGISTERED_SAMPLES_PER_G,
+    )
+    parser.add_argument(
+        "--spectral-samples",
+        type=int,
+        default=REGISTERED_SPECTRAL_SAMPLES,
+    )
+    parser.add_argument(
+        "--quadrature-order",
+        type=int,
+        default=REGISTERED_QUADRATURE_ORDER,
+    )
+    parser.add_argument(
+        "--rank-form-factor-samples",
+        type=int,
+        default=REGISTERED_RANK_FORM_FACTOR_SAMPLES,
+    )
+    args = parser.parse_args()
+    result = run(
+        args.output_json,
+        args.output_npz,
+        samples_per_g=args.samples_per_g,
+        spectral_samples=args.spectral_samples,
+        quadrature_order=args.quadrature_order,
+        rank_form_factor_samples=args.rank_form_factor_samples,
+    )
+    print(json.dumps(result, indent=2))
+    if not result["all_checks_pass"]:
+        raise SystemExit("spectral-silence production audit failed")
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/run_statistical_analysis_v1.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/run_statistical_analysis_v1.py
new file mode 100644
index 000000000..8d4b47dd3
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/run_statistical_analysis_v1.py
@@ -0,0 +1,597 @@
+#!/usr/bin/env python3
+"""Matrix-level inference for the large-scale Geometric-ETH ensembles."""
+
+from __future__ import annotations
+
+import argparse
+import json
+import platform
+import time
+from datetime import datetime, timezone
+from pathlib import Path
+from typing import Any
+
+import numpy as np
+from scipy.ndimage import gaussian_filter1d
+
+from lgeth.statistics import (
+    bulk_gap_ratio_per_spectrum,
+    fit_size_models,
+    matrix_bootstrap_band,
+    number_variance_matrix_curves,
+    unfold_spectra,
+)
+
+
+VERSION = "v1"
+BOOTSTRAP_REPLICATES = 10_000
+DENSITY_GRID = np.linspace(-1.05, 1.05, 301)
+KDE_BANDWIDTH = 0.025
+RATIO_EDGES = np.linspace(0.0, 1.0, 61)
+LENGTHS = np.linspace(0.25, 8.0, 32)
+FORM_FACTOR_TIMES = np.linspace(0.0, 3.0, 61)
+
+
+def _kde_matrix_curves(
+    spectra: np.ndarray,
+    grid: np.ndarray,
+    bandwidth: float,
+) -> np.ndarray:
+    values = np.asarray(spectra, dtype=float)
+    result = np.empty((values.shape[0], grid.size), dtype=np.float32)
+    normalization = bandwidth * np.sqrt(2.0 * np.pi)
+    for start in range(0, values.shape[0], 256):
+        stop = min(start + 256, values.shape[0])
+        difference = (
+            grid[None, :, None] - values[start:stop, None, :]
+        ) / bandwidth
+        curves = np.mean(
+            np.exp(-0.5 * difference * difference),
+            axis=2,
+        ) / normalization
+        integral = np.trapezoid(curves, grid, axis=1)
+        result[start:stop] = curves / integral[:, None]
+    return result
+
+
+def _ratio_matrix_curves(spectra: np.ndarray) -> np.ndarray:
+    values = np.sort(np.asarray(spectra, dtype=float), axis=1)
+    curves = np.empty(
+        (values.shape[0], RATIO_EDGES.size - 1),
+        dtype=np.float32,
+    )
+    width = np.diff(RATIO_EDGES)
+    for matrix, levels in enumerate(values):
+        trim = int(np.floor(0.15 * levels.size))
+        bulk = levels[trim : levels.size - trim]
+        gaps = np.diff(bulk)
+        ratios = np.minimum(gaps[:-1], gaps[1:]) / np.maximum(
+            gaps[:-1],
+            gaps[1:],
+        )
+        counts, _ = np.histogram(ratios, bins=RATIO_EDGES)
+        curves[matrix] = counts / (np.sum(counts) * width)
+    return curves
+
+
+def _rigidity_from_number(
+    number_curves: np.ndarray,
+    lengths: np.ndarray,
+) -> np.ndarray:
+    result = np.empty_like(number_curves)
+    extended_x = np.concatenate([[0.0], lengths])
+    for column, length in enumerate(lengths):
+        x = extended_x[: column + 2]
+        values = np.concatenate(
+            [
+                np.zeros((number_curves.shape[0], 1)),
+                number_curves[:, : column + 1],
+            ],
+            axis=1,
+        )
+        kernel = length**3 - 2.0 * length * length * x + x**3
+        result[:, column] = (
+            2.0
+            / length**4
+            * np.trapezoid(values * kernel[None, :], x, axis=1)
+        )
+    return result
+
+
+def _form_factor_matrix_curves(
+    unfolded: np.ndarray,
+    times: np.ndarray,
+) -> np.ndarray:
+    levels = unfolded.shape[1]
+    partition = np.empty(
+        (unfolded.shape[0], times.size),
+        dtype=np.complex128,
+    )
+    for start in range(0, unfolded.shape[0], 512):
+        stop = min(start + 512, unfolded.shape[0])
+        phases = np.exp(
+            -2j
+            * np.pi
+            * unfolded[start:stop, :, None]
+            * times[None, None, :]
+        )
+        partition[start:stop] = np.sum(phases, axis=1)
+    mean_partition = np.mean(partition, axis=0)
+    return (
+        np.abs(partition) ** 2
+        - np.abs(mean_partition)[None, :] ** 2
+    ) / levels
+
+
+def _band_arrays(prefix: str, band, output: dict[str, np.ndarray]) -> None:
+    output[f"{prefix}_mean"] = band.mean.astype(np.float32)
+    output[f"{prefix}_lower"] = band.lower.astype(np.float32)
+    output[f"{prefix}_upper"] = band.upper.astype(np.float32)
+    output[f"{prefix}_pointwise_lower"] = band.pointwise_lower.astype(
+        np.float32
+    )
+    output[f"{prefix}_pointwise_upper"] = band.pointwise_upper.astype(
+        np.float32
+    )
+    output[f"{prefix}_standard_error"] = band.standard_error.astype(
+        np.float32
+    )
+
+
+def _curve_suite(
+    spectra: np.ndarray,
+    seed: int,
+    output: dict[str, np.ndarray],
+    prefix: str,
+    groups: np.ndarray | None,
+    replicates: int,
+) -> dict[str, Any]:
+    density_curves = _kde_matrix_curves(
+        spectra,
+        DENSITY_GRID,
+        KDE_BANDWIDTH,
+    )
+    ratio_curves = _ratio_matrix_curves(spectra)
+    unfolded = unfold_spectra(spectra, "ensemble_cdf")
+    number_curves = number_variance_matrix_curves(unfolded, LENGTHS)
+    rigidity_curves = _rigidity_from_number(number_curves, LENGTHS)
+    form_curves = _form_factor_matrix_curves(
+        unfolded,
+        FORM_FACTOR_TIMES,
+    )
+    moments = np.column_stack(
+        [np.mean(spectra.astype(float) ** order, axis=1) for order in (2,4,6,8)]
+    )
+    curve_sets = {
+        "density": density_curves,
+        "ratio": ratio_curves,
+        "number": number_curves,
+        "rigidity": rigidity_curves,
+        "form_factor": form_curves,
+        "moments": moments,
+    }
+    metadata: dict[str, Any] = {}
+    for offset, (name, curves) in enumerate(curve_sets.items()):
+        band = matrix_bootstrap_band(
+            curves,
+            replicates=replicates,
+            seed=seed + offset,
+            groups=groups,
+        )
+        _band_arrays(f"{prefix}_{name}", band, output)
+        metadata[name] = {
+            "method": band.method,
+            "units": band.units,
+            "replicates": band.replicates,
+            "critical_value": band.critical_value,
+        }
+    return metadata
+
+
+def _smoothed_density(
+    spectra: np.ndarray,
+    bandwidth: float,
+) -> np.ndarray:
+    fine_edges = np.linspace(-1.1, 1.1, 2202)
+    density, _ = np.histogram(
+        spectra.ravel(),
+        bins=fine_edges,
+        density=True,
+    )
+    centers = 0.5 * (fine_edges[:-1] + fine_edges[1:])
+    spacing = centers[1] - centers[0]
+    smoothed = gaussian_filter1d(
+        density,
+        bandwidth / spacing,
+        mode="constant",
+    )
+    interpolated = np.interp(DENSITY_GRID, centers, smoothed)
+    return interpolated / np.trapezoid(interpolated, DENSITY_GRID)
+
+
+def _sensitivity(
+    physical: np.ndarray,
+    haar: np.ndarray,
+    deformed: np.ndarray,
+) -> dict[str, Any]:
+    bandwidth_results = {}
+    for bandwidth in (0.015, 0.02, 0.025, 0.035, 0.05):
+        first = _smoothed_density(physical, bandwidth)
+        second = _smoothed_density(haar, bandwidth)
+        third = _smoothed_density(deformed, bandwidth)
+        bandwidth_results[str(bandwidth)] = {
+            "physical_haar_l1": float(
+                np.trapezoid(np.abs(first - second), DENSITY_GRID)
+            ),
+            "physical_deformed_l1": float(
+                np.trapezoid(np.abs(first - third), DENSITY_GRID)
+            ),
+        }
+    bulk_results = {}
+    for fraction in (0.5, 0.6, 0.7, 0.8, 0.9):
+        bulk_results[str(fraction)] = {
+            "physical": float(
+                np.mean(
+                    bulk_gap_ratio_per_spectrum(
+                        physical,
+                        bulk_fraction=fraction,
+                    )
+                )
+            ),
+            "haar": float(
+                np.mean(
+                    bulk_gap_ratio_per_spectrum(
+                        haar,
+                        bulk_fraction=fraction,
+                    )
+                )
+            ),
+            "deformed": float(
+                np.mean(
+                    bulk_gap_ratio_per_spectrum(
+                        deformed,
+                        bulk_fraction=fraction,
+                    )
+                )
+            ),
+        }
+    unfolding_results = {}
+    for method in ("ensemble_cdf", "polynomial"):
+        unfolding_results[method] = {}
+        for name, spectra in (
+            ("physical", physical),
+            ("haar", haar),
+            ("deformed", deformed),
+        ):
+            unfolded = unfold_spectra(spectra, method)
+            unfolding_results[method][name] = float(
+                np.mean(bulk_gap_ratio_per_spectrum(unfolded))
+            )
+    binning_results = {}
+    for bins in (30, 50, 70):
+        edges = np.linspace(0.0, 1.0, bins + 1)
+        distributions = {}
+        for name, spectra in (
+            ("physical", physical),
+            ("haar", haar),
+            ("deformed", deformed),
+        ):
+            ordered = np.sort(spectra, axis=1)
+            gaps = np.diff(ordered, axis=1)
+            ratios = np.minimum(gaps[:, :-1], gaps[:, 1:]) / np.maximum(
+                gaps[:, :-1], gaps[:, 1:]
+            )
+            distributions[name], _ = np.histogram(
+                ratios,
+                bins=edges,
+                density=True,
+            )
+        binning_results[str(bins)] = {
+            "physical_haar_l1": float(
+                np.sum(
+                    np.abs(
+                        distributions["physical"] - distributions["haar"]
+                    )
+                    * np.diff(edges)
+                )
+            ),
+            "physical_deformed_l1": float(
+                np.sum(
+                    np.abs(
+                        distributions["physical"]
+                        - distributions["deformed"]
+                    )
+                    * np.diff(edges)
+                )
+            ),
+        }
+    return {
+        "bandwidth": bandwidth_results,
+        "bulk_fraction": bulk_results,
+        "unfolding": unfolding_results,
+        "ratio_binning": binning_results,
+    }
+
+
+def _scaling_inference(
+    scaling_json: dict[str, Any],
+    scaling_arrays: Any,
+) -> tuple[dict[str, Any], dict[str, np.ndarray]]:
+    cases = scaling_json["cases"]
+    D = np.asarray([case["D"] for case in cases], dtype=float)
+    M = np.asarray([case["M"] for case in cases], dtype=float)
+    density = np.asarray(
+        [case["interior_density_l1"] for case in cases],
+        dtype=float,
+    )
+    gap = np.asarray(
+        [case["gap_ratio_difference"] for case in cases],
+        dtype=float,
+    )
+    participation = np.asarray(
+        [case["mean_participation"] for case in cases],
+        dtype=float,
+    )
+    density_se = np.empty(D.size)
+    gap_se = np.empty(D.size)
+    participation_se = np.empty(D.size)
+    for index, case in enumerate(cases):
+        n = case["n"]
+        labels = scaling_arrays[f"n{n}_seed_block"]
+        root = scaling_arrays[f"n{n}_interior_spectra"]
+        reference = scaling_arrays[f"n{n}_reference_interior_spectra"]
+        root_ratio = scaling_arrays[f"n{n}_gap_ratios"]
+        reference_ratio = scaling_arrays[f"n{n}_reference_gap_ratios"]
+        root_participation = scaling_arrays[f"n{n}_participation"]
+        block_density = []
+        block_gap = []
+        block_participation = []
+        edges = np.linspace(-1.0, 1.0, 161)
+        reference_density, _ = np.histogram(
+            reference.ravel(),
+            bins=edges,
+            density=True,
+        )
+        for block in np.unique(labels):
+            keep = labels == block
+            block_hist, _ = np.histogram(
+                root[keep].ravel(),
+                bins=edges,
+                density=True,
+            )
+            block_density.append(
+                np.sum(np.abs(block_hist - reference_density) * np.diff(edges))
+            )
+            block_gap.append(
+                abs(
+                    float(np.mean(root_ratio[keep]))
+                    - float(np.mean(reference_ratio))
+                )
+            )
+            block_participation.append(
+                float(np.mean(root_participation[keep]))
+            )
+        density_se[index] = np.std(block_density, ddof=1) / np.sqrt(
+            len(block_density)
+        )
+        gap_se[index] = np.std(block_gap, ddof=1) / np.sqrt(len(block_gap))
+        participation_se[index] = np.std(
+            block_participation,
+            ddof=1,
+        ) / np.sqrt(len(block_participation))
+    density_se = np.maximum(density_se, 1e-4)
+    gap_se = np.maximum(gap_se, 1e-4)
+    participation_se = np.maximum(participation_se, 1e-5)
+    fits = {
+        "density_l1": fit_size_models(D, density, density_se),
+        "gap_ratio_difference": fit_size_models(D, gap, gap_se),
+        "participation_deficit": fit_size_models(
+            D,
+            1.0 - participation,
+            participation_se,
+        ),
+    }
+    arrays = {
+        "scaling_D": D.astype(np.float32),
+        "scaling_M": M.astype(np.float32),
+        "scaling_density_l1": density.astype(np.float32),
+        "scaling_density_se": density_se.astype(np.float32),
+        "scaling_gap_difference": gap.astype(np.float32),
+        "scaling_gap_se": gap_se.astype(np.float32),
+        "scaling_participation": participation.astype(np.float32),
+        "scaling_participation_se": participation_se.astype(np.float32),
+        "scaling_atom_weight": np.asarray(
+            [
+                2.0 * case["plus_atoms_per_matrix"] / case["D"]
+                for case in cases
+            ],
+            dtype=np.float32,
+        ),
+    }
+    return fits, arrays
+
+
+def run(
+    physical_npz: Path,
+    covariance_npz: Path,
+    scaling_json_path: Path,
+    scaling_npz: Path,
+    output_json: Path,
+    output_npz: Path,
+    bootstrap_replicates: int = BOOTSTRAP_REPLICATES,
+) -> dict[str, Any]:
+    """Generate confidence bands, long-range diagnostics, and size fits."""
+
+    started = time.perf_counter()
+    replicates = int(bootstrap_replicates)
+    if replicates < 100:
+        raise ValueError("at least 100 bootstrap replicates are required")
+    with np.load(physical_npz) as physical_arrays:
+        test_indices = physical_arrays["test_indices"]
+        physical = physical_arrays["normalized_spectra"][
+            test_indices
+        ].astype(float)
+        physical_groups = physical_arrays["seed_block"][test_indices]
+    with np.load(covariance_npz) as covariance_arrays:
+        haar = covariance_arrays["haar_spectra"].astype(float)
+        deformed = covariance_arrays["deformed_spectra"].astype(float)
+    scaling_json = json.loads(
+        scaling_json_path.read_text(encoding="utf-8")
+    )
+    output_arrays: dict[str, np.ndarray] = {
+        "density_grid": DENSITY_GRID.astype(np.float32),
+        "ratio_centers": (
+            0.5 * (RATIO_EDGES[:-1] + RATIO_EDGES[1:])
+        ).astype(np.float32),
+        "lengths": LENGTHS.astype(np.float32),
+        "form_factor_times": FORM_FACTOR_TIMES.astype(np.float32),
+        "moment_orders": np.asarray([2, 4, 6, 8], dtype=np.int16),
+    }
+    ensemble_metadata = {}
+    for offset, (name, spectra, groups) in enumerate(
+        (
+            ("physical", physical, physical_groups),
+            ("haar", haar, None),
+            ("deformed", deformed, None),
+        )
+    ):
+        print(f"statistical curves: {name}", flush=True)
+        ensemble_metadata[name] = _curve_suite(
+            spectra,
+            seed=20260728600 + 20 * offset,
+            output=output_arrays,
+            prefix=name,
+            groups=groups,
+            replicates=replicates,
+        )
+    sensitivity = _sensitivity(physical, haar, deformed)
+    with np.load(scaling_npz) as scaling_arrays:
+        fits, scaling_output = _scaling_inference(
+            scaling_json,
+            scaling_arrays,
+        )
+    output_arrays.update(scaling_output)
+    density_band_ordering = all(
+        values["physical_deformed_l1"]
+        < values["physical_haar_l1"]
+        for values in sensitivity["bandwidth"].values()
+    )
+    checks = {
+        "registered_bootstrap_count": (
+            replicates == BOOTSTRAP_REPLICATES
+        ),
+        "physical_uses_seed_block_hierarchy": (
+            ensemble_metadata["physical"]["density"]["method"]
+            == "hierarchical_seed_block_bootstrap"
+        ),
+        "reference_uses_matrix_level_inference": (
+            ensemble_metadata["haar"]["density"]["method"].startswith(
+                "matrix_"
+            )
+            and ensemble_metadata["deformed"]["density"][
+                "method"
+            ].startswith("matrix_")
+        ),
+        "covariance_improvement_bandwidth_stable": density_band_ordering,
+        "all_size_fits_registered": all(
+            fit["best_by_loo"] in {"D^-1/2", "D^-1", "free"}
+            for fit in fits.values()
+        ),
+        "all_curves_finite": all(
+            bool(np.all(np.isfinite(value)))
+            for value in output_arrays.values()
+        ),
+    }
+    result = {
+        "schema_version": 1,
+        "version": VERSION,
+        "generated_utc": datetime.now(timezone.utc).isoformat(),
+        "sources": {
+            "physical": str(physical_npz),
+            "covariance": str(covariance_npz),
+            "scaling_json": str(scaling_json_path),
+            "scaling_npz": str(scaling_npz),
+        },
+        "bootstrap_replicates": replicates,
+        "kde_bandwidth": KDE_BANDWIDTH,
+        "bulk_fraction": 0.7,
+        "unfolding": "ensemble_cdf",
+        "physical_test_matrices": int(physical.shape[0]),
+        "haar_matrices": int(haar.shape[0]),
+        "deformed_matrices": int(deformed.shape[0]),
+        "ensemble_inference": ensemble_metadata,
+        "sensitivity": sensitivity,
+        "finite_size_fits": fits,
+        "checks": checks,
+        "all_checks_pass": bool(all(checks.values())),
+        "runtime_seconds": time.perf_counter() - started,
+        "environment": {
+            "python": platform.python_version(),
+            "numpy": np.__version__,
+            "platform": platform.platform(),
+        },
+    }
+    output_json.parent.mkdir(parents=True, exist_ok=True)
+    output_npz.parent.mkdir(parents=True, exist_ok=True)
+    output_json.write_text(
+        json.dumps(result, indent=2) + "\n",
+        encoding="utf-8",
+    )
+    np.savez_compressed(output_npz, **output_arrays)
+    return result
+
+
+def main() -> None:
+    parser = argparse.ArgumentParser()
+    parser.add_argument(
+        "--physical-npz",
+        type=Path,
+        default=Path("output/physical_ensemble_v1.npz"),
+    )
+    parser.add_argument(
+        "--covariance-npz",
+        type=Path,
+        default=Path("output/covariance_model_v1.npz"),
+    )
+    parser.add_argument(
+        "--scaling-json",
+        type=Path,
+        default=Path("output/rank_scaling_v1.json"),
+    )
+    parser.add_argument(
+        "--scaling-npz",
+        type=Path,
+        default=Path("output/rank_scaling_v1.npz"),
+    )
+    parser.add_argument(
+        "--output-json",
+        type=Path,
+        default=Path("output/statistical_analysis_v1.json"),
+    )
+    parser.add_argument(
+        "--output-npz",
+        type=Path,
+        default=Path("output/statistical_analysis_v1.npz"),
+    )
+    parser.add_argument(
+        "--bootstrap-replicates",
+        type=int,
+        default=BOOTSTRAP_REPLICATES,
+    )
+    args = parser.parse_args()
+    result = run(
+        args.physical_npz,
+        args.covariance_npz,
+        args.scaling_json,
+        args.scaling_npz,
+        args.output_json,
+        args.output_npz,
+        bootstrap_replicates=args.bootstrap_replicates,
+    )
+    print(json.dumps(result, indent=2))
+    if not result["all_checks_pass"]:
+        raise SystemExit("statistical-analysis audit failed")
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/run_topological_holonomy_v3.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/run_topological_holonomy_v3.py
new file mode 100644
index 000000000..85c3ff5a1
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/run_topological_holonomy_v3.py
@@ -0,0 +1,877 @@
+#!/usr/bin/env python3
+"""Run fixed-Chern isospectral Wilson-holonomy statistics."""
+
+from __future__ import annotations
+
+import argparse
+import concurrent.futures
+import hashlib
+import json
+import platform
+import time
+from datetime import datetime, timezone
+from pathlib import Path
+from typing import Any
+
+import numpy as np
+
+from lgeth.bundle_geometry import (
+    analyze_frame_bundle,
+    random_local_gauge,
+    sorted_wilson_eigenphases,
+)
+from lgeth.holonomy import (
+    cue_wilson_reference,
+    deform_orbital_mesh,
+    wilson_statistics,
+)
+from lgeth.lattice import BosonBasis
+from lgeth.twist_bundle import (
+    default_checkpoint_path,
+    load_twist_bundle,
+)
+
+
+VERSION = "v3"
+SCRIPT_ROOT = Path(__file__).resolve().parent
+OUTPUT_ROOT = SCRIPT_ROOT / "output"
+OUTPUT_JSON = OUTPUT_ROOT / "topological_holonomy_v3.json"
+OUTPUT_NPZ = OUTPUT_ROOT / "topological_holonomy_v3.npz"
+REGISTERED_SIZES = ((3, 8, 16), (4, 10, 25))
+REGISTERED_PRIMARY_MESH = 16
+REGISTERED_CONVERGENCE_MESH = 20
+REGISTERED_G = (0.0, 0.25, 0.5, 0.75, 1.0)
+REGISTERED_GENERATOR_SEEDS = tuple(20260728400 + index for index in range(8))
+REGISTERED_COMMUTING_SEED = 20260728499
+REGISTERED_CUE_SAMPLES = 10_000
+REGISTERED_SEED = 20260728480
+REGISTERED_BOOTSTRAP_SAMPLES = 20_000
+MESH_ALIAS_AUDIT_JSON = (
+    OUTPUT_ROOT / "topological_holonomy_mesh12_alias_audit_v3.json"
+)
+MESH_ALIAS_AUDIT_NPZ = (
+    OUTPUT_ROOT / "topological_holonomy_mesh12_alias_audit_v3.npz"
+)
+
+
+def _sha256(path: Path) -> str:
+    return hashlib.sha256(path.read_bytes()).hexdigest()
+
+
+def _atomic_json(path: Path, payload: dict[str, Any]) -> None:
+    path.parent.mkdir(parents=True, exist_ok=True)
+    temporary = path.with_suffix(path.suffix + ".tmp")
+    temporary.write_text(
+        json.dumps(payload, indent=2, sort_keys=True),
+        encoding="utf-8",
+    )
+    temporary.replace(path)
+
+
+def _atomic_npz(path: Path, **arrays: np.ndarray) -> None:
+    path.parent.mkdir(parents=True, exist_ok=True)
+    temporary = path.with_suffix(path.suffix + ".tmp")
+    with temporary.open("wb") as handle:
+        np.savez_compressed(handle, **arrays)
+    temporary.replace(path)
+
+
+def _raw_bundle_arrays(
+    N: int,
+    mesh: int,
+) -> tuple[np.ndarray, np.ndarray, np.ndarray, np.ndarray]:
+    metadata = default_checkpoint_path(N, mesh)
+    arrays_path = metadata.with_suffix(".npz")
+    with np.load(arrays_path, allow_pickle=False) as arrays:
+        return (
+            np.asarray(arrays["energies"], dtype=float),
+            np.asarray(arrays["external_gap"], dtype=float),
+            np.asarray(arrays["coefficient_frames"], dtype=complex),
+            np.asarray(arrays["orbital_frames"], dtype=complex),
+        )
+
+
+def _geometry_record(
+    geometry,
+    k_values: np.ndarray,
+) -> dict[str, Any]:
+    statistics = wilson_statistics(geometry, k_values=k_values)
+    return {
+        "chern_determinant": geometry.chern_determinant,
+        "chern_trace_log": geometry.chern_trace_log,
+        "branch_margin": geometry.determinant_branch_margin,
+        "minimum_overlap": geometry.minimum_overlap_singular_value,
+        "maximum_link_error": geometry.maximum_link_unitarity_error,
+        "maximum_plaquette_error": (
+            geometry.maximum_plaquette_unitarity_error
+        ),
+        "gap_ratio": np.asarray(statistics["gap_ratio"]),
+        "mean_gap_ratio": float(statistics["mean_gap_ratio"]),
+        "form_factor": np.asarray(statistics["form_factor"]),
+        "mean_form_factor": np.asarray(statistics["mean_form_factor"]),
+        "determinant_phase_x": np.asarray(
+            statistics["determinant_phase_x"]
+        ),
+        "determinant_phase_y": np.asarray(
+            statistics["determinant_phase_y"]
+        ),
+    }
+
+
+def _seed_worker(arguments: tuple[Any, ...]) -> dict[str, Any]:
+    (
+        N,
+        n_flux,
+        rank,
+        primary_mesh,
+        convergence_mesh,
+        positive_g,
+        seed,
+        commuting,
+    ) = arguments
+    _, _, coefficients, orbitals = _raw_bundle_arrays(N, primary_mesh)
+    basis = BosonBasis(n_flux, N)
+    k_values = np.arange(1, rank + 1, dtype=int)
+    primary_records: list[dict[str, Any]] = []
+    for coupling in positive_g:
+        deformed = deform_orbital_mesh(
+            orbitals,
+            g=float(coupling),
+            seed=int(seed),
+            commuting=bool(commuting),
+        )
+        geometry = analyze_frame_bundle(
+            coefficients,
+            deformed,
+            basis,
+        )
+        primary_records.append(_geometry_record(geometry, k_values))
+    endpoint_record = None
+    if not commuting:
+        _, _, endpoint_coefficients, endpoint_orbitals = _raw_bundle_arrays(
+            N,
+            convergence_mesh,
+        )
+        endpoint_deformed = deform_orbital_mesh(
+            endpoint_orbitals,
+            g=float(positive_g[-1]),
+            seed=int(seed),
+            commuting=False,
+        )
+        endpoint_geometry = analyze_frame_bundle(
+            endpoint_coefficients,
+            endpoint_deformed,
+            basis,
+        )
+        endpoint_record = _geometry_record(
+            endpoint_geometry,
+            k_values,
+        )
+    return {
+        "N": int(N),
+        "seed": int(seed),
+        "commuting": bool(commuting),
+        "primary": primary_records,
+        "endpoint": endpoint_record,
+    }
+
+
+def _run_workers(
+    arguments: list[tuple[Any, ...]],
+    workers: int,
+) -> list[dict[str, Any]]:
+    if int(workers) <= 1:
+        return [_seed_worker(item) for item in arguments]
+    results: list[dict[str, Any]] = []
+    with concurrent.futures.ProcessPoolExecutor(
+        max_workers=int(workers)
+    ) as executor:
+        futures = [executor.submit(_seed_worker, item) for item in arguments]
+        for future in concurrent.futures.as_completed(futures):
+            result = future.result()
+            results.append(result)
+            print(
+                f"completed N={result['N']} seed={result['seed']} "
+                f"commuting={result['commuting']}",
+                flush=True,
+            )
+    return results
+
+
+def _interval(values: np.ndarray) -> list[float]:
+    return np.quantile(
+        np.asarray(values, dtype=float),
+        [0.025, 0.5, 0.975],
+    ).tolist()
+
+
+def _bootstrap_mean_interval(
+    values: np.ndarray,
+    seed: int,
+    samples: int = REGISTERED_BOOTSTRAP_SAMPLES,
+) -> list[float]:
+    """Return a seed-cluster bootstrap interval for the mean."""
+
+    observations = np.asarray(values, dtype=float)
+    if observations.ndim != 1 or observations.size < 1:
+        raise ValueError("bootstrap values must be a nonempty vector")
+    if observations.size == 1:
+        value = float(observations[0])
+        return [value, value, value]
+    rng = np.random.default_rng(int(seed))
+    indices = rng.integers(
+        0,
+        observations.size,
+        size=(int(samples), observations.size),
+    )
+    means = np.mean(observations[indices], axis=1)
+    return np.quantile(means, [0.025, 0.5, 0.975]).tolist()
+
+
+def _cue_simultaneous_band(
+    form_factor: np.ndarray,
+    stop: int,
+) -> tuple[np.ndarray, np.ndarray, np.ndarray, float]:
+    """Build an empirical 95% simultaneous CUE band over ``k < stop``."""
+
+    values = np.asarray(form_factor, dtype=float)
+    if values.ndim != 2 or not 1 <= int(stop) <= values.shape[1]:
+        raise ValueError("invalid CUE form-factor window")
+    window = values[:, : int(stop)]
+    center = np.mean(window, axis=0)
+    scale = np.std(window, axis=0, ddof=1)
+    if np.any(scale <= 0.0):
+        raise RuntimeError("CUE reference has a singular pointwise scale")
+    maximum_standardized_deviation = np.max(
+        np.abs((window - center[None, :]) / scale[None, :]),
+        axis=1,
+    )
+    critical = float(
+        np.quantile(maximum_standardized_deviation, 0.95)
+    )
+    return (
+        center,
+        center - critical * scale,
+        center + critical * scale,
+        critical,
+    )
+
+
+def _size_summary(
+    size: tuple[int, int, int],
+    primary_mesh: int,
+    convergence_mesh: int,
+    g_values: tuple[float, ...],
+    seeds: tuple[int, ...],
+    records: list[dict[str, Any]],
+    commuting_record: dict[str, Any],
+    cue_samples: int,
+    cue_seed: int,
+) -> tuple[dict[str, Any], dict[str, np.ndarray]]:
+    N, n_flux, rank = size
+    primary_base = load_twist_bundle(
+        default_checkpoint_path(N, primary_mesh),
+        N,
+        n_flux,
+        rank,
+        primary_mesh,
+    )
+    convergence_base = load_twist_bundle(
+        default_checkpoint_path(N, convergence_mesh),
+        N,
+        n_flux,
+        rank,
+        convergence_mesh,
+    )
+    k_values = np.arange(1, rank + 1, dtype=int)
+    base_record = _geometry_record(primary_base.geometry, k_values)
+    convergence_base_record = _geometry_record(
+        convergence_base.geometry,
+        k_values,
+    )
+    by_seed = {
+        int(record["seed"]): record
+        for record in records
+        if record["N"] == N and not record["commuting"]
+    }
+    if set(by_seed) != set(seeds):
+        raise RuntimeError(f"missing noncommuting records for N={N}")
+    positive_count = len(g_values) - 1
+    gap_mean = np.empty((len(seeds), len(g_values)), dtype=float)
+    form_mean = np.empty(
+        (len(seeds), len(g_values), rank),
+        dtype=float,
+    )
+    loop_count = 2 * primary_mesh
+    gap_loops = np.empty(
+        (len(seeds), len(g_values), loop_count),
+        dtype=float,
+    )
+    form_loops = np.empty(
+        (len(seeds), len(g_values), loop_count, rank),
+        dtype=float,
+    )
+    chern = np.empty((len(seeds), len(g_values)), dtype=float)
+    trace_chern = np.empty_like(chern)
+    branch_margin = np.empty_like(chern)
+    minimum_overlap = np.empty_like(chern)
+    endpoint_chern = np.empty(len(seeds), dtype=float)
+    endpoint_trace_chern = np.empty(len(seeds), dtype=float)
+    endpoint_branch_margin = np.empty(len(seeds), dtype=float)
+    endpoint_overlap = np.empty(len(seeds), dtype=float)
+    endpoint_gap_loops = np.empty(
+        (len(seeds), 2 * convergence_mesh),
+        dtype=float,
+    )
+    endpoint_form_loops = np.empty(
+        (len(seeds), 2 * convergence_mesh, rank),
+        dtype=float,
+    )
+    for seed_index, seed in enumerate(seeds):
+        gap_mean[seed_index, 0] = base_record["mean_gap_ratio"]
+        form_mean[seed_index, 0] = base_record["mean_form_factor"]
+        gap_loops[seed_index, 0] = base_record["gap_ratio"]
+        form_loops[seed_index, 0] = base_record["form_factor"]
+        chern[seed_index, 0] = base_record["chern_determinant"]
+        trace_chern[seed_index, 0] = base_record["chern_trace_log"]
+        branch_margin[seed_index, 0] = base_record["branch_margin"]
+        minimum_overlap[seed_index, 0] = base_record["minimum_overlap"]
+        record = by_seed[seed]
+        if len(record["primary"]) != positive_count:
+            raise RuntimeError("deformation grid is incomplete")
+        for offset, point in enumerate(record["primary"], start=1):
+            gap_mean[seed_index, offset] = point["mean_gap_ratio"]
+            form_mean[seed_index, offset] = point["mean_form_factor"]
+            gap_loops[seed_index, offset] = point["gap_ratio"]
+            form_loops[seed_index, offset] = point["form_factor"]
+            chern[seed_index, offset] = point["chern_determinant"]
+            trace_chern[seed_index, offset] = point["chern_trace_log"]
+            branch_margin[seed_index, offset] = point["branch_margin"]
+            minimum_overlap[seed_index, offset] = point["minimum_overlap"]
+        endpoint = record["endpoint"]
+        endpoint_chern[seed_index] = endpoint["chern_determinant"]
+        endpoint_trace_chern[seed_index] = endpoint["chern_trace_log"]
+        endpoint_branch_margin[seed_index] = endpoint["branch_margin"]
+        endpoint_overlap[seed_index] = endpoint["minimum_overlap"]
+        endpoint_gap_loops[seed_index] = endpoint["gap_ratio"]
+        endpoint_form_loops[seed_index] = endpoint["form_factor"]
+    commuting_gap = np.empty(len(g_values), dtype=float)
+    commuting_form = np.empty((len(g_values), rank), dtype=float)
+    commuting_chern = np.empty(len(g_values), dtype=float)
+    commuting_gap_loops = np.empty(
+        (len(g_values), loop_count),
+        dtype=float,
+    )
+    commuting_form_loops = np.empty(
+        (len(g_values), loop_count, rank),
+        dtype=float,
+    )
+    commuting_gap[0] = base_record["mean_gap_ratio"]
+    commuting_form[0] = base_record["mean_form_factor"]
+    commuting_chern[0] = base_record["chern_determinant"]
+    commuting_gap_loops[0] = base_record["gap_ratio"]
+    commuting_form_loops[0] = base_record["form_factor"]
+    for offset, point in enumerate(
+        commuting_record["primary"],
+        start=1,
+    ):
+        commuting_gap[offset] = point["mean_gap_ratio"]
+        commuting_form[offset] = point["mean_form_factor"]
+        commuting_chern[offset] = point["chern_determinant"]
+        commuting_gap_loops[offset] = point["gap_ratio"]
+        commuting_form_loops[offset] = point["form_factor"]
+    cue = cue_wilson_reference(
+        D=rank,
+        samples=int(cue_samples),
+        k_values=k_values,
+        seed=int(cue_seed),
+    )
+    cue_gap_interval = _interval(cue["gap_ratio"])
+    nonplateau_stop = max(2, rank // 2)
+    (
+        cue_form_window_mean,
+        cue_form_simultaneous_lower,
+        cue_form_simultaneous_upper,
+        cue_form_simultaneous_critical,
+    ) = _cue_simultaneous_band(
+        cue["form_factor"],
+        stop=nonplateau_stop,
+    )
+    cue_form_mean = np.mean(cue["form_factor"], axis=0)
+    gap_by_g = [
+        _interval(gap_mean[:, index])
+        for index in range(len(g_values))
+    ]
+    form_by_g = np.median(form_mean, axis=0)
+    final_gap_compatible = (
+        cue_gap_interval[0]
+        <= gap_by_g[-1][1]
+        <= cue_gap_interval[2]
+    )
+    nonplateau = slice(0, max(2, rank // 2))
+    final_form_compatible = bool(np.all(
+        (
+            form_by_g[-1, :nonplateau_stop]
+            >= cue_form_simultaneous_lower
+        )
+        & (
+            form_by_g[-1, :nonplateau_stop]
+            <= cue_form_simultaneous_upper
+        )
+    ))
+    base_residual = float(
+        np.sqrt(
+            np.mean(
+                (
+                    base_record["mean_form_factor"][nonplateau]
+                    - cue_form_mean[nonplateau]
+                )
+                ** 2
+            )
+        )
+    )
+    final_residual = np.sqrt(
+        np.mean(
+            (
+                form_mean[:, -1, nonplateau]
+                - cue_form_mean[None, nonplateau]
+            )
+            ** 2,
+            axis=1,
+        )
+    )
+    residual_improvement = base_residual - final_residual
+    gap_change = gap_mean[:, -1] - gap_mean[:, 0]
+    gap_change_interval = _bootstrap_mean_interval(
+        gap_change,
+        seed=cue_seed + 10_000,
+    )
+    improvement_interval = _bootstrap_mean_interval(
+        residual_improvement,
+        seed=cue_seed + 20_000,
+    )
+    change_significant = (
+        gap_change_interval[0] > 0.0
+        or gap_change_interval[2] < 0.0
+        or improvement_interval[0] > 0.0
+        or improvement_interval[2] < 0.0
+    )
+    base_integer = int(round(base_record["chern_determinant"]))
+    all_chern_values = np.concatenate(
+        [
+            chern.ravel(),
+            endpoint_chern,
+            commuting_chern,
+            np.asarray(
+                [convergence_base_record["chern_determinant"]]
+            ),
+        ]
+    )
+    summary = {
+        "N": N,
+        "n_flux": n_flux,
+        "rank": rank,
+        "primary_mesh": primary_mesh,
+        "convergence_mesh": convergence_mesh,
+        "base_chern_integer": base_integer,
+        "base_chern_primary": base_record["chern_determinant"],
+        "base_chern_convergence": convergence_base_record[
+            "chern_determinant"
+        ],
+        "primary_chern_range": [
+            float(np.min(chern)),
+            float(np.max(chern)),
+        ],
+        "convergence_endpoint_chern_range": [
+            float(np.min(endpoint_chern)),
+            float(np.max(endpoint_chern)),
+        ],
+        "commuting_chern_range": [
+            float(np.min(commuting_chern)),
+            float(np.max(commuting_chern)),
+        ],
+        "minimum_branch_margin": float(
+            min(
+                np.min(branch_margin),
+                np.min(endpoint_branch_margin),
+                base_record["branch_margin"],
+                convergence_base_record["branch_margin"],
+            )
+        ),
+        "minimum_overlap_singular_value": float(
+            min(
+                np.min(minimum_overlap),
+                np.min(endpoint_overlap),
+                base_record["minimum_overlap"],
+                convergence_base_record["minimum_overlap"],
+            )
+        ),
+        "maximum_determinant_trace_difference": float(
+            max(
+                np.max(np.abs(chern - trace_chern)),
+                np.max(
+                    np.abs(endpoint_chern - endpoint_trace_chern)
+                ),
+            )
+        ),
+        "maximum_energy_spectrum_error": 0.0,
+        "maximum_gap_error": 0.0,
+        "isospectrality_mode": (
+            "exact_coordinate_identity_under_periodic_ambient_conjugation"
+        ),
+        "minimum_external_gap": float(
+            min(
+                np.min(primary_base.external_gap),
+                np.min(convergence_base.external_gap),
+            )
+        ),
+        "gap_ratio_by_g": gap_by_g,
+        "base_gap_ratio": base_record["mean_gap_ratio"],
+        "final_gap_ratio_interval": gap_by_g[-1],
+        "cue_gap_ratio_interval": cue_gap_interval,
+        "gap_change_interval": gap_change_interval,
+        "base_form_factor_residual": base_residual,
+        "final_form_factor_residual_interval": _interval(final_residual),
+        "form_factor_improvement_interval": improvement_interval,
+        "cue_form_simultaneous_critical": (
+            cue_form_simultaneous_critical
+        ),
+        "cue_nonplateau_stop": nonplateau_stop,
+        "cue_compatible_at_largest_g": (
+            final_gap_compatible and final_form_compatible
+        ),
+        "holonomy_change_significant": bool(change_significant),
+        "all_chern_equal": bool(
+            np.max(np.abs(all_chern_values - base_integer)) < 1e-8
+        ),
+        "determinant_phase_x_base": base_record[
+            "determinant_phase_x"
+        ].tolist(),
+        "determinant_phase_x_final_seed0": by_seed[seeds[0]][
+            "primary"
+        ][-1]["determinant_phase_x"].tolist(),
+    }
+    arrays = {
+        "gap_mean": gap_mean,
+        "form_mean": form_mean,
+        "gap_loops": gap_loops,
+        "form_loops": form_loops,
+        "chern": chern,
+        "trace_chern": trace_chern,
+        "branch_margin": branch_margin,
+        "minimum_overlap": minimum_overlap,
+        "endpoint_chern": endpoint_chern,
+        "endpoint_trace_chern": endpoint_trace_chern,
+        "endpoint_branch_margin": endpoint_branch_margin,
+        "endpoint_overlap": endpoint_overlap,
+        "endpoint_gap_loops": endpoint_gap_loops,
+        "endpoint_form_loops": endpoint_form_loops,
+        "commuting_gap": commuting_gap,
+        "commuting_form": commuting_form,
+        "commuting_chern": commuting_chern,
+        "commuting_gap_loops": commuting_gap_loops,
+        "commuting_form_loops": commuting_form_loops,
+        "cue_gap": cue["gap_ratio"],
+        "cue_form": cue["form_factor"],
+        "cue_form_simultaneous_mean": cue_form_window_mean,
+        "cue_form_simultaneous_lower": cue_form_simultaneous_lower,
+        "cue_form_simultaneous_upper": cue_form_simultaneous_upper,
+        "base_form": base_record["mean_form_factor"],
+        "base_determinant_phase_x": base_record[
+            "determinant_phase_x"
+        ],
+        "final_determinant_phase_x": by_seed[seeds[0]][
+            "primary"
+        ][-1]["determinant_phase_x"],
+    }
+    return summary, arrays
+
+
+def _random_gauge_error(
+    size: tuple[int, int, int],
+    mesh: int,
+    g: float,
+    seed: int,
+) -> dict[str, float]:
+    N, n_flux, rank = size
+    _, _, coefficients, orbitals = _raw_bundle_arrays(N, mesh)
+    deformed = deform_orbital_mesh(
+        orbitals,
+        g=float(g),
+        seed=int(seed),
+        commuting=False,
+    )
+    basis = BosonBasis(n_flux, N)
+    original = analyze_frame_bundle(coefficients, deformed, basis)
+    transformed = analyze_frame_bundle(
+        random_local_gauge(coefficients, seed=seed + 50_000),
+        deformed,
+        basis,
+    )
+    original_phases = sorted_wilson_eigenphases(original)
+    transformed_phases = sorted_wilson_eigenphases(transformed)
+    return {
+        "chern_error": abs(
+            original.chern_determinant
+            - transformed.chern_determinant
+        ),
+        "wilson_phase_error": float(
+            np.max(
+                np.abs(
+                    np.exp(1j * original_phases)
+                    - np.exp(1j * transformed_phases)
+                )
+            )
+        ),
+    }
+
+
+def select_topology_branch(payload: dict[str, Any]) -> str:
+    """Select the preregistered topology/holonomy result branch."""
+
+    if not all(payload.get("checks", {}).values()):
+        return "topology_mesh_unresolved"
+    sizes = payload.get("sizes", [])
+    if sizes and all(
+        size["cue_compatible_at_largest_g"] for size in sizes
+    ):
+        return "fixed_chern_chaotic_holonomy"
+    if any(size["holonomy_change_significant"] for size in sizes):
+        return "fixed_chern_deformed_holonomy"
+    return "topology_without_holonomy_crossover"
+
+
+def run(
+    output_json: Path = OUTPUT_JSON,
+    output_npz: Path = OUTPUT_NPZ,
+    sizes: tuple[tuple[int, int, int], ...] = REGISTERED_SIZES,
+    primary_mesh: int = REGISTERED_PRIMARY_MESH,
+    convergence_mesh: int = REGISTERED_CONVERGENCE_MESH,
+    g_values: tuple[float, ...] = REGISTERED_G,
+    generator_seeds: tuple[int, ...] = REGISTERED_GENERATOR_SEEDS,
+    cue_samples: int = REGISTERED_CUE_SAMPLES,
+    workers: int = 4,
+    production: bool = True,
+) -> dict[str, Any]:
+    """Run the registered or reduced closed-surface calculation."""
+
+    started = time.perf_counter()
+    if (
+        len(g_values) < 2
+        or g_values[0] != 0.0
+        or any(right <= left for left, right in zip(g_values, g_values[1:]))
+    ):
+        raise ValueError("g grid must be strictly increasing from zero")
+    positive_g = tuple(float(value) for value in g_values[1:])
+    validated_checkpoints: dict[str, str] = {}
+    base_bundles = []
+    for N, n_flux, rank in sizes:
+        for mesh in (primary_mesh, convergence_mesh):
+            path = default_checkpoint_path(N, mesh)
+            bundle = load_twist_bundle(
+                path,
+                N,
+                n_flux,
+                rank,
+                mesh,
+            )
+            base_bundles.append(bundle)
+            validated_checkpoints[str(path.relative_to(SCRIPT_ROOT))] = (
+                _sha256(path)
+            )
+            arrays_path = path.with_suffix(".npz")
+            validated_checkpoints[
+                str(arrays_path.relative_to(SCRIPT_ROOT))
+            ] = _sha256(arrays_path)
+    worker_arguments: list[tuple[Any, ...]] = []
+    for N, n_flux, rank in sizes:
+        for seed in generator_seeds:
+            worker_arguments.append(
+                (
+                    N,
+                    n_flux,
+                    rank,
+                    primary_mesh,
+                    convergence_mesh,
+                    positive_g,
+                    seed,
+                    False,
+                )
+            )
+        worker_arguments.append(
+            (
+                N,
+                n_flux,
+                rank,
+                primary_mesh,
+                convergence_mesh,
+                positive_g,
+                REGISTERED_COMMUTING_SEED,
+                True,
+            )
+        )
+    records = _run_workers(worker_arguments, workers=workers)
+    size_summaries: list[dict[str, Any]] = []
+    size_arrays: list[dict[str, np.ndarray]] = []
+    for size_index, size in enumerate(sizes):
+        commuting = next(
+            record
+            for record in records
+            if record["N"] == size[0] and record["commuting"]
+        )
+        summary, arrays = _size_summary(
+            size=size,
+            primary_mesh=primary_mesh,
+            convergence_mesh=convergence_mesh,
+            g_values=g_values,
+            seeds=generator_seeds,
+            records=records,
+            commuting_record=commuting,
+            cue_samples=cue_samples,
+            cue_seed=REGISTERED_SEED + size_index,
+        )
+        size_summaries.append(summary)
+        size_arrays.append(arrays)
+    gauge = _random_gauge_error(
+        sizes[0],
+        primary_mesh,
+        g_values[-1],
+        generator_seeds[0],
+    )
+    checks = {
+        "kernel_count": all(
+            bundle.observed_rank_min
+            == bundle.observed_rank_max
+            == bundle.rank
+            for bundle in base_bundles
+        ),
+        "gap_open": all(
+            float(np.min(bundle.external_gap)) > 0.0
+            for bundle in base_bundles
+        ),
+        "mesh_chern_integer": all(
+            size["all_chern_equal"] for size in size_summaries
+        ),
+        "mesh_chern_agreement": all(
+            abs(
+                size["base_chern_primary"]
+                - size["base_chern_convergence"]
+            )
+            < 1e-8
+            for size in size_summaries
+        ),
+        "determinant_trace_agreement": all(
+            size["maximum_determinant_trace_difference"] < 1e-8
+            for size in size_summaries
+        ),
+        "branch_margin": all(
+            size["minimum_branch_margin"] > 0.0
+            for size in size_summaries
+        ),
+        "overlap_floor": all(
+            size["minimum_overlap_singular_value"] > 5e-2
+            for size in size_summaries
+        ),
+        "random_gauge_invariance": (
+            gauge["chern_error"] < 1e-9
+            and gauge["wilson_phase_error"] < 1e-8
+        ),
+        "isospectral_orbit": all(
+            size["maximum_energy_spectrum_error"] < 1e-13
+            and size["maximum_gap_error"] < 1e-13
+            for size in size_summaries
+        ),
+        "cue_reference_count": int(cue_samples) >= 64,
+    }
+    payload: dict[str, Any] = {
+        "version": VERSION,
+        "generated_utc": datetime.now(timezone.utc).isoformat(),
+        "configuration": {
+            "sizes": [list(size) for size in sizes],
+            "primary_mesh": int(primary_mesh),
+            "convergence_mesh": int(convergence_mesh),
+            "g_values": list(g_values),
+            "generator_seeds": list(generator_seeds),
+            "commuting_seed": REGISTERED_COMMUTING_SEED,
+            "cue_samples": int(cue_samples),
+            "workers": int(workers),
+            "production": bool(production),
+            "mesh_upgrade_rationale": (
+                "mesh12 aliases one N4 seed at g=1; mesh16 and mesh20 "
+                "are the accepted converged pair"
+            ),
+        },
+        "sizes": size_summaries,
+        "random_gauge_errors": gauge,
+        "checks": checks,
+        "checkpoint_hashes": validated_checkpoints,
+        "mesh_alias_audit": {
+            "json": str(MESH_ALIAS_AUDIT_JSON.relative_to(SCRIPT_ROOT)),
+            "json_sha256": (
+                _sha256(MESH_ALIAS_AUDIT_JSON)
+                if MESH_ALIAS_AUDIT_JSON.exists()
+                else None
+            ),
+            "npz": str(MESH_ALIAS_AUDIT_NPZ.relative_to(SCRIPT_ROOT)),
+            "npz_sha256": (
+                _sha256(MESH_ALIAS_AUDIT_NPZ)
+                if MESH_ALIAS_AUDIT_NPZ.exists()
+                else None
+            ),
+        },
+        "runtime_seconds": time.perf_counter() - started,
+        "environment": {
+            "python": platform.python_version(),
+            "numpy": np.__version__,
+            "platform": platform.platform(),
+        },
+    }
+    payload["result_branch"] = select_topology_branch(payload)
+    output_arrays: dict[str, np.ndarray] = {
+        "g_values": np.asarray(g_values, dtype=float),
+        "generator_seeds": np.asarray(generator_seeds, dtype=np.int64),
+    }
+    for size_index, arrays in enumerate(size_arrays):
+        for key, values in arrays.items():
+            output_arrays[f"size_{size_index}_{key}"] = np.asarray(values)
+    _atomic_npz(output_npz, **output_arrays)
+    payload["npz_sha256"] = _sha256(output_npz)
+    _atomic_json(output_json, payload)
+    if production and not all(checks.values()):
+        raise RuntimeError(f"production topology gates failed: {checks}")
+    return payload
+
+
+def main() -> None:
+    parser = argparse.ArgumentParser()
+    parser.add_argument("--reduced", action="store_true")
+    parser.add_argument("--workers", type=int, default=4)
+    arguments = parser.parse_args()
+    if arguments.reduced:
+        payload = run(
+            sizes=((3, 8, 16),),
+            primary_mesh=6,
+            convergence_mesh=8,
+            g_values=(0.0, 0.25),
+            generator_seeds=(20260728400,),
+            cue_samples=64,
+            workers=1,
+            production=False,
+            output_json=OUTPUT_ROOT / "topological_holonomy_reduced_v3.json",
+            output_npz=OUTPUT_ROOT / "topological_holonomy_reduced_v3.npz",
+        )
+    else:
+        payload = run(workers=arguments.workers)
+    print(json.dumps(
+        {
+            "result_branch": payload["result_branch"],
+            "checks": payload["checks"],
+            "runtime_seconds": payload["runtime_seconds"],
+        },
+        indent=2,
+        sort_keys=True,
+    ))
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_bundle_geometry_v3.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_bundle_geometry_v3.py
new file mode 100644
index 000000000..af7cf45d5
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_bundle_geometry_v3.py
@@ -0,0 +1,144 @@
+"""Tests for task-local closed-surface non-Abelian bundle geometry."""
+
+from __future__ import annotations
+
+import numpy as np
+import pytest
+from scipy.linalg import expm
+
+from lgeth.bundle_geometry import (
+    analyze_ambient_frame_mesh,
+    apply_bosonic_fock_lift,
+    manybody_frame_overlap,
+    polar_unitary,
+    random_local_gauge,
+    sorted_wilson_eigenphases,
+)
+from lgeth.lattice import BosonBasis
+
+
+def _seeded_unitary(dimension: int, seed: int) -> np.ndarray:
+    rng = np.random.default_rng(seed)
+    matrix = rng.normal(size=(dimension, dimension))
+    matrix = matrix + 1j * rng.normal(size=matrix.shape)
+    unitary, _ = np.linalg.qr(matrix)
+    return unitary
+
+
+def _qiwuzhang_lower_band_mesh(mesh: int, mass: float) -> np.ndarray:
+    frames = np.empty((mesh, mesh, 2, 1), dtype=complex)
+    momenta = 2.0 * np.pi * np.arange(mesh) / mesh
+    for ix, kx in enumerate(momenta):
+        for iy, ky in enumerate(momenta):
+            hamiltonian = np.array(
+                [
+                    [
+                        mass + np.cos(kx) + np.cos(ky),
+                        np.sin(kx) - 1j * np.sin(ky),
+                    ],
+                    [
+                        np.sin(kx) + 1j * np.sin(ky),
+                        -mass - np.cos(kx) - np.cos(ky),
+                    ],
+                ],
+                dtype=complex,
+            )
+            _, vectors = np.linalg.eigh(hamiltonian)
+            frames[ix, iy, :, 0] = vectors[:, 0]
+    return frames
+
+
+def _synthetic_rank_three_bundle(mesh: int) -> np.ndarray:
+    rng = np.random.default_rng(5)
+    generators = []
+    for _ in range(2):
+        matrix = rng.normal(size=(6, 6))
+        matrix = matrix + 1j * rng.normal(size=matrix.shape)
+        matrix = 0.5 * (matrix + matrix.conj().T)
+        generators.append(matrix / np.linalg.norm(matrix))
+    base = _seeded_unitary(6, seed=6)[:, :3]
+    frames = np.empty((mesh, mesh, 6, 3), dtype=complex)
+    angles = 2 * np.pi * np.arange(mesh) / mesh
+    for ix, theta_x in enumerate(angles):
+        for iy, theta_y in enumerate(angles):
+            unitary = expm(0.4j * np.sin(theta_x) * generators[0])
+            unitary = unitary @ expm(
+                0.3j * np.sin(theta_y) * generators[1]
+            )
+            frames[ix, iy] = unitary @ base
+    return frames
+
+
+def test_one_particle_fock_lift_equals_single_particle_overlap() -> None:
+    basis = BosonBasis(n_orbitals=4, n_particles=1)
+    overlap = _seeded_unitary(4, seed=1)
+    frames = np.eye(4, dtype=complex)
+    basis_to_orbital = np.zeros((4, 4), dtype=complex)
+    for basis_index, state in enumerate(basis.states):
+        basis_to_orbital[state.index(1), basis_index] = 1.0
+    np.testing.assert_allclose(
+        apply_bosonic_fock_lift(basis, overlap, frames),
+        basis_to_orbital.conj().T @ overlap @ basis_to_orbital,
+        atol=1e-12,
+    )
+
+
+def test_identity_orbital_overlap_reduces_to_coefficient_overlap() -> None:
+    basis = BosonBasis(n_orbitals=4, n_particles=2)
+    left = _seeded_unitary(basis.dimension, seed=2)[:, :3]
+    right = _seeded_unitary(basis.dimension, seed=3)[:, :3]
+    orbitals = _seeded_unitary(6, seed=4)[:, :4]
+    observed = manybody_frame_overlap(
+        basis,
+        left,
+        right,
+        orbitals,
+        orbitals,
+    )
+    np.testing.assert_allclose(
+        observed,
+        left.conj().T @ right,
+        atol=1e-12,
+    )
+
+
+def test_polar_link_is_unitary_and_retains_singular_values() -> None:
+    rng = np.random.default_rng(7)
+    matrix = rng.normal(size=(6, 6))
+    matrix = matrix + 1j * rng.normal(size=matrix.shape)
+    unitary, values = polar_unitary(matrix)
+    np.testing.assert_allclose(
+        unitary.conj().T @ unitary,
+        np.eye(6),
+        atol=1e-12,
+    )
+    np.testing.assert_allclose(
+        values,
+        np.linalg.svd(matrix, compute_uv=False),
+    )
+
+
+def test_rank_one_qwz_bundle_has_unit_chern_number() -> None:
+    frames = _qiwuzhang_lower_band_mesh(mesh=20, mass=-1.0)
+    result = analyze_ambient_frame_mesh(frames)
+    assert abs(round(result.chern_determinant)) == 1
+    assert abs(
+        result.chern_determinant - result.chern_trace_log
+    ) < 1e-10
+
+
+def test_bundle_outputs_are_invariant_under_local_ud_gauges() -> None:
+    bundle = _synthetic_rank_three_bundle(mesh=5)
+    original = analyze_ambient_frame_mesh(bundle)
+    transformed = analyze_ambient_frame_mesh(
+        random_local_gauge(bundle, seed=8)
+    )
+    assert transformed.chern_determinant == pytest.approx(
+        original.chern_determinant,
+        abs=1e-10,
+    )
+    np.testing.assert_allclose(
+        np.exp(1j * sorted_wilson_eigenphases(transformed)),
+        np.exp(1j * sorted_wilson_eigenphases(original)),
+        atol=1e-9,
+    )
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_controls_v2.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_controls_v2.py
new file mode 100644
index 000000000..b1a2e8dd7
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_controls_v2.py
@@ -0,0 +1,109 @@
+"""Causal-control tests for spectral and geometric chaos channels."""
+
+from __future__ import annotations
+
+import numpy as np
+
+from lgeth.channels import (
+    build_physical_channel_cache,
+    cached_channel,
+)
+from lgeth.controls import (
+    fixed_projector_spectral_ensemble,
+    fourier_tangent_pairs,
+    scrambled_tangent_pair,
+)
+from lgeth.jacobi import normalized_curvature
+
+
+def test_fourier_pairs_cover_all_nonzero_momenta_without_fake_phase_samples():
+    pairs = fourier_tangent_pairs(5)
+    assert len(pairs) == 24
+    assert {(pair.kx, pair.ky) for pair in pairs} == {
+        (kx, ky)
+        for ky in range(5)
+        for kx in range(5)
+        if (kx, ky) != (0, 0)
+    }
+    assert len({pair.orbit_key for pair in pairs}) == 12
+    assert all(abs(pair.v.mean()) < 1e-14 for pair in pairs)
+    assert all(abs(pair.w.mean()) < 1e-14 for pair in pairs)
+    assert all(abs(np.linalg.norm(pair.v) - 1.0) < 1e-14 for pair in pairs)
+    assert all(abs(np.linalg.norm(pair.w) - 1.0) < 1e-14 for pair in pairs)
+
+
+def test_scrambling_endpoints_are_exact():
+    pair = fourier_tangent_pairs(5)[0]
+    random_v = np.arange(25.0) - 12.0
+    random_w = np.roll(random_v, 3)
+    gram = np.eye(25)
+    v0, w0 = scrambled_tangent_pair(
+        pair,
+        random_v,
+        random_w,
+        0.0,
+        gram,
+    )
+    v1, w1 = scrambled_tangent_pair(
+        pair,
+        random_v,
+        random_w,
+        1.0,
+        gram,
+    )
+    centered_v = random_v - random_v.mean()
+    centered_w = random_w - random_w.mean()
+    assert abs(abs(v0 @ pair.v) - 1.0) < 1e-12
+    assert abs(abs(w0 @ pair.w) - 1.0) < 1e-12
+    assert (
+        abs(
+            abs(v1 @ centered_v)
+            / np.linalg.norm(centered_v)
+            - 1.0
+        )
+        < 1e-12
+    )
+    assert (
+        abs(
+            abs(w1 @ centered_w)
+            / np.linalg.norm(centered_w)
+            - 1.0
+        )
+        < 1e-12
+    )
+
+
+def test_fixed_projector_changes_energy_not_geometry():
+    control = fixed_projector_spectral_ensemble(
+        dimension=50,
+        samples=256,
+        alphas=np.array([0.0, 1.0]),
+        seed=19,
+        reference_curvature_spectrum=np.linspace(-0.9, 0.9, 50),
+    )
+    assert (
+        control.mean_gap_ratio[-1]
+        > control.mean_gap_ratio[0] + 0.12
+    )
+    assert np.max(control.projector_distance) < 1e-13
+    assert np.max(control.curvature_spectrum_error) < 1e-14
+    assert control.energy_spectra.shape == (2, 256, 50)
+
+
+def test_physical_fourier_controls_are_full_rank_but_multiplet_structured():
+    cache = build_physical_channel_cache()
+    unique_counts = []
+    for pair in fourier_tangent_pairs(5):
+        channel_v = cached_channel(pair.v, cache)
+        channel_w = cached_channel(pair.w, cache)
+        normalized = normalized_curvature(
+            channel_v,
+            channel_w,
+            rtol=1e-10,
+        )
+        spectrum = np.linalg.eigvalsh(normalized.omega)
+        assert normalized.rank == cache.rank == 50
+        unique_counts.append(
+            np.unique(np.round(spectrum, 10)).size
+        )
+    assert max(unique_counts) <= 10
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_covariance_model_runner.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_covariance_model_runner.py
new file mode 100644
index 000000000..8485f896d
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_covariance_model_runner.py
@@ -0,0 +1,41 @@
+from __future__ import annotations
+
+import importlib
+from pathlib import Path
+
+import numpy as np
+
+
+physical_runner = importlib.import_module("run_physical_ensemble_v1")
+covariance_runner = importlib.import_module("run_covariance_model_v1")
+
+
+def test_reduced_covariance_model_uses_strict_splits(tmp_path: Path) -> None:
+    physical_npz = tmp_path / "physical.npz"
+    physical_runner.run(
+        tmp_path / "physical.json",
+        physical_npz,
+        samples=96,
+        seed_blocks=8,
+    )
+    result = covariance_runner.run(
+        physical_npz,
+        tmp_path / "covariance.json",
+        tmp_path / "covariance.npz",
+        diagnostic_rows=32,
+        model_samples=32,
+    )
+    assert result["all_checks_pass"]
+    assert result["diagnostic_training_rows"] == 32
+    assert result["haar_samples"] == 32
+    assert result["deformed_samples"] == 32
+    assert len(result["validation_scores"]) == 5
+    with np.load(tmp_path / "covariance.npz") as arrays:
+        assert arrays["haar_spectra"].shape == (32, 50)
+        assert arrays["deformed_spectra"].shape == (32, 50)
+        train = arrays["diagnostic_indices"]
+        validation = arrays["validation_indices"]
+        test = arrays["test_indices"]
+        assert np.intersect1d(train, validation).size == 0
+        assert np.intersect1d(train, test).size == 0
+        assert np.intersect1d(validation, test).size == 0
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_form_factors_v2.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_form_factors_v2.py
new file mode 100644
index 000000000..08690264a
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_form_factors_v2.py
@@ -0,0 +1,152 @@
+"""Analytic and empirical form-factor tests for the v2 expansion."""
+
+from __future__ import annotations
+
+import numpy as np
+import pytest
+
+from lgeth.form_factors import (
+    atom_raw_decomposition,
+    degenerate_energy_form_factor,
+    finite_jacobi_form_factor,
+    form_factor_parts,
+)
+from lgeth.jacobi import sample_jacobi_compression
+from lgeth.statistics import unfold_spectra
+
+
+def test_exact_degenerate_energy_is_raw_constant_and_connected_zero():
+    times = np.linspace(0.0, 4.0, 41)
+    parts = degenerate_energy_form_factor(50, times)
+    assert np.allclose(parts.raw, 50.0, atol=1e-14)
+    assert np.allclose(parts.disconnected, 50.0, atol=1e-14)
+    assert np.allclose(parts.connected, 0.0, atol=1e-14)
+    assert parts.normalization == 50
+
+
+def test_form_factor_decomposition_closes():
+    spectra = np.array(
+        [
+            [-1.0, 0.2, 0.9],
+            [-0.8, 0.0, 1.1],
+            [-0.7, 0.1, 0.8],
+        ]
+    )
+    parts = form_factor_parts(
+        spectra,
+        np.linspace(0.0, 2.0, 9),
+        phase_scale=2.0 * np.pi,
+    )
+    assert np.allclose(
+        parts.raw,
+        parts.disconnected + parts.connected,
+        atol=1e-14,
+    )
+    assert np.all(parts.connected >= -1e-14)
+
+
+def test_form_factor_rejects_invalid_inputs():
+    times = np.linspace(0.0, 1.0, 5)
+    for invalid in (
+        np.ones(5),
+        np.ones((0, 4)),
+        np.ones((3, 0)),
+        np.array([[0.0, np.nan]]),
+    ):
+        try:
+            form_factor_parts(invalid, times)
+        except ValueError:
+            pass
+        else:
+            raise AssertionError("invalid spectra were accepted")
+
+
+def test_finite_jacobi_connected_starts_at_zero_and_reaches_plateau():
+    result = finite_jacobi_form_factor(
+        16,
+        80,
+        np.array([0.0, 4.0]),
+        quadrature_order=256,
+    )
+    assert abs(result.connected_continuous[0]) < 2e-10
+    assert result.connected_continuous[-1] > 0.95
+    assert result.plateau_full == pytest.approx(1.0)
+
+
+def test_boundary_atoms_suppress_full_connected_plateau_exactly():
+    result = finite_jacobi_form_factor(
+        800,
+        680,
+        np.array([0.0, 4.0]),
+        quadrature_order=768,
+    )
+    assert result.interior_dimension == 560
+    assert result.atom_count_each == 120
+    assert np.allclose(
+        result.connected_full,
+        (560.0 / 800.0) * result.connected_continuous,
+        atol=2e-10,
+    )
+    assert result.plateau_full == pytest.approx(0.7)
+
+
+def test_raw_atom_decomposition_closes():
+    decomposition = atom_raw_decomposition(
+        np.array([[-0.4, 0.3], [-0.2, 0.6]]),
+        minus_atoms=1,
+        plus_atoms=1,
+        times=np.linspace(0.0, 2.0, 17),
+    )
+    assert np.allclose(
+        decomposition["full"],
+        decomposition["atom_atom"]
+        + decomposition["atom_continuum"]
+        + decomposition["continuum_continuum"],
+        atol=1e-14,
+    )
+
+
+def test_finite_jacobi_curve_matches_independent_monte_carlo():
+    times = np.linspace(0.25, 2.5, 46)
+    spectra = sample_jacobi_compression(
+        r=16,
+        M=80,
+        samples=1500,
+        seed=20260728191,
+    )
+    empirical = form_factor_parts(
+        unfold_spectra(spectra, "ensemble_cdf"),
+        times,
+    ).connected
+    analytic = finite_jacobi_form_factor(
+        16,
+        80,
+        times,
+        quadrature_order=256,
+    ).connected_continuous
+    assert np.max(np.abs(empirical - analytic)) < 0.075
+
+
+def test_rank50_quadrature_is_stable_on_registered_time_window():
+    times = np.linspace(0.0, 3.0, 61)
+    first = finite_jacobi_form_factor(
+        50,
+        170,
+        times,
+        quadrature_order=384,
+    )
+    second = finite_jacobi_form_factor(
+        50,
+        170,
+        times,
+        quadrature_order=512,
+    )
+    assert (
+        np.max(
+            np.abs(
+                first.connected_continuous
+                - second.connected_continuous
+            )
+        )
+        < 5e-5
+    )
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_geometric_eth_topology_article_v3.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_geometric_eth_topology_article_v3.py
new file mode 100644
index 000000000..47c8e4639
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_geometric_eth_topology_article_v3.py
@@ -0,0 +1,34 @@
+"""Delivery tests for the integrated v3 article."""
+
+from __future__ import annotations
+
+import json
+
+from verify_geometric_eth_topology_article_v3 import (
+    AUDIT_JSON,
+    FINAL_PDF,
+)
+
+
+def test_final_article_audit_passes() -> None:
+    audit = json.loads(AUDIT_JSON.read_text(encoding="utf-8"))
+    assert audit["passed"] is True
+    assert all(audit["checks"].values())
+    assert audit["matrix_branch"] == "deformed_geometric_eth"
+    assert audit["topology_branch"] == "fixed_chern_deformed_holonomy"
+    assert audit["page_count"] == 17
+    assert audit["main_pdf_sha256"] == audit["archived_pdf_sha256"]
+    assert FINAL_PDF.exists()
+
+
+def test_delivery_audit_links_all_seven_figures() -> None:
+    audit = json.loads(AUDIT_JSON.read_text(encoding="utf-8"))
+    assert len(audit["figures"]) == 7
+    assert all(item["exists"] for item in audit["figures"])
+    assert all(item["source_hash_matches"] for item in audit["figures"])
+
+
+def test_delivery_audit_records_every_rendered_page() -> None:
+    audit = json.loads(AUDIT_JSON.read_text(encoding="utf-8"))
+    assert len(audit["rendered_pages"]) == audit["page_count"]
+    assert all(item["sha256"] for item in audit["rendered_pages"])
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_geometric_eth_topology_assets_v3.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_geometric_eth_topology_assets_v3.py
new file mode 100644
index 000000000..5d8a7219b
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_geometric_eth_topology_assets_v3.py
@@ -0,0 +1,73 @@
+"""Tests for generated v3 manuscript assets."""
+
+from __future__ import annotations
+
+import hashlib
+import json
+import re
+from pathlib import Path
+
+import pytest
+
+
+SCRIPT_ROOT = Path(__file__).resolve().parents[1]
+OUTPUT = SCRIPT_ROOT / "output"
+NUMBERS = OUTPUT / "generated_numbers_v3.tex"
+TABLES = OUTPUT / "generated_tables_v3.tex"
+MANIFEST = OUTPUT / "geometric_eth_topology_assets_v3.json"
+
+
+def _sha256(path: Path) -> str:
+    return hashlib.sha256(path.read_bytes()).hexdigest()
+
+
+def _macros() -> dict[str, str]:
+    pattern = re.compile(r"\\newcommand\{\\([^}]+)\}\{(.*)\}")
+    result: dict[str, str] = {}
+    for line in NUMBERS.read_text(encoding="utf-8").splitlines():
+        match = pattern.fullmatch(line)
+        if match:
+            result[match.group(1)] = match.group(2)
+    return result
+
+
+def test_generated_macros_match_raw_v3_results() -> None:
+    matrix = json.loads(
+        (OUTPUT / "matrix_element_geometric_eth_v3.json").read_text()
+    )
+    topology = json.loads(
+        (OUTPUT / "topological_holonomy_v3.json").read_text()
+    )
+    macros = _macros()
+    assert float(macros["LargestNRFour"]) == pytest.approx(
+        matrix["cases"][-1]["physical_R4_median"],
+        abs=5e-6,
+    )
+    assert int(macros["TopologyNFourChern"]) == topology["sizes"][-1][
+        "base_chern_integer"
+    ]
+    assert macros["MatrixElementBranch"].replace(r"\_", "_") == matrix[
+        "result_branch"
+    ]
+    assert macros["TopologyBranch"].replace(r"\_", "_") == topology[
+        "result_branch"
+    ]
+
+
+def test_generated_tables_contain_all_registered_rows() -> None:
+    text = TABLES.read_text(encoding="utf-8")
+    assert "3 & 8 & 16 & 120" in text
+    assert "5 & 12 & 36 & 4368" in text
+    assert "4 & 25 & 10" in text
+
+
+def test_asset_manifest_hashes_all_outputs() -> None:
+    manifest = json.loads(MANIFEST.read_text(encoding="utf-8"))
+    assert manifest["output_hashes"]["output/generated_numbers_v3.tex"] == _sha256(
+        NUMBERS
+    )
+    assert manifest["output_hashes"]["output/generated_tables_v3.tex"] == _sha256(
+        TABLES
+    )
+    assert manifest["matrix_branch"] == "deformed_geometric_eth"
+    assert manifest["topology_branch"] == "fixed_chern_deformed_holonomy"
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_holonomy_v3.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_holonomy_v3.py
new file mode 100644
index 000000000..b4debe0d2
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_holonomy_v3.py
@@ -0,0 +1,132 @@
+"""Tests for periodic isospectral holonomy deformations and CUE statistics."""
+
+from __future__ import annotations
+
+import numpy as np
+import pytest
+
+from lgeth.bundle_geometry import analyze_frame_bundle
+from lgeth.holonomy import (
+    ambient_unitary,
+    cue_wilson_reference,
+    deform_orbital_mesh,
+    local_generator_pair,
+    wilson_statistics,
+)
+from lgeth.lattice import BosonBasis
+from lgeth.twist_bundle import build_twist_bundle
+
+
+def _nearest_neighbor_support_only(
+    matrix: np.ndarray,
+    length: int,
+) -> bool:
+    sites = length * length
+    for left in range(sites):
+        lx, ly = left % length, left // length
+        for right in range(sites):
+            if left == right or abs(matrix[left, right]) < 1e-12:
+                continue
+            rx, ry = right % length, right // length
+            dx = min(abs(lx - rx), length - abs(lx - rx))
+            dy = min(abs(ly - ry), length - abs(ly - ry))
+            if dx + dy != 1:
+                return False
+    return True
+
+
+def test_generator_pair_is_hermitian_local_and_noncommuting() -> None:
+    gx, gy = local_generator_pair(length=4, seed=41, commuting=False)
+    np.testing.assert_allclose(gx, gx.conj().T)
+    np.testing.assert_allclose(gy, gy.conj().T)
+    assert _nearest_neighbor_support_only(gx, length=4)
+    assert _nearest_neighbor_support_only(gy, length=4)
+    assert np.linalg.norm(gx @ gy - gy @ gx) > 1e-3
+
+
+def test_commuting_control_generators_commute() -> None:
+    gx, gy = local_generator_pair(length=4, seed=42, commuting=True)
+    assert np.linalg.norm(gx @ gy - gy @ gx) < 1e-14
+
+
+def test_ambient_unitary_is_periodic_and_unitary() -> None:
+    generators = local_generator_pair(4, seed=41, commuting=False)
+    first = ambient_unitary(0.2, 0.7, 0.8, generators)
+    wrapped = ambient_unitary(
+        0.2 + 2 * np.pi,
+        0.7 - 2 * np.pi,
+        0.8,
+        generators,
+    )
+    np.testing.assert_allclose(first, wrapped, atol=1e-12)
+    np.testing.assert_allclose(
+        first.conj().T @ first,
+        np.eye(first.shape[0]),
+        atol=1e-12,
+    )
+
+
+def test_periodic_orbit_preserves_gap_and_chern() -> None:
+    bundle = build_twist_bundle(N=3, n_flux=8, rank=16, mesh=6)
+    deformed_orbitals = deform_orbital_mesh(
+        bundle.orbital_frames,
+        g=0.7,
+        seed=43,
+        commuting=False,
+    )
+    geometry = analyze_frame_bundle(
+        bundle.coefficient_frames,
+        deformed_orbitals,
+        BosonBasis(bundle.n_flux, bundle.N),
+    )
+    assert geometry.chern_determinant == pytest.approx(
+        bundle.geometry.chern_determinant,
+        abs=1e-9,
+    )
+    assert np.min(bundle.external_gap) > 0.0
+
+
+def test_wilson_statistics_are_common_phase_invariant() -> None:
+    bundle = build_twist_bundle(N=3, n_flux=8, rank=16, mesh=3)
+    original = wilson_statistics(bundle.geometry)
+    shifted_geometry = bundle.geometry
+    shifted_x = np.exp(0.37j) * shifted_geometry.wilson_x
+    shifted_y = np.exp(-0.29j) * shifted_geometry.wilson_y
+    shifted = wilson_statistics(
+        shifted_geometry,
+        wilson_x=shifted_x,
+        wilson_y=shifted_y,
+    )
+    np.testing.assert_allclose(
+        shifted["gap_ratio"],
+        original["gap_ratio"],
+        atol=1e-12,
+    )
+    np.testing.assert_allclose(
+        shifted["form_factor"],
+        original["form_factor"],
+        atol=1e-10,
+    )
+
+
+def test_cue_reference_is_seed_reproducible() -> None:
+    first = cue_wilson_reference(
+        D=8,
+        samples=64,
+        k_values=np.arange(1, 9),
+        seed=51,
+    )
+    second = cue_wilson_reference(
+        D=8,
+        samples=64,
+        k_values=np.arange(1, 9),
+        seed=51,
+    )
+    np.testing.assert_array_equal(
+        first["gap_ratio"],
+        second["gap_ratio"],
+    )
+    np.testing.assert_array_equal(
+        first["form_factor"],
+        second["form_factor"],
+    )
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_independent_core.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_independent_core.py
new file mode 100644
index 000000000..fbf2917b6
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_independent_core.py
@@ -0,0 +1,65 @@
+from __future__ import annotations
+
+import ast
+from pathlib import Path
+
+import numpy as np
+
+from lgeth.combinatorics import laughlin_zero_mode_count
+from lgeth.jacobi import (
+    haar_row_isometry,
+    jacobi_parameters,
+    normalized_curvature,
+    sample_jacobi_interior,
+)
+from lgeth.channels import root_response_partition
+
+
+SCRIPT_ROOT = Path(__file__).resolve().parents[1]
+
+
+def test_task05_imports_are_isolated() -> None:
+    for source in SCRIPT_ROOT.rglob("*.py"):
+        tree = ast.parse(source.read_text(encoding="utf-8"))
+        for node in ast.walk(tree):
+            if isinstance(node, ast.Import):
+                modules = [alias.name for alias in node.names]
+            elif isinstance(node, ast.ImportFrom):
+                modules = [node.module or ""]
+            else:
+                continue
+            assert all("task_04" not in module for module in modules)
+            assert all("gaccess" not in module for module in modules)
+
+
+def test_registered_rank_and_external_dimension() -> None:
+    assert laughlin_zero_mode_count(3, 20) == 800
+    partition = root_response_partition(3, 20)
+    assert len(partition.zero_modes) == 800
+    assert len(partition.descendant_external) == 680
+
+
+def test_atom_multiplicity_and_interior_labels() -> None:
+    parameters = jacobi_parameters(800, 680)
+    assert parameters.plus_atoms == 120
+    assert parameters.minus_atoms == 120
+    assert parameters.interior_dimension == 560
+    interior, labels = sample_jacobi_interior(8, 6, 3, 2026072801)
+    assert interior.shape == (3, 4)
+    assert labels.shape == (3, 8)
+    assert np.all(labels.sum(axis=1) == 4)
+
+
+def test_whitening_isometry_identity() -> None:
+    rng = np.random.default_rng(2026072802)
+    rows = haar_row_isometry(8, 20, rng)
+    channel_v = rows[:, :10]
+    channel_w = rows[:, 10:]
+    normalized = normalized_curvature(channel_v, channel_w)
+    assert normalized.rank == 8
+    np.testing.assert_allclose(
+        normalized.Y @ normalized.Y.conj().T,
+        np.eye(8),
+        atol=1e-10,
+        rtol=0.0,
+    )
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_large_scale_delivery.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_large_scale_delivery.py
new file mode 100644
index 000000000..faaf0bbc0
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_large_scale_delivery.py
@@ -0,0 +1,34 @@
+from __future__ import annotations
+
+import importlib
+from pathlib import Path
+
+import pytest
+
+
+verifier = importlib.import_module("verify_large_scale_article_v1")
+EXTERNAL_PHYSICAL = (
+    Path(__file__).resolve().parents[1]
+    / "output"
+    / "physical_ensemble_v1.npz"
+)
+
+
+@pytest.mark.skipif(
+    not EXTERNAL_PHYSICAL.exists(),
+    reason=(
+        "activates with production arrays listed in release_manifest_v1.json"
+    ),
+)
+def test_registered_delivery_gates_pass(tmp_path: Path) -> None:
+    audit = verifier.run(tmp_path / "audit.json")
+    assert audit["all_checks_pass"]
+    assert audit["registered_scale"] == {
+        "physical_matrices": 20_000,
+        "haar_matrices": 10_000,
+        "deformed_matrices": 10_000,
+        "root_matrices": 8_750,
+        "maximum_rank": 800,
+    }
+    assert audit["pdf"]["pages"] == 10
+    assert len(audit["rendered_pages"]) == 10
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_large_scale_figures.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_large_scale_figures.py
new file mode 100644
index 000000000..9c86eee95
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_large_scale_figures.py
@@ -0,0 +1,35 @@
+from __future__ import annotations
+
+import json
+from pathlib import Path
+
+from PIL import Image
+from pypdf import PdfReader
+
+
+def test_registered_figure_package() -> None:
+    output = Path(__file__).resolve().parents[1] / "output"
+    manifest = json.loads(
+        (output / "figure_manifest_v1.json").read_text(encoding="utf-8")
+    )
+    assert manifest["atom_annotations"] == {
+        "D546_each_boundary": 6,
+        "D800_each_boundary": 120,
+        "D800_total_weight": 0.30,
+    }
+    assert len(manifest["inputs"]) == 7
+    for figure in manifest["figures"].values():
+        pdf = Path(figure["pdf"])
+        png = Path(figure["png"])
+        reader = PdfReader(str(pdf))
+        width = float(reader.pages[0].mediabox.width) / 72.0
+        assert abs(width - 7.0) < 0.01
+        with Image.open(png) as image:
+            assert image.width >= 2100
+            assert image.info["dpi"][0] >= 299.0
+    numbers = (output / "generated_numbers_v1.tex").read_text(
+        encoding="utf-8"
+    )
+    assert r"\newcommand{\LargestRank}{800}" in numbers
+    assert r"\newcommand{\LargestAtomMultiplicity}{120}" in numbers
+    assert r"\newcommand{\BootstrapReplicates}{10000}" in numbers
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_large_scale_statistics.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_large_scale_statistics.py
new file mode 100644
index 000000000..2855f6e59
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_large_scale_statistics.py
@@ -0,0 +1,59 @@
+from __future__ import annotations
+
+import numpy as np
+
+from lgeth.statistics import (
+    connected_form_factor,
+    fit_size_models,
+    matrix_bootstrap_band,
+    sample_gue_spectra,
+    sample_poisson_spectra,
+    spectral_rigidity,
+    unfold_spectra,
+)
+
+
+def test_simultaneous_band_contract() -> None:
+    rng = np.random.default_rng(20260728700)
+    curves = rng.normal(size=(40, 12))
+    band = matrix_bootstrap_band(curves, 500, 20260728701)
+    assert band.mean.shape == (12,)
+    assert np.all(band.lower <= band.mean)
+    assert np.all(band.mean <= band.upper)
+    assert band.critical_value > 1.0
+    groups = np.repeat(np.arange(8), 5)
+    hierarchical = matrix_bootstrap_band(
+        curves,
+        500,
+        20260728702,
+        groups=groups,
+    )
+    assert hierarchical.units == 8
+    assert hierarchical.method == "hierarchical_seed_block_bootstrap"
+
+
+def test_gue_is_more_rigid_than_poisson() -> None:
+    poisson = unfold_spectra(
+        sample_poisson_spectra(240, 60, 20260728703),
+        "ensemble_cdf",
+    )
+    gue = unfold_spectra(
+        sample_gue_spectra(240, 60, 20260728704),
+        "ensemble_cdf",
+    )
+    lengths = (1.0, 2.0, 3.0, 4.0)
+    poisson_rigidity = spectral_rigidity(poisson, lengths)
+    gue_rigidity = spectral_rigidity(gue, lengths)
+    assert poisson_rigidity[-1] > gue_rigidity[-1]
+    form = connected_form_factor(gue, (0.0, 0.2, 0.5, 1.0))
+    assert abs(form[0]) < 1e-12
+    assert np.all(np.isfinite(form))
+
+
+def test_finite_size_model_selection_recovers_half_power() -> None:
+    D = np.asarray([16, 32, 64, 128, 256, 512, 1024], dtype=float)
+    values = 0.02 + 1.5 * D ** -0.5
+    sigma = np.full_like(D, 0.003)
+    fits = fit_size_models(D, values, sigma)
+    assert fits["best_by_loo"] in {"D^-1/2", "free"}
+    assert abs(fits["models"]["free"]["exponent"] - 0.5) < 0.05
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_manybody_response_v3.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_manybody_response_v3.py
new file mode 100644
index 000000000..66c6814dc
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_manybody_response_v3.py
@@ -0,0 +1,136 @@
+"""Tests for the genuine particle-number response backend."""
+
+from __future__ import annotations
+
+import numpy as np
+import pytest
+
+from lgeth.lattice import build_kapit_laughlin_parent
+from lgeth.manybody_response import (
+    ManyBodyCase,
+    audit_unregistered_small_case,
+    build_site_response_cache,
+    dense_resolvent_response,
+    registered_fixed_two_qh_cases,
+    response_pair_grams,
+    rotate_response_target_gauge,
+    solve_kernel_frame,
+)
+
+
+def _seeded_unitary(dimension: int, seed: int) -> np.ndarray:
+    rng = np.random.default_rng(seed)
+    matrix = rng.normal(size=(dimension, dimension))
+    matrix = matrix + 1j * rng.normal(size=matrix.shape)
+    unitary, _ = np.linalg.qr(matrix)
+    return unitary
+
+
+def test_registered_sequence_is_fixed_two_quasiholes() -> None:
+    cases = registered_fixed_two_qh_cases()
+    assert [
+        (case.N, case.n_flux, case.expected_rank)
+        for case in cases
+    ] == [(3, 8, 16), (4, 10, 25), (5, 12, 36)]
+    assert all(case.n_flux == 2 * case.N + 2 for case in cases)
+
+
+def test_n2_physical_parent_is_rejected_by_counting_gate() -> None:
+    audit = audit_unregistered_small_case(
+        N=2,
+        n_flux=6,
+        theta_x=0.17,
+        theta_y=0.29,
+    )
+    assert audit.expected_rank == 9
+    assert audit.observed_rank == 12
+    assert audit.accepted is False
+
+
+@pytest.mark.parametrize(
+    ("N", "n_flux", "rank"),
+    [(3, 8, 16), (4, 10, 25)],
+)
+def test_dense_kernel_has_registered_rank_and_open_gap(
+    N: int,
+    n_flux: int,
+    rank: int,
+) -> None:
+    case = ManyBodyCase(N, n_flux, rank, 0.17, 0.29)
+    system = build_kapit_laughlin_parent(
+        N,
+        n_flux,
+        case.theta_x,
+        case.theta_y,
+    )
+    kernel = solve_kernel_frame(system, case, seed=20260728301)
+    assert kernel.frame.shape == (system.basis.dimension, rank)
+    assert kernel.external_gap > 0.0
+    assert kernel.residual_norm < 1e-10
+    assert kernel.orthonormality_error < 1e-11
+    assert kernel.method == "dense"
+
+
+def test_richardson_response_matches_dense_spectral_inverse() -> None:
+    case = registered_fixed_two_qh_cases()[0]
+    system = build_kapit_laughlin_parent(
+        case.N,
+        case.n_flux,
+        case.theta_x,
+        case.theta_y,
+    )
+    kernel = solve_kernel_frame(system, case, seed=20260728302)
+    cache = build_site_response_cache(
+        system,
+        kernel,
+        relative_shifts=(1e-3, 5e-4),
+        site_indices=(0, 3),
+    )
+    exact = dense_resolvent_response(
+        system,
+        kernel,
+        site_indices=(0, 3),
+    )
+    relative = np.linalg.norm(cache.solutions - exact) / np.linalg.norm(exact)
+    assert relative < 2e-4
+    assert cache.maximum_relative_residual < 2e-4
+    assert cache.maximum_kernel_leakage < 1e-10
+
+
+def test_kernel_rotation_does_not_change_site_response_grams() -> None:
+    case = registered_fixed_two_qh_cases()[0]
+    system = build_kapit_laughlin_parent(
+        case.N,
+        case.n_flux,
+        case.theta_x,
+        case.theta_y,
+    )
+    kernel = solve_kernel_frame(system, case, seed=20260728303)
+    cache = build_site_response_cache(
+        system,
+        kernel,
+        relative_shifts=(1e-3, 5e-4),
+        site_indices=(0, 1, 2),
+    )
+    unitary = _seeded_unitary(case.expected_rank, seed=11)
+    rotated = rotate_response_target_gauge(cache, unitary)
+    original_grams = response_pair_grams(cache.solutions)
+    rotated_grams = response_pair_grams(rotated.solutions)
+    original_invariant = np.einsum(
+        "stij,uvji->stuv",
+        original_grams,
+        original_grams,
+        optimize=True,
+    )
+    rotated_invariant = np.einsum(
+        "stij,uvji->stuv",
+        rotated_grams,
+        rotated_grams,
+        optimize=True,
+    )
+    np.testing.assert_allclose(
+        original_invariant,
+        rotated_invariant,
+        atol=2e-9,
+        rtol=2e-9,
+    )
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_matrix_element_geometric_eth_delivery_v3.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_matrix_element_geometric_eth_delivery_v3.py
new file mode 100644
index 000000000..fd8cfaaf2
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_matrix_element_geometric_eth_delivery_v3.py
@@ -0,0 +1,40 @@
+"""Fail-closed delivery tests for the matrix-element extension."""
+
+from __future__ import annotations
+
+import copy
+import json
+from pathlib import Path
+
+import pytest
+
+from run_matrix_element_geometric_eth_v3 import OUTPUT_JSON
+from verify_matrix_element_geometric_eth_v3 import (
+    AUDIT_JSON,
+    audit_payload,
+)
+
+
+def test_matrix_element_delivery_audit_passes_all_gates() -> None:
+    audit = json.loads(AUDIT_JSON.read_text(encoding="utf-8"))
+    assert audit["passed"] is True
+    assert all(audit["checks"].values())
+    assert audit["result_branch"] == "deformed_geometric_eth"
+    assert audit["registered_cases"] == [[3, 8, 16], [4, 10, 25], [5, 12, 36]]
+
+
+def test_audit_rejects_branch_metric_mismatch() -> None:
+    payload = json.loads(OUTPUT_JSON.read_text(encoding="utf-8"))
+    corrupted = copy.deepcopy(payload)
+    corrupted["result_branch"] = "wick_compatible_trend"
+    corrupted["cases"][-1]["physical_R4_median"] = 100.0
+    with pytest.raises(AssertionError):
+        audit_payload(corrupted)
+
+
+def test_audit_records_figure_and_checkpoint_hashes() -> None:
+    audit = json.loads(AUDIT_JSON.read_text(encoding="utf-8"))
+    assert len(audit["checkpoint_hashes"]) == 6
+    assert audit["figure"]["pdf_sha256"]
+    assert audit["figure"]["png_sha256"]
+    assert Path(audit["figure"]["pdf"]).name == "figure_6_wick_factorization_v3.pdf"
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_matrix_element_geometric_eth_figure_v3.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_matrix_element_geometric_eth_figure_v3.py
new file mode 100644
index 000000000..4583b90fa
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_matrix_element_geometric_eth_figure_v3.py
@@ -0,0 +1,47 @@
+"""Publication-asset tests for the matrix-element Geometric-ETH figure."""
+
+from __future__ import annotations
+
+import hashlib
+import json
+from pathlib import Path
+
+from PIL import Image
+
+
+SCRIPT_ROOT = Path(__file__).resolve().parents[1]
+OUTPUT = SCRIPT_ROOT / "output"
+ARTIFACT_JSON = OUTPUT / "matrix_element_geometric_eth_v3.json"
+MANIFEST = OUTPUT / "figure_manifest_v3.json"
+FIGURE_PNG = OUTPUT / "figure_6_wick_factorization_v3.png"
+FIGURE_PDF = OUTPUT / "figure_6_wick_factorization_v3.pdf"
+
+
+def _sha256(path: Path) -> str:
+    return hashlib.sha256(path.read_bytes()).hexdigest()
+
+
+def test_figure_6_has_registered_dimensions_and_source_hash() -> None:
+    manifest = json.loads(MANIFEST.read_text(encoding="utf-8"))
+    figure = manifest["figure_6_wick_factorization_v3"]
+    assert figure["width_inches"] == 7.0
+    assert figure["png_width_pixels"] == 2100
+    assert figure["source_sha256"] == _sha256(ARTIFACT_JSON)
+    assert figure["pdf_sha256"] == _sha256(FIGURE_PDF)
+    assert figure["png_sha256"] == _sha256(FIGURE_PNG)
+    with Image.open(FIGURE_PNG) as image:
+        assert image.width == 2100
+        assert image.height >= 1450
+
+
+def test_figure_6_manifest_records_result_branch() -> None:
+    artifact = json.loads(ARTIFACT_JSON.read_text(encoding="utf-8"))
+    manifest = json.loads(MANIFEST.read_text(encoding="utf-8"))
+    figure = manifest["figure_6_wick_factorization_v3"]
+    assert figure["result_branch"] == artifact["result_branch"]
+    assert figure["panels"] == [
+        "genuine_manybody_sequence",
+        "four_channel_residual",
+        "non_gaussian_excess",
+        "covariance_geometry",
+    ]
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_matrix_element_geometric_eth_runner_v3.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_matrix_element_geometric_eth_runner_v3.py
new file mode 100644
index 000000000..737636f51
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_matrix_element_geometric_eth_runner_v3.py
@@ -0,0 +1,91 @@
+"""Runner tests for the matrix-element Geometric-ETH production artifact."""
+
+from __future__ import annotations
+
+import json
+from pathlib import Path
+
+import numpy as np
+import pytest
+
+from run_matrix_element_geometric_eth_v3 import (
+    OUTPUT_JSON,
+    run,
+    select_result_branch,
+)
+
+
+def test_reduced_runner_emits_all_gate_families(tmp_path: Path) -> None:
+    result = run(
+        output_json=tmp_path / "result.json",
+        output_npz=tmp_path / "result.npz",
+        checkpoint_dir=tmp_path / "checkpoints",
+        case_indices=(0,),
+        panels=3,
+        gaussian_samples=32,
+        production=False,
+    )
+    assert set(result["checks"]) >= {
+        "kernel_count",
+        "external_gap",
+        "resolvent_residual",
+        "channel_support",
+        "gauge_invariance",
+        "reference_reproducibility",
+    }
+    assert result["configuration"]["panel_size"] == 8
+    assert result["cases"][0]["N"] == 3
+    assert result["cases"][0]["rank"] == 16
+    assert result["result_branch"] in {
+        "wick_compatible_trend",
+        "deformed_geometric_eth",
+        "no_matrix_element_eth_trend",
+        "manybody_sequence_incomplete",
+    }
+
+
+def test_reduced_runner_reuses_hash_identical_checkpoint(
+    tmp_path: Path,
+) -> None:
+    arguments = {
+        "output_json": tmp_path / "first.json",
+        "output_npz": tmp_path / "first.npz",
+        "checkpoint_dir": tmp_path / "checkpoints",
+        "case_indices": (0,),
+        "panels": 2,
+        "gaussian_samples": 8,
+        "production": False,
+    }
+    first = run(**arguments)
+    arguments["output_json"] = tmp_path / "second.json"
+    arguments["output_npz"] = tmp_path / "second.npz"
+    second = run(**arguments)
+    assert first["cases"][0]["checkpoint_reused"] is False
+    assert second["cases"][0]["checkpoint_reused"] is True
+    np.testing.assert_allclose(
+        first["cases"][0]["physical_R4"],
+        second["cases"][0]["physical_R4"],
+    )
+
+
+@pytest.mark.skipif(
+    not OUTPUT_JSON.exists(),
+    reason="production artifact has not been generated",
+)
+def test_production_artifact_uses_true_particle_number_sequence() -> None:
+    payload = json.loads(OUTPUT_JSON.read_text(encoding="utf-8"))
+    assert [row["N"] for row in payload["cases"]] == [3, 4, 5]
+    assert [row["rank"] for row in payload["cases"]] == [16, 25, 36]
+    assert all(
+        row["n_flux"] == 2 * row["N"] + 2
+        for row in payload["cases"]
+    )
+
+
+@pytest.mark.skipif(
+    not OUTPUT_JSON.exists(),
+    reason="production artifact has not been generated",
+)
+def test_claim_branch_is_recomputed_from_raw_metrics() -> None:
+    payload = json.loads(OUTPUT_JSON.read_text(encoding="utf-8"))
+    assert payload["result_branch"] == select_result_branch(payload)
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_matrix_element_topology_theory_v3.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_matrix_element_topology_theory_v3.py
new file mode 100644
index 000000000..ecd7a8148
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_matrix_element_topology_theory_v3.py
@@ -0,0 +1,27 @@
+"""Executable theory tests for the v3 manuscript derivations."""
+
+from __future__ import annotations
+
+from verify_matrix_element_topology_theory_v3 import (
+    gauge_and_gram_check,
+    periodic_unitary_chern_check,
+    wick_identity_check,
+)
+
+
+def test_wick_coefficients_match_direct_monte_carlo() -> None:
+    result = wick_identity_check(samples=8_000)
+    assert result["relative_error"] < 0.065
+
+
+def test_gauge_invariance_and_gram_reduction() -> None:
+    result = gauge_and_gram_check()
+    assert result["R4_error"] < 1e-10
+    assert result["tensor_error"] < 1e-10
+    assert result["gram_spectrum_error"] < 1e-10
+
+
+def test_periodic_unitary_orbit_keeps_synthetic_chern() -> None:
+    result = periodic_unitary_chern_check(mesh=20)
+    assert result["chern_error"] < 1e-10
+    assert result["minimum_branch_margin"] > 0.0
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_physical_ensemble_runner.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_physical_ensemble_runner.py
new file mode 100644
index 000000000..4e790aa14
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_physical_ensemble_runner.py
@@ -0,0 +1,38 @@
+from __future__ import annotations
+
+import importlib
+from pathlib import Path
+
+import numpy as np
+
+
+runner = importlib.import_module("run_physical_ensemble_v1")
+
+
+def test_reduced_physical_run_is_deterministic(tmp_path: Path) -> None:
+    first_json = tmp_path / "first.json"
+    first_npz = tmp_path / "first.npz"
+    second_json = tmp_path / "second.json"
+    second_npz = tmp_path / "second.npz"
+    first = runner.run(first_json, first_npz, samples=96, seed_blocks=8)
+    second = runner.run(second_json, second_npz, samples=96, seed_blocks=8)
+    assert first["split"] == {
+        "train": 60,
+        "validation": 18,
+        "test": 18,
+        "split_seed": runner.REGISTERED_SEED + 1,
+    }
+    assert first["all_checks_pass"] and second["all_checks_pass"]
+    with np.load(first_npz) as left, np.load(second_npz) as right:
+        np.testing.assert_array_equal(
+            left["normalized_spectra"], right["normalized_spectra"]
+        )
+        assert left["normalized_spectra"].shape == (96, 50)
+        assert np.all(left["active_ranks"] == 50)
+        assert np.unique(left["seed_block"]).size == 8
+        train = left["train_indices"]
+        validation = left["validation_indices"]
+        test = left["test_indices"]
+        assert np.intersect1d(train, validation).size == 0
+        assert np.intersect1d(train, test).size == 0
+        assert np.intersect1d(validation, test).size == 0
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_rank_scaling_runner.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_rank_scaling_runner.py
new file mode 100644
index 000000000..9d517747a
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_rank_scaling_runner.py
@@ -0,0 +1,59 @@
+from __future__ import annotations
+
+import importlib
+from pathlib import Path
+
+import numpy as np
+
+from lgeth.jacobi import sample_jacobi_wishart
+
+
+runner = importlib.import_module("run_rank_scaling_v1")
+
+
+def test_qr_curvature_matches_metric_normalization() -> None:
+    from lgeth.jacobi import normalized_curvature
+
+    rng = np.random.default_rng(20260728500)
+    first = rng.normal(size=(7, 9))
+    second = rng.normal(size=(7, 9))
+    _, qr_spectrum, _ = runner.qr_normalized_curvature(first, second)
+    direct = normalized_curvature(first, second)
+    np.testing.assert_allclose(
+        qr_spectrum,
+        np.linalg.eigvalsh(direct.omega),
+        atol=1e-10,
+        rtol=0.0,
+    )
+
+
+def test_exact_wishart_jacobi_atoms() -> None:
+    full, interior, labels = sample_jacobi_wishart(
+        8, 6, 4, 20260728501
+    )
+    assert full.shape == (4, 8)
+    assert interior.shape == (4, 4)
+    assert np.all(full[:, :2] == -1.0)
+    assert np.all(full[:, -2:] == 1.0)
+    assert np.all(labels.sum(axis=1) == 4)
+
+
+def test_reduced_runner_and_explicit_resource_rejection(
+    tmp_path: Path,
+) -> None:
+    result = runner.run(
+        tmp_path / "scaling.json",
+        tmp_path / "scaling.npz",
+        cases=((8, 4),),
+    )
+    assert result["all_checks_pass"]
+    assert result["cases"][0]["D"] == 16
+    assert result["cases"][0]["M"] == 80
+    rejected = runner.run(
+        tmp_path / "rejected.json",
+        tmp_path / "rejected.npz",
+        cases=((20, 4),),
+        response_entry_ceiling=100,
+    )
+    assert rejected["all_checks_pass"]
+    assert rejected["cases"][0]["status"] == "resource_rejected"
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_release_contract_v1.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_release_contract_v1.py
new file mode 100644
index 000000000..db3ee030f
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_release_contract_v1.py
@@ -0,0 +1,73 @@
+from __future__ import annotations
+
+import copy
+import json
+from pathlib import Path
+
+import pytest
+
+from make_release_manifest_v1 import build_manifest
+from verify_release_contract_v1 import verify_manifest
+
+
+SCRIPT_ROOT = Path(__file__).resolve().parents[1]
+OUTPUT = SCRIPT_ROOT / "output"
+REPO_ROOT = SCRIPT_ROOT.parents[2]
+RELEASE_MANIFEST = OUTPUT / "release_manifest_v1.json"
+
+
+def _production_manifest() -> dict:
+    return json.loads(RELEASE_MANIFEST.read_text(encoding="utf-8"))
+
+
+def test_release_manifest_captures_public_contract() -> None:
+    manifest = build_manifest(
+        repo_root=REPO_ROOT,
+        bulk_output=OUTPUT,
+        generated_utc="2026-07-30T00:00:00+00:00",
+    )
+
+    assert manifest["schema_version"] == 1
+    assert manifest["release_id"] == "task05-geometric-chaos-v1"
+    assert manifest["result_branches"] == {
+        "matrix_element": "deformed_geometric_eth",
+        "topology": "fixed_chern_deformed_holonomy",
+    }
+    assert manifest["paper"]["page_count"] == 17
+    assert len(manifest["paper"]["sha256"]) == 64
+    assert len(manifest["figures"]) == 7
+    assert all(len(item["sha256"]) == 64 for item in manifest["figures"])
+    assert manifest["verification"]["quick"] == "bash run_quick_verify_v1.sh"
+    assert manifest["verification"]["full"] == "bash run_full_recompute_v1.sh"
+
+    report = verify_manifest(RELEASE_MANIFEST, repo_root=REPO_ROOT)
+    assert report["passed"]
+    assert all(report["checks"].values())
+
+
+def test_release_verifier_detects_changed_result_label(
+    tmp_path: Path,
+) -> None:
+    manifest = copy.deepcopy(_production_manifest())
+    manifest["result_branches"]["matrix_element"] = "full_haar"
+    path = tmp_path / "changed.json"
+    path.write_text(json.dumps(manifest), encoding="utf-8")
+
+    report = verify_manifest(path, repo_root=REPO_ROOT)
+    assert report["passed"] is False
+    assert report["checks"]["registered_result_branches"] is False
+
+
+def test_release_verifier_detects_blob_above_policy(
+    tmp_path: Path, monkeypatch: pytest.MonkeyPatch
+) -> None:
+    path = tmp_path / "manifest.json"
+    path.write_text(
+        json.dumps(_production_manifest()),
+        encoding="utf-8",
+    )
+
+    monkeypatch.setenv("TASK05_RELEASE_MAX_TRACKED_BYTES", "1")
+    report = verify_manifest(path, repo_root=REPO_ROOT)
+    assert report["passed"] is False
+    assert report["checks"]["tracked_blob_limit"] is False
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_spectral_silence_delivery_v2.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_spectral_silence_delivery_v2.py
new file mode 100644
index 000000000..42bae1c21
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_spectral_silence_delivery_v2.py
@@ -0,0 +1,55 @@
+from __future__ import annotations
+
+import importlib
+from pathlib import Path
+
+import pytest
+
+
+verifier = importlib.import_module(
+    "verify_spectral_silence_article_v2"
+)
+EXTERNAL_SPECTRAL = (
+    Path(__file__).resolve().parents[1]
+    / "output"
+    / "spectral_silence_v2.npz"
+)
+
+
+@pytest.mark.skipif(
+    not EXTERNAL_SPECTRAL.exists(),
+    reason=(
+        "activates with production arrays listed in release_manifest_v1.json"
+    ),
+)
+def test_registered_spectral_silence_delivery_passes(
+    tmp_path: Path,
+) -> None:
+    audit = verifier.run(tmp_path / "audit.json")
+    assert audit["all_checks_pass"]
+    assert audit["pdf"]["title"] == (
+        "Spectral Silence and Geometric Chaos in an Exactly Degenerate "
+        "Topological Manifold"
+    )
+    assert 10 <= audit["pdf"]["pages"] <= 15
+    assert len(audit["rendered_pages"]) == audit["pdf"]["pages"]
+    assert audit["supported_conclusion"] == {
+        "energy_connected_sff": 0.0,
+        "physical_jacobi_tau_onset": 0.25,
+        "geometric_local_onset": 0.20000000298023224,
+        "geometric_ramp_onset": 0.4000000059604645,
+        "number_variance_compatibility_extent": 1.0,
+        "D800_connected_plateau": 0.7,
+    }
+    assert audit["registered_scale"] == {
+        "physical_matrices": 20_000,
+        "physical_test_matrices": 4_000,
+        "structured_momenta": 24,
+        "structured_orbits": 12,
+        "geometric_interpolation_matrices": 28_000,
+        "spectral_interpolation_matrices": 32_000,
+        "haar_matrices": 10_000,
+        "root_matrices": 8_750,
+        "maximum_rank": 800,
+        "bootstrap_replicates": 10_000,
+    }
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_spectral_silence_figures_v2.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_spectral_silence_figures_v2.py
new file mode 100644
index 000000000..7712f2c88
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_spectral_silence_figures_v2.py
@@ -0,0 +1,72 @@
+"""Publication-figure contract for the v2 article."""
+
+from __future__ import annotations
+
+import json
+from pathlib import Path
+
+from PIL import Image
+from pypdf import PdfReader
+import pytest
+
+from make_spectral_silence_figures_v2 import run
+
+
+EXTERNAL_SPECTRAL = (
+    Path(__file__).resolve().parents[1]
+    / "output"
+    / "spectral_silence_v2.npz"
+)
+
+
+def _audit_manifest(manifest_path: Path) -> None:
+    manifest = json.loads(
+        manifest_path.read_text(encoding="utf-8")
+    )
+    assert len(manifest["figures"]) == 5
+    assert manifest["scientific_annotations"] == {
+        "energy_raw": 50.0,
+        "energy_connected": 0.0,
+        "local_g": 0.2,
+        "ramp_g": 0.4,
+        "number_extent": 1.0,
+        "D800_atom_each": 120,
+        "D800_connected_plateau": 0.7,
+    }
+    for figure in manifest["figures"].values():
+        pdf = Path(figure["pdf"])
+        png = Path(figure["png"])
+        assert pdf.is_file() and png.is_file()
+        width = (
+            float(PdfReader(str(pdf)).pages[0].mediabox.width)
+            / 72.0
+        )
+        assert abs(width - 7.0) < 0.01
+        with Image.open(png) as image:
+            assert image.width >= 2100
+            assert image.info["dpi"][0] >= 299.0
+        assert len(figure["pdf_sha256"]) == 64
+        assert len(figure["png_sha256"]) == 64
+
+
+@pytest.mark.skipif(
+    not EXTERNAL_SPECTRAL.exists(),
+    reason=(
+        "activates with production arrays listed in release_manifest_v1.json"
+    ),
+)
+def test_reduced_figure_build(tmp_path):
+    result = run(tmp_path)
+    assert result["all_checks_pass"]
+    _audit_manifest(tmp_path / "figure_manifest_v2.json")
+    numbers = (tmp_path / "generated_numbers_v2.tex").read_text(
+        encoding="utf-8"
+    )
+    assert r"\newcommand{\EnergyRawSFF}{50}" in numbers
+    assert r"\newcommand{\GeometricLocalOnset}{0.20}" in numbers
+    assert r"\newcommand{\GeometricRampOnset}{0.40}" in numbers
+
+
+def test_registered_figure_package():
+    output = Path(__file__).resolve().parents[1] / "output"
+    _audit_manifest(output / "figure_manifest_v2.json")
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_spectral_silence_runner_v2.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_spectral_silence_runner_v2.py
new file mode 100644
index 000000000..962ca3fbe
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_spectral_silence_runner_v2.py
@@ -0,0 +1,51 @@
+"""Reduced-run tests for the spectral-silence production artifact."""
+
+from __future__ import annotations
+
+import json
+from pathlib import Path
+
+import numpy as np
+import pytest
+
+from run_spectral_silence_v2 import run
+
+
+EXTERNAL_PHYSICAL = (
+    Path(__file__).resolve().parents[1]
+    / "output"
+    / "physical_ensemble_v1.npz"
+)
+
+
+@pytest.mark.skipif(
+    not EXTERNAL_PHYSICAL.exists(),
+    reason=(
+        "activates with production arrays listed in release_manifest_v1.json"
+    ),
+)
+def test_reduced_spectral_silence_runner(tmp_path):
+    output_json = tmp_path / "spectral_silence_v2.json"
+    output_npz = tmp_path / "spectral_silence_v2.npz"
+    result = run(
+        output_json,
+        output_npz,
+        samples_per_g=64,
+        spectral_samples=64,
+        quadrature_order=128,
+        rank_form_factor_samples=64,
+    )
+    assert result["checks"]["exact_energy_silence"]
+    assert result["checks"]["structured_control_full_rank"]
+    assert result["checks"]["structured_control_multiplets"]
+    assert result["checks"]["fixed_projector_invariance"]
+    assert result["checks"]["spectral_axis_resolved"]
+    assert result["checks"]["atom_plateau_theorem"]
+    assert result["all_checks_pass"]
+    loaded = json.loads(output_json.read_text(encoding="utf-8"))
+    assert loaded["sample_counts"]["per_positive_g"] == 64
+    arrays = np.load(output_npz, allow_pickle=False)
+    assert arrays["structured_spectra"].shape == (24, 50)
+    assert arrays["g_spectra"].shape == (7, 64, 50)
+    assert arrays["energy_spectra_alpha"].shape == (8, 64, 50)
+    assert arrays["rank_reference_connected_full"].shape[0] == 7
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_spectral_silence_statistics_v2.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_spectral_silence_statistics_v2.py
new file mode 100644
index 000000000..3ac3af4e5
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_spectral_silence_statistics_v2.py
@@ -0,0 +1,87 @@
+"""Inference tests for the spectral-silence expansion."""
+
+from __future__ import annotations
+
+import json
+from pathlib import Path
+
+import numpy as np
+import pytest
+
+from run_spectral_silence_statistics_v2 import (
+    registered_compatibility_extent,
+    registered_compatibility_onset,
+    run,
+)
+
+
+EXTERNAL_SPECTRAL = (
+    Path(__file__).resolve().parents[1]
+    / "output"
+    / "spectral_silence_v2.npz"
+)
+
+
+def test_registered_crossover_requires_all_later_nonplateau_points():
+    grid = np.array([0.2, 0.4, 0.6, 0.8])
+    lower = np.array([0.1, -0.1, -0.1, -0.1])
+    upper = np.array([0.2, 0.1, 0.1, 0.1])
+    assert (
+        registered_compatibility_onset(
+            grid,
+            lower,
+            upper,
+            minimum=0.2,
+            maximum=0.8,
+        )
+        == 0.4
+    )
+
+
+def test_unresolved_crossover_is_explicit():
+    assert (
+        registered_compatibility_onset(
+            np.array([0.2, 0.4]),
+            np.array([0.1, 0.1]),
+            np.array([0.2, 0.2]),
+            minimum=0.2,
+            maximum=0.4,
+        )
+        is None
+    )
+
+
+def test_compatibility_extent_stops_before_first_resolved_deviation():
+    extent = registered_compatibility_extent(
+        np.array([0.5, 1.0, 1.5, 2.0]),
+        np.array([-0.1, -0.1, 0.05, 0.1]),
+        np.array([0.1, 0.1, 0.15, 0.2]),
+        minimum=0.5,
+        maximum=2.0,
+    )
+    assert extent == 1.0
+
+
+@pytest.mark.skipif(
+    not EXTERNAL_SPECTRAL.exists(),
+    reason=(
+        "activates with production arrays listed in release_manifest_v1.json"
+    ),
+)
+def test_production_statistics_artifact(tmp_path):
+    output_json = tmp_path / "statistics.json"
+    output_npz = tmp_path / "statistics.npz"
+    result = run(
+        output_json,
+        output_npz,
+        bootstrap_replicates=500,
+    )
+    assert result["checks"]["structured_control_rejects_jacobi"]
+    assert result["checks"]["physical_has_registered_jacobi_window"]
+    assert result["checks"]["spectral_axis_confidence_separated"]
+    assert result["all_checks_pass"]
+    loaded = json.loads(output_json.read_text(encoding="utf-8"))
+    assert loaded["bootstrap_replicates"] == 500
+    arrays = np.load(output_npz, allow_pickle=False)
+    assert arrays["g_form_mean"].shape[0] == 7
+    assert arrays["energy_gap_ratio_mean"].shape[0] == 8
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_topological_holonomy_delivery_v3.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_topological_holonomy_delivery_v3.py
new file mode 100644
index 000000000..42aeb46f8
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_topological_holonomy_delivery_v3.py
@@ -0,0 +1,69 @@
+"""Publication and fail-closed tests for fixed-Chern holonomy."""
+
+from __future__ import annotations
+
+import copy
+import hashlib
+import json
+from pathlib import Path
+
+import pytest
+from PIL import Image
+
+from run_topological_holonomy_v3 import OUTPUT_JSON, OUTPUT_NPZ
+from verify_topological_holonomy_v3 import (
+    AUDIT_JSON,
+    FIGURE_MANIFEST,
+    FIGURE_PDF,
+    FIGURE_PNG,
+    audit_topology_payload,
+)
+
+
+def _sha256(path: Path) -> str:
+    return hashlib.sha256(path.read_bytes()).hexdigest()
+
+
+def test_figure_7_has_registered_dimensions_and_source_hashes() -> None:
+    manifest = json.loads(FIGURE_MANIFEST.read_text(encoding="utf-8"))
+    figure = manifest["figure_7_topological_holonomy_v3"]
+    assert figure["width_inches"] == 7.0
+    assert figure["png_width_pixels"] == 2100
+    assert figure["source_json_sha256"] == _sha256(OUTPUT_JSON)
+    assert figure["source_npz_sha256"] == _sha256(OUTPUT_NPZ)
+    assert figure["pdf_sha256"] == _sha256(FIGURE_PDF)
+    assert figure["png_sha256"] == _sha256(FIGURE_PNG)
+    assert figure["panels"] == [
+        "fixed_chern_and_gap",
+        "determinant_winding",
+        "wilson_gap_ratio",
+        "wilson_form_factor",
+    ]
+    with Image.open(FIGURE_PNG) as image:
+        assert image.width == 2100
+        assert image.height >= 1450
+
+
+def test_topology_delivery_audit_passes_all_gates() -> None:
+    audit = json.loads(AUDIT_JSON.read_text(encoding="utf-8"))
+    assert audit["passed"] is True
+    assert all(audit["checks"].values())
+    assert audit["result_branch"] == "fixed_chern_deformed_holonomy"
+    assert audit["registered_sizes"] == [[3, 8, 16], [4, 10, 25]]
+    assert audit["registered_meshes"] == [16, 20]
+
+
+def test_topology_audit_rejects_changed_chern() -> None:
+    payload = json.loads(OUTPUT_JSON.read_text(encoding="utf-8"))
+    corrupted = copy.deepcopy(payload)
+    corrupted["sizes"][0]["primary_chern_range"][-1] += 1.0
+    with pytest.raises(AssertionError):
+        audit_topology_payload(corrupted)
+
+
+def test_topology_audit_rejects_false_cue_branch() -> None:
+    payload = json.loads(OUTPUT_JSON.read_text(encoding="utf-8"))
+    corrupted = copy.deepcopy(payload)
+    corrupted["result_branch"] = "fixed_chern_chaotic_holonomy"
+    with pytest.raises(AssertionError):
+        audit_topology_payload(corrupted)
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_topological_holonomy_runner_v3.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_topological_holonomy_runner_v3.py
new file mode 100644
index 000000000..aeb6e968c
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_topological_holonomy_runner_v3.py
@@ -0,0 +1,82 @@
+"""Runner tests for fixed-Chern Wilson holonomy production."""
+
+from __future__ import annotations
+
+import json
+from pathlib import Path
+
+import pytest
+
+from run_topological_holonomy_v3 import (
+    OUTPUT_JSON,
+    run,
+    select_topology_branch,
+)
+
+
+EXTERNAL_REDUCED_BUNDLE = (
+    Path(__file__).resolve().parents[1]
+    / "output"
+    / "topology_v3_checkpoints"
+    / "N3_mesh6_twist_bundle_v3.json"
+)
+
+
+@pytest.mark.skipif(
+    not EXTERNAL_REDUCED_BUNDLE.exists(),
+    reason=(
+        "activates with production arrays listed in release_manifest_v1.json"
+    ),
+)
+def test_reduced_runner_contains_topology_and_holonomy_gates(
+    tmp_path: Path,
+) -> None:
+    payload = run(
+        output_json=tmp_path / "result.json",
+        output_npz=tmp_path / "result.npz",
+        sizes=((3, 8, 16),),
+        primary_mesh=6,
+        convergence_mesh=8,
+        g_values=(0.0, 0.25),
+        generator_seeds=(20260728400,),
+        cue_samples=64,
+        workers=1,
+        production=False,
+    )
+    assert set(payload["checks"]) >= {
+        "kernel_count",
+        "gap_open",
+        "mesh_chern_integer",
+        "mesh_chern_agreement",
+        "determinant_trace_agreement",
+        "branch_margin",
+        "random_gauge_invariance",
+        "isospectral_orbit",
+    }
+    assert payload["sizes"][0]["base_chern_integer"] == 6
+    assert payload["configuration"]["g_values"] == [0.0, 0.25]
+
+
+@pytest.mark.skipif(
+    not OUTPUT_JSON.exists(),
+    reason="production topology artifact has not been generated",
+)
+def test_chern_and_energy_are_fixed_across_g() -> None:
+    payload = json.loads(OUTPUT_JSON.read_text(encoding="utf-8"))
+    for size in payload["sizes"]:
+        assert (
+            max(size["primary_chern_range"])
+            - min(size["primary_chern_range"])
+            < 1e-8
+        )
+        assert size["maximum_energy_spectrum_error"] < 1e-13
+        assert size["maximum_gap_error"] < 1e-13
+
+
+@pytest.mark.skipif(
+    not OUTPUT_JSON.exists(),
+    reason="production topology artifact has not been generated",
+)
+def test_result_branch_is_recomputed_from_raw_topology_metrics() -> None:
+    payload = json.loads(OUTPUT_JSON.read_text(encoding="utf-8"))
+    assert payload["result_branch"] == select_topology_branch(payload)
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_twist_bundle_v3.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_twist_bundle_v3.py
new file mode 100644
index 000000000..31a05dd1f
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_twist_bundle_v3.py
@@ -0,0 +1,74 @@
+"""Tests for physical closed twist-torus bundle checkpoints."""
+
+from __future__ import annotations
+
+from pathlib import Path
+
+import numpy as np
+import pytest
+
+from lgeth.twist_bundle import (
+    build_twist_bundle,
+    load_twist_bundle,
+    save_twist_bundle,
+)
+
+
+@pytest.fixture(scope="module")
+def reduced_bundle():
+    return build_twist_bundle(N=3, n_flux=8, rank=16, mesh=3)
+
+
+def test_reduced_twist_bundle_has_exact_kernel_and_open_gap(
+    reduced_bundle,
+) -> None:
+    bundle = reduced_bundle
+    assert bundle.coefficient_frames.shape[:2] == (3, 3)
+    assert bundle.coefficient_frames.shape[-1] == 16
+    assert np.max(bundle.kernel_bandwidth) < 1e-9
+    assert np.min(bundle.external_gap) > 0.0
+    assert bundle.geometry.minimum_overlap_singular_value > 0.0
+    assert bundle.observed_rank_min == bundle.observed_rank_max == 16
+
+
+def test_checkpoint_round_trip_preserves_frames_and_geometry(
+    reduced_bundle,
+    tmp_path: Path,
+) -> None:
+    metadata = tmp_path / "bundle.json"
+    save_twist_bundle(reduced_bundle, metadata)
+    loaded = load_twist_bundle(
+        metadata,
+        expected_N=3,
+        expected_n_flux=8,
+        expected_rank=16,
+        expected_mesh=3,
+    )
+    np.testing.assert_allclose(
+        loaded.coefficient_frames,
+        reduced_bundle.coefficient_frames,
+    )
+    np.testing.assert_allclose(
+        loaded.orbital_frames,
+        reduced_bundle.orbital_frames,
+    )
+    assert loaded.geometry.chern_determinant == pytest.approx(
+        reduced_bundle.geometry.chern_determinant,
+        abs=1e-12,
+    )
+
+
+def test_checkpoint_rejects_mesh_mismatch(
+    reduced_bundle,
+    tmp_path: Path,
+) -> None:
+    metadata = tmp_path / "bundle.json"
+    save_twist_bundle(reduced_bundle, metadata)
+    with pytest.raises(ValueError, match="checkpoint identity"):
+        load_twist_bundle(
+            metadata,
+            expected_N=3,
+            expected_n_flux=8,
+            expected_rank=16,
+            expected_mesh=4,
+        )
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_wick_channels_v3.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_wick_channels_v3.py
new file mode 100644
index 000000000..0827d7829
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_wick_channels_v3.py
@@ -0,0 +1,190 @@
+"""Tests for gauge-invariant four-channel Wick statistics."""
+
+from __future__ import annotations
+
+import numpy as np
+import pytest
+
+from lgeth.wick_channels import (
+    channel_covariance,
+    covariance_matched_wick,
+    external_covariance_eigenvalues,
+    fourier_density_panel,
+    gaussian_r4_reference,
+    local_density_panels,
+    sample_matched_gaussian_channels,
+    whiten_channel_labels,
+)
+
+
+def _synthetic_channels(
+    seed: int,
+    channels: int = 8,
+    ambient: int = 20,
+    rank: int = 5,
+) -> np.ndarray:
+    rng = np.random.default_rng(seed)
+    return (
+        rng.normal(size=(channels, ambient, rank))
+        + 1j * rng.normal(size=(channels, ambient, rank))
+    ) / np.sqrt(2.0 * ambient)
+
+
+def _seeded_unitary(dimension: int, seed: int) -> np.ndarray:
+    rng = np.random.default_rng(seed)
+    matrix = rng.normal(size=(dimension, dimension))
+    matrix = matrix + 1j * rng.normal(size=matrix.shape)
+    unitary, _ = np.linalg.qr(matrix)
+    return unitary
+
+
+def test_local_panels_are_mean_zero_distinct_site_densities() -> None:
+    panels = local_density_panels(
+        length=4,
+        panel_size=8,
+        panels=6,
+        seed=71,
+    )
+    assert panels.shape == (6, 8, 16)
+    np.testing.assert_allclose(np.sum(panels, axis=-1), 0.0, atol=1e-14)
+    assert np.all(
+        np.count_nonzero(np.abs(panels) > 1e-14, axis=-1) == 16
+    )
+    assert np.array_equal(
+        panels,
+        local_density_panels(4, 8, 6, 71),
+    )
+
+
+def test_fourier_panel_is_not_a_relabeling_of_local_panel() -> None:
+    local = local_density_panels(4, 8, 1, 71)[0]
+    fourier = fourier_density_panel(4, 8)
+    assert fourier.shape == local.shape
+    assert np.linalg.matrix_rank(
+        np.concatenate([local, fourier], axis=0)
+    ) > 8
+
+
+def test_channel_label_whitening_sets_covariance_to_identity() -> None:
+    channels = _synthetic_channels(seed=9)
+    whitened = whiten_channel_labels(channels, rtol=1e-12)
+    covariance = channel_covariance(whitened.channels)
+    np.testing.assert_allclose(
+        covariance,
+        np.eye(channels.shape[0]),
+        atol=1e-10,
+    )
+
+
+def test_singular_channel_support_fails_closed() -> None:
+    channels = _synthetic_channels(seed=9)
+    channels[1] = channels[0]
+    with pytest.raises(ValueError, match="channel-label support"):
+        whiten_channel_labels(channels, rtol=1e-10)
+
+
+def test_isotropic_wick_coefficients_reduce_to_known_limits() -> None:
+    rng = np.random.default_rng(12)
+    channels = (
+        rng.normal(size=(16, 20, 5))
+        + 1j * rng.normal(size=(16, 20, 5))
+    ) / np.sqrt(40.0)
+    result = covariance_matched_wick(channels)
+    assert result.A_left == pytest.approx(1.0, rel=0.08)
+    assert result.B_right == pytest.approx(5.0 / 20.0, rel=0.25)
+
+
+def test_gram_reduction_matches_explicit_external_covariance() -> None:
+    channels = _synthetic_channels(seed=17, channels=4, ambient=9, rank=3)
+    explicit = np.mean(
+        np.einsum(
+            "mai,mbi->mab",
+            channels,
+            channels.conj(),
+            optimize=True,
+        ),
+        axis=0,
+    )
+    explicit_values = np.linalg.eigvalsh(explicit)
+    explicit_values = explicit_values[explicit_values > 1e-12]
+    reduced = external_covariance_eigenvalues(channels)
+    np.testing.assert_allclose(
+        reduced,
+        explicit_values,
+        rtol=1e-10,
+        atol=1e-12,
+    )
+
+
+def test_r4_is_invariant_under_target_external_and_label_unitaries() -> None:
+    channels = _synthetic_channels(seed=21)
+    reference = covariance_matched_wick(channels).R4
+    label = _seeded_unitary(channels.shape[0], seed=22)
+    external = _seeded_unitary(channels.shape[1], seed=23)
+    target = _seeded_unitary(channels.shape[2], seed=24)
+    transformed = np.einsum(
+        "mn,ab,nbj,jk->mak",
+        label,
+        external,
+        channels,
+        target,
+        optimize=True,
+    )
+    observed = covariance_matched_wick(transformed).R4
+    assert observed == pytest.approx(reference, abs=2e-10)
+
+
+def test_matched_gaussian_reference_is_seed_reproducible() -> None:
+    physical = covariance_matched_wick(_synthetic_channels(seed=31))
+    first = gaussian_r4_reference(
+        physical.left_eigenvalues,
+        physical.right_eigenvalues,
+        channel_count=8,
+        samples=64,
+        seed=32,
+    )
+    second = gaussian_r4_reference(
+        physical.left_eigenvalues,
+        physical.right_eigenvalues,
+        channel_count=8,
+        samples=64,
+        seed=32,
+    )
+    np.testing.assert_array_equal(first, second)
+    assert np.all(np.isfinite(first))
+    assert np.quantile(first, 0.025) < np.quantile(first, 0.975)
+
+
+def test_matched_gaussian_sampler_has_requested_shape() -> None:
+    rng = np.random.default_rng(41)
+    sample = sample_matched_gaussian_channels(
+        left_eigenvalues=np.array([0.4, 0.6]),
+        right_eigenvalues=np.array([0.2, 0.3, 0.5]),
+        channel_count=5,
+        rng=rng,
+    )
+    assert sample.shape == (5, 3, 2)
+    assert np.all(np.isfinite(sample))
+
+
+def test_fast_gaussian_reference_estimator_matches_full_result() -> None:
+    channels = _synthetic_channels(seed=51)
+    physical = covariance_matched_wick(channels)
+    reference = gaussian_r4_reference(
+        physical.left_eigenvalues,
+        physical.right_eigenvalues,
+        channel_count=8,
+        samples=1,
+        seed=52,
+    )
+    rng = np.random.default_rng(52)
+    sample = sample_matched_gaussian_channels(
+        physical.left_eigenvalues,
+        physical.right_eigenvalues,
+        channel_count=8,
+        rng=rng,
+    )
+    assert reference[0] == pytest.approx(
+        covariance_matched_wick(sample).R4,
+        abs=2e-10,
+    )
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/validate_citations_v1.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/validate_citations_v1.py
new file mode 100644
index 000000000..ac168dbdb
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/validate_citations_v1.py
@@ -0,0 +1,685 @@
+#!/usr/bin/env python3
+"""Validate the large-scale companion bibliography against primary metadata.
+
+The audit is intentionally explicit: every bibliography key is registered,
+assigned to an intended manuscript section, and checked against a primary
+identifier.  No task_03 files or bibliography are imported.
+"""
+
+from __future__ import annotations
+
+import argparse
+import json
+import re
+import unicodedata
+import urllib.parse
+import urllib.request
+import xml.etree.ElementTree as ET
+from difflib import SequenceMatcher
+from pathlib import Path
+from typing import Any
+
+
+SCRIPT_DIR = Path(__file__).resolve().parent
+REPO_ROOT = SCRIPT_DIR.parents[2]
+DEFAULT_BIB = (
+    REPO_ROOT
+    / "overleaf_sync"
+    / "geometric_eth_large_scale"
+    / "references.bib"
+)
+DEFAULT_JSON = SCRIPT_DIR / "output" / "citation_audit_v1.json"
+DEFAULT_MARKDOWN = (
+    REPO_ROOT
+    / "docs"
+    / "literature"
+    / "2026-07-28-geometric-eth-large-scale-citation-audit.md"
+)
+USER_AGENT = (
+    "Chaos-of-Quantum-Geometry citation audit/1.0 "
+    "(mailto:thomasjwang@users.noreply.github.com)"
+)
+
+
+def _record(
+    key: str,
+    title: str,
+    year: int,
+    authors: tuple[str, ...],
+    section: str,
+    *,
+    doi: str | None = None,
+    arxiv: str | None = None,
+) -> dict[str, Any]:
+    return {
+        "key": key,
+        "title": title,
+        "year": year,
+        "authors": list(authors),
+        "section": section,
+        "doi": doi,
+        "arxiv": arxiv,
+    }
+
+
+REGISTRY = (
+    _record(
+        "berry1984",
+        "Quantal phase factors accompanying adiabatic changes",
+        1984,
+        ("Berry",),
+        "geometric foundations",
+        doi="10.1098/rspa.1984.0023",
+    ),
+    _record(
+        "wilczekzee1984",
+        "Appearance of gauge structure in simple dynamical systems",
+        1984,
+        ("Wilczek", "Zee"),
+        "geometric foundations",
+        doi="10.1103/PhysRevLett.52.2111",
+    ),
+    _record(
+        "provostvallee1980",
+        "Riemannian structure on manifolds of quantum states",
+        1980,
+        ("Provost", "Vallee"),
+        "geometric foundations",
+        doi="10.1007/BF02193559",
+    ),
+    _record(
+        "kato1950",
+        "On the adiabatic theorem of quantum mechanics",
+        1950,
+        ("Kato",),
+        "isolated-projector formalism",
+        doi="10.1143/JPSJ.5.435",
+    ),
+    _record(
+        "chen2026",
+        "Chaos of Berry curvature for BPS microstates",
+        2026,
+        ("Chen", "Colin-Ellerin", "Mamroud", "Papadodimas"),
+        "geometric chaos motivation",
+        arxiv="2604.23287",
+    ),
+    _record(
+        "laughlin1983",
+        (
+            "Anomalous quantum Hall effect: An incompressible quantum "
+            "fluid with fractionally charged excitations"
+        ),
+        1983,
+        ("Laughlin",),
+        "Laughlin zero modes",
+        doi="10.1103/PhysRevLett.50.1395",
+    ),
+    _record(
+        "haldane1983",
+        (
+            "Fractional quantization of the Hall effect: A hierarchy of "
+            "incompressible quantum fluid states"
+        ),
+        1983,
+        ("Haldane",),
+        "fractional quantum Hall hierarchy",
+        doi="10.1103/PhysRevLett.51.605",
+    ),
+    _record(
+        "bernevighaldane2008",
+        "Model fractional quantum Hall states and Jack polynomials",
+        2008,
+        ("Bernevig", "Haldane"),
+        "generalized exclusion rules",
+        doi="10.1103/PhysRevLett.100.246802",
+    ),
+    _record(
+        "chenseidel2015",
+        (
+            "Algebraic approach to the study of zero modes of Haldane "
+            "pseudopotentials"
+        ),
+        2015,
+        ("Chen", "Seidel"),
+        "zero-mode algebra",
+        doi="10.1103/PhysRevB.91.085103",
+    ),
+    _record(
+        "mooreread1991",
+        "Nonabelions in the fractional quantum Hall effect",
+        1991,
+        ("Moore", "Read"),
+        "higher clustering",
+        doi="10.1016/0550-3213(91)90407-O",
+    ),
+    _record(
+        "readrezayi1999",
+        (
+            "Beyond paired quantum Hall states: Parafermions and "
+            "incompressible states in the first excited Landau level"
+        ),
+        1999,
+        ("Read", "Rezayi"),
+        "higher clustering",
+        doi="10.1103/PhysRevB.59.8084",
+    ),
+    _record(
+        "zhang2023",
+        (
+            "From frustration-free parent Hamiltonians to off-diagonal "
+            "long-range order: Moore-Read and related states in second "
+            "quantization"
+        ),
+        2023,
+        ("Fanmao Zhang", "Matheus Schossler", "Seidel", "Chen"),
+        "clustered root spaces",
+        doi="10.1103/PhysRevB.108.075142",
+    ),
+    _record(
+        "mazaheri2015",
+        (
+            "Zero modes, bosonization, and topological quantum order: "
+            "The Laughlin state in second quantization"
+        ),
+        2015,
+        ("Mazaheri", "Ortiz", "Nussinov", "Seidel"),
+        "zero-mode algebra",
+        doi="10.1103/PhysRevB.91.085115",
+    ),
+    _record(
+        "kapitmueller2010",
+        "Exact parent Hamiltonian for the quantum Hall states in a lattice",
+        2010,
+        ("Kapit", "Mueller"),
+        "lattice validation",
+        doi="10.1103/PhysRevLett.105.215303",
+    ),
+    _record(
+        "leeqi2014",
+        (
+            "Lattice construction of pseudopotential Hamiltonians for "
+            "fractional Chern insulators"
+        ),
+        2014,
+        ("Lee", "Qi"),
+        "lattice pseudopotentials",
+        doi="10.1103/PhysRevB.90.085103",
+    ),
+    _record(
+        "neupert2011",
+        "Fractional quantum Hall states at zero magnetic field",
+        2011,
+        ("Neupert", "Santos", "Chamon", "Mudry"),
+        "fractional Chern insulators",
+        doi="10.1103/PhysRevLett.106.236804",
+    ),
+    _record(
+        "bravyi2010",
+        "Topological quantum order: Stability under local perturbations",
+        2010,
+        ("Bravyi", "Hastings", "Michalakis"),
+        "gapped-phase stability",
+        doi="10.1063/1.3490195",
+    ),
+    _record(
+        "bachmann2011",
+        (
+            "Automorphic equivalence within gapped phases of quantum "
+            "lattice systems"
+        ),
+        2011,
+        ("Bachmann", "Michalakis", "Nachtergaele", "Sims"),
+        "gapped-phase transport",
+        doi="10.1007/s00220-011-1380-0",
+    ),
+    _record(
+        "schuch2011",
+        (
+            "Classifying quantum phases using matrix product states and "
+            "projected entangled pair states"
+        ),
+        2011,
+        ("Schuch", "David Perez", "Cirac"),
+        "phase classification",
+        doi="10.1103/PhysRevB.84.165139",
+    ),
+    _record(
+        "hastingswen2005",
+        (
+            "Quasiadiabatic continuation of quantum states: The stability "
+            "of topological ground-state degeneracy and emergent gauge "
+            "invariance"
+        ),
+        2005,
+        ("Hastings", "Wen"),
+        "gapped-projector transport",
+        doi="10.1103/PhysRevB.72.045141",
+    ),
+    _record(
+        "collins2005",
+        (
+            "Product of random projections, Jacobi ensembles and "
+            "universality problems arising from free probability"
+        ),
+        2005,
+        ("Collins",),
+        "Jacobi null model",
+        doi="10.1007/s00440-005-0428-5",
+    ),
+    _record(
+        "zyczkowski2000",
+        "Truncations of random unitary matrices",
+        2000,
+        ("Zyczkowski", "Sommers"),
+        "Haar compressions",
+        doi="10.1088/0305-4470/33/10/307",
+    ),
+    _record(
+        "atas2013",
+        (
+            "Distribution of the ratio of consecutive level spacings in "
+            "random matrix ensembles"
+        ),
+        2013,
+        ("Atas", "Bogomolny", "Giraud", "Roux"),
+        "local spectral statistics",
+        doi="10.1103/PhysRevLett.110.084101",
+    ),
+    _record(
+        "niuthoulesswu1985",
+        "Quantized Hall conductance as a topological invariant",
+        1985,
+        ("Niu", "Thouless", "Wu"),
+        "many-body topology",
+        doi="10.1103/PhysRevB.31.3372",
+    ),
+    _record(
+        "kolodrubetz2017",
+        "Geometry and non-adiabatic response in quantum and classical systems",
+        2017,
+        ("Kolodrubetz", "Sels", "Mehta", "Polkovnikov"),
+        "quantum geometric response",
+        doi="10.1016/j.physrep.2017.07.001",
+    ),
+    _record(
+        "bohigas1984",
+        (
+            "Characterization of chaotic quantum spectra and universality "
+            "of level fluctuation laws"
+        ),
+        1984,
+        ("Bohigas", "Giannoni", "Schmit"),
+        "random-matrix quantum chaos",
+        doi="10.1103/PhysRevLett.52.1",
+    ),
+    _record(
+        "deutsch1991",
+        "Quantum statistical mechanics in a closed system",
+        1991,
+        ("Deutsch",),
+        "eigenstate thermalization",
+        doi="10.1103/PhysRevA.43.2046",
+    ),
+    _record(
+        "srednicki1994",
+        "Chaos and quantum thermalization",
+        1994,
+        ("Srednicki",),
+        "eigenstate thermalization",
+        doi="10.1103/PhysRevE.50.888",
+    ),
+    _record(
+        "dalessio2016",
+        (
+            "From quantum chaos and eigenstate thermalization to "
+            "statistical mechanics and thermodynamics"
+        ),
+        2016,
+        ("D'Alessio", "Kafri", "Polkovnikov", "Rigol"),
+        "ETH review",
+        doi="10.1080/00018732.2016.1198134",
+    ),
+    _record(
+        "foinikurchan2019",
+        (
+            "Eigenstate thermalization hypothesis and out of time order "
+            "correlators"
+        ),
+        2019,
+        ("Foini", "Kurchan"),
+        "higher matrix-element correlations",
+        doi="10.1103/PhysRevE.99.042139",
+    ),
+    _record(
+        "pappalardi2022",
+        "Eigenstate Thermalization Hypothesis and Free Probability",
+        2022,
+        ("Pappalardi", "Foini", "Kurchan"),
+        "full ETH and free cumulants",
+        doi="10.1103/PhysRevLett.129.170603",
+    ),
+    _record(
+        "fukui2005",
+        (
+            "Chern Numbers in Discretized Brillouin Zone: Efficient Method "
+            "of Computing (Spin) Hall Conductances"
+        ),
+        2005,
+        ("Fukui", "Hatsugai", "Suzuki"),
+        "discrete Chern links",
+        doi="10.1143/JPSJ.74.1674",
+    ),
+    _record(
+        "chenludwig2018",
+        (
+            "Universal spectral correlations in the chaotic wave function, "
+            "and the development of quantum chaos"
+        ),
+        2018,
+        ("Chen", "Ludwig"),
+        "non-energy spectral correlations",
+        doi="10.1103/PhysRevB.98.064309",
+    ),
+    _record(
+        "pandey2020",
+        "Adiabatic eigenstate deformations as a sensitive probe for quantum chaos",
+        2020,
+        ("Pandey", "Claeys", "Campbell", "Polkovnikov", "Sels"),
+        "adiabatic deformation chaos diagnostic",
+        doi="10.1103/PhysRevX.10.041017",
+    ),
+    _record(
+        "sharipov2024",
+        "Hilbert space geometry and quantum chaos",
+        2024,
+        ("Sharipov", "Tiutiakina", "Gorsky", "Gritsev", "Polkovnikov"),
+        "Hilbert-space geometry",
+        arxiv="2411.11968",
+    ),
+)
+
+
+def normalize(value: str) -> str:
+    """Return an accent-, punctuation-, and case-insensitive comparison key."""
+    decomposed = unicodedata.normalize("NFKD", value)
+    ascii_text = decomposed.encode("ascii", "ignore").decode("ascii")
+    return "".join(character for character in ascii_text.lower() if character.isalnum())
+
+
+def _display_path(path: Path) -> str:
+    try:
+        return str(path.resolve().relative_to(REPO_ROOT))
+    except ValueError:
+        return str(path.resolve())
+
+
+def parse_bibtex(path: Path) -> dict[str, str]:
+    """Parse entry blocks sufficiently strictly for a controlled local BibTeX."""
+    text = path.read_text(encoding="utf-8")
+    matches = list(
+        re.finditer(
+            r"@\w+\s*\{\s*([^,\s]+)\s*,(.*?)(?=^@\w+\s*\{|\Z)",
+            text,
+            flags=re.DOTALL | re.MULTILINE,
+        )
+    )
+    keys = [match.group(1) for match in matches]
+    if len(keys) != len(set(keys)):
+        duplicates = sorted(
+            key for key in set(keys) if keys.count(key) > 1
+        )
+        raise ValueError(f"duplicate BibTeX keys: {duplicates}")
+    return {match.group(1): match.group(0) for match in matches}
+
+
+def _request_json(url: str) -> dict[str, Any]:
+    request = urllib.request.Request(
+        url,
+        headers={"User-Agent": USER_AGENT, "Accept": "application/json"},
+    )
+    with urllib.request.urlopen(request, timeout=30) as response:
+        return json.loads(response.read().decode("utf-8"))
+
+
+def fetch_doi_record(doi: str) -> dict[str, Any]:
+    encoded = urllib.parse.quote(doi, safe="")
+    data = _request_json(
+        f"https://api.openalex.org/works/https://doi.org/{encoded}"
+    )
+    return {
+        "title": data["title"],
+        "year": int(data["publication_year"]),
+        "authors": [
+            authorship["author"]["display_name"]
+            for authorship in data["authorships"]
+        ],
+        "identifier": data.get("doi", f"https://doi.org/{doi}"),
+        "metadata_source": "OpenAlex DOI resolution",
+    }
+
+
+def fetch_arxiv_record(arxiv_id: str) -> dict[str, Any]:
+    url = (
+        "https://export.arxiv.org/api/query?id_list="
+        + urllib.parse.quote(arxiv_id)
+    )
+    request = urllib.request.Request(url, headers={"User-Agent": USER_AGENT})
+    with urllib.request.urlopen(request, timeout=30) as response:
+        root = ET.fromstring(response.read())
+    namespace = {"atom": "http://www.w3.org/2005/Atom"}
+    entry = root.find("atom:entry", namespace)
+    if entry is None:
+        raise LookupError(f"arXiv did not return {arxiv_id}")
+    title = " ".join(
+        (entry.findtext("atom:title", default="", namespaces=namespace)).split()
+    )
+    published = entry.findtext(
+        "atom:published",
+        default="",
+        namespaces=namespace,
+    )
+    authors = [
+        author.findtext("atom:name", default="", namespaces=namespace)
+        for author in entry.findall("atom:author", namespace)
+    ]
+    return {
+        "title": title,
+        "year": int(published[:4]),
+        "authors": authors,
+        "identifier": f"https://arxiv.org/abs/{arxiv_id}",
+        "metadata_source": "arXiv Atom API",
+    }
+
+
+def validate_record(
+    expected: dict[str, Any],
+    observed: dict[str, Any],
+) -> dict[str, Any]:
+    expected_title = normalize(expected["title"])
+    observed_title = normalize(observed["title"])
+    title_similarity = SequenceMatcher(
+        None,
+        expected_title,
+        observed_title,
+    ).ratio()
+    observed_authors = normalize(" ".join(observed["authors"]))
+    author_matches = {
+        author: normalize(author) in observed_authors
+        for author in expected["authors"]
+    }
+    checks = {
+        "title": title_similarity >= 0.90,
+        "year": int(expected["year"]) == int(observed["year"]),
+        "authors": all(author_matches.values()),
+    }
+    return {
+        **expected,
+        "observed": observed,
+        "title_similarity": title_similarity,
+        "author_matches": author_matches,
+        "checks": checks,
+        "verified": all(checks.values()),
+    }
+
+
+def _write_markdown(audit: dict[str, Any], path: Path) -> None:
+    lines = [
+        "# Citation audit: *From Local Repulsion to Global Geometry*",
+        "",
+        (
+            "Generated on 2026-07-28 by the task-local citation validator. "
+            "Each bibliography entry is assigned to an intended manuscript "
+            "section and resolved through a DOI or arXiv identifier."
+        ),
+        "",
+        f"Overall status: **{'PASS' if audit['all_checks_pass'] else 'FAIL'}**.",
+        "",
+        "| Key | Intended use | Verified metadata | Result |",
+        "|---|---|---|---|",
+    ]
+    for record in audit["records"]:
+        if record.get("doi"):
+            link = f"https://doi.org/{record['doi']}"
+            label = f"DOI {record['doi']}"
+        else:
+            link = f"https://arxiv.org/abs/{record['arxiv']}"
+            label = f"arXiv:{record['arxiv']}"
+        status = "PASS" if record["verified"] else "FAIL"
+        lines.append(
+            f"| `{record['key']}` | {record['section']} | "
+            f"[{label}]({link}) | **{status}** |"
+        )
+    lines.extend(
+        [
+            "",
+            "## Audit contract",
+            "",
+            (
+                "The validator rejects an unresolved identifier, a title "
+                "similarity below 0.90, an incorrect publication year, a "
+                "missing registered author, a duplicate BibTeX key, an "
+                "unregistered bibliography entry, or a registered source "
+                "missing from the bibliography."
+            ),
+            "",
+            (
+                "The citation map is intentionally article-specific. Passing "
+                "this audit establishes bibliographic identity; the final "
+                "delivery audit separately verifies that every key is cited "
+                "in the compiled manuscript or supplement."
+            ),
+            "",
+        ]
+    )
+    path.parent.mkdir(parents=True, exist_ok=True)
+    path.write_text("\n".join(lines), encoding="utf-8")
+
+
+def run(
+    bib_path: Path = DEFAULT_BIB,
+    output_json: Path = DEFAULT_JSON,
+    output_markdown: Path = DEFAULT_MARKDOWN,
+    *,
+    observed_override: dict[str, dict[str, Any]] | None = None,
+) -> dict[str, Any]:
+    entries = parse_bibtex(bib_path)
+    registry_by_key = {record["key"]: record for record in REGISTRY}
+    entry_keys = set(entries)
+    registry_keys = set(registry_by_key)
+    missing_bib = sorted(registry_keys - entry_keys)
+    unregistered_bib = sorted(entry_keys - registry_keys)
+
+    results = []
+    errors = []
+    for expected in REGISTRY:
+        key = expected["key"]
+        try:
+            if observed_override is not None:
+                observed = observed_override[key]
+            elif expected["doi"]:
+                observed = fetch_doi_record(expected["doi"])
+            else:
+                observed = fetch_arxiv_record(expected["arxiv"])
+            result = validate_record(expected, observed)
+        except Exception as exc:  # network/metadata failures are audit failures
+            result = {
+                **expected,
+                "verified": False,
+                "checks": {
+                    "title": False,
+                    "year": False,
+                    "authors": False,
+                },
+                "error": f"{type(exc).__name__}: {exc}",
+            }
+            errors.append({"key": key, "error": result["error"]})
+
+        entry = entries.get(key, "")
+        identifier_present = bool(
+            (
+                expected["doi"]
+                and normalize(expected["doi"]) in normalize(entry)
+            )
+            or (
+                expected["arxiv"]
+                and expected["arxiv"] in entry
+            )
+        )
+        result["checks"]["identifier_in_bib"] = identifier_present
+        result["verified"] = bool(result["verified"] and identifier_present)
+        results.append(result)
+
+    all_checks_pass = bool(
+        not missing_bib
+        and not unregistered_bib
+        and not errors
+        and all(result["verified"] for result in results)
+    )
+    audit = {
+        "schema_version": 1,
+        "article": (
+            "From Local Repulsion to Global Geometry: "
+            "Large-Scale Tests of Geometric ETH"
+        ),
+        "bibliography": _display_path(bib_path),
+        "registered_records": len(REGISTRY),
+        "bibliography_records": len(entries),
+        "missing_bibliography_keys": missing_bib,
+        "unregistered_bibliography_keys": unregistered_bib,
+        "errors": errors,
+        "records": results,
+        "all_checks_pass": all_checks_pass,
+    }
+    output_json.parent.mkdir(parents=True, exist_ok=True)
+    output_json.write_text(
+        json.dumps(audit, indent=2, sort_keys=True) + "\n",
+        encoding="utf-8",
+    )
+    _write_markdown(audit, output_markdown)
+    if not all_checks_pass:
+        raise RuntimeError(
+            "citation audit failed; inspect "
+            f"{_display_path(output_json)}"
+        )
+    return audit
+
+
+def _parse_args() -> argparse.Namespace:
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument("--bib", type=Path, default=DEFAULT_BIB)
+    parser.add_argument("--json", type=Path, default=DEFAULT_JSON)
+    parser.add_argument("--markdown", type=Path, default=DEFAULT_MARKDOWN)
+    return parser.parse_args()
+
+
+def main() -> None:
+    arguments = _parse_args()
+    audit = run(arguments.bib, arguments.json, arguments.markdown)
+    print(
+        "citation audit: PASS "
+        f"({audit['registered_records']} verified records)"
+    )
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/verify_geometric_eth_topology_article_v3.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/verify_geometric_eth_topology_article_v3.py
new file mode 100644
index 000000000..70760c08e
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/verify_geometric_eth_topology_article_v3.py
@@ -0,0 +1,282 @@
+#!/usr/bin/env python3
+"""Fail-closed delivery audit for the v3 integrated article."""
+
+from __future__ import annotations
+
+import hashlib
+import json
+import re
+import shutil
+import subprocess
+import tempfile
+from datetime import datetime, timezone
+from pathlib import Path
+from typing import Any
+
+from PIL import Image
+from pypdf import PdfReader
+
+
+SCRIPT_ROOT = Path(__file__).resolve().parent
+REPO_ROOT = SCRIPT_ROOT.parents[2]
+OUTPUT = SCRIPT_ROOT / "output"
+ARTICLE = REPO_ROOT / "overleaf_sync" / "geometric_eth_large_scale"
+FINAL_PDF = OUTPUT / "spectral_silence_and_geometric_chaos_v3.pdf"
+AUDIT_JSON = OUTPUT / "geometric_eth_topology_delivery_audit_v3.json"
+ARTICLE_TITLE = (
+    "Spectral Silence and Geometric Chaos in an Exactly Degenerate "
+    "Topological Manifold"
+)
+MAIN_FIGURES = (
+    "figure_1_spectral_silence_v2.pdf",
+    "figure_2_falsification_triangle_v2.pdf",
+    "figure_3_independent_channels_v2.pdf",
+    "figure_4_geometric_hierarchy_v2.pdf",
+    "figure_5_jacobi_atoms_v2.pdf",
+    "figure_6_wick_factorization_v3.pdf",
+    "figure_7_topological_holonomy_v3.pdf",
+)
+
+
+def _sha256(path: Path) -> str:
+    digest = hashlib.sha256()
+    with path.open("rb") as handle:
+        for block in iter(lambda: handle.read(1024 * 1024), b""):
+            digest.update(block)
+    return digest.hexdigest()
+
+
+def _load(path: Path) -> dict[str, Any]:
+    return json.loads(path.read_text(encoding="utf-8"))
+
+
+def _render_records(pdf: Path) -> list[dict[str, Any]]:
+    with tempfile.TemporaryDirectory(
+        prefix="task05_v3_article_render_"
+    ) as directory:
+        root = Path(directory)
+        subprocess.run(
+            [
+                "pdftoppm",
+                "-png",
+                "-r",
+                "180",
+                str(pdf),
+                str(root / "page"),
+            ],
+            check=True,
+            stdout=subprocess.DEVNULL,
+            stderr=subprocess.DEVNULL,
+        )
+        records = []
+        for index, path in enumerate(sorted(root.glob("page-*.png")), 1):
+            with Image.open(path) as image:
+                records.append(
+                    {
+                        "page": index,
+                        "width": image.width,
+                        "height": image.height,
+                        "sha256": _sha256(path),
+                    }
+                )
+        return records
+
+
+def _latex_checks(path: Path) -> dict[str, bool]:
+    text = path.read_text(encoding="utf-8", errors="replace").lower()
+    return {
+        "latex_control_sequences_resolved": (
+            "undefined control sequence" not in text
+        ),
+        "latex_references_resolved": (
+            "there were undefined references" not in text
+            and not re.search(r"reference [`'][^\n]+ undefined", text)
+        ),
+        "latex_citations_resolved": (
+            "undefined citations" not in text
+            and not re.search(r"citation [`'][^\n]+ undefined", text)
+        ),
+        "latex_boxes_within_width": "overfull \\hbox" not in text,
+        "latex_floats_placed": "float is stuck" not in text,
+    }
+
+
+def _normalize_pdf_text(text: str) -> str:
+    """Remove layout-only PDF extraction breaks without changing wording."""
+    text = re.sub(r"(?<=\w)-\s+(?=\w)", "", text)
+    return re.sub(r"\s+", " ", text)
+
+
+def run_audit() -> dict[str, Any]:
+    matrix = _load(OUTPUT / "matrix_element_geometric_eth_v3.json")
+    topology = _load(OUTPUT / "topological_holonomy_v3.json")
+    matrix_audit = _load(OUTPUT / "matrix_element_delivery_audit_v3.json")
+    topology_audit = _load(
+        OUTPUT / "topological_holonomy_delivery_audit_v3.json"
+    )
+    theory = _load(OUTPUT / "matrix_element_topology_theory_v3.json")
+    assets = _load(OUTPUT / "geometric_eth_topology_assets_v3.json")
+    citations = _load(OUTPUT / "citation_audit_v1.json")
+    main_pdf = ARTICLE / "main.pdf"
+    shutil.copyfile(main_pdf, FINAL_PDF)
+    reader = PdfReader(str(main_pdf))
+    metadata = reader.metadata or {}
+    extracted = _normalize_pdf_text(
+        "\n".join(page.extract_text() or "" for page in reader.pages)
+    )
+    extracted_lower = extracted.lower()
+    render_records = _render_records(main_pdf)
+    figure_records = []
+    for name in MAIN_FIGURES:
+        path = ARTICLE / "figures" / name
+        record = {
+            "name": name,
+            "sha256": _sha256(path),
+            "exists": path.is_file(),
+        }
+        if name.startswith("figure_6"):
+            record["source_hash_matches"] = (
+                _sha256(path)
+                == _sha256(OUTPUT / "figure_6_wick_factorization_v3.pdf")
+            )
+        elif name.startswith("figure_7"):
+            record["source_hash_matches"] = (
+                _sha256(path)
+                == _sha256(OUTPUT / "figure_7_topological_holonomy_v3.pdf")
+            )
+        else:
+            record["source_hash_matches"] = True
+        figure_records.append(record)
+    generated_sync = all(
+        _sha256(OUTPUT / name)
+        == _sha256(ARTICLE / "generated" / name)
+        for name in ("generated_numbers_v3.tex", "generated_tables_v3.tex")
+    )
+    checks = {
+        "matrix_audit_passes": matrix_audit["passed"],
+        "topology_audit_passes": topology_audit["passed"],
+        "theory_audit_passes": theory["passed"],
+        "citation_audit_passes": citations["all_checks_pass"],
+        "matrix_branch_exact": (
+            matrix["result_branch"] == "deformed_geometric_eth"
+        ),
+        "topology_branch_exact": (
+            topology["result_branch"]
+            == "fixed_chern_deformed_holonomy"
+        ),
+        "asset_branches_exact": (
+            assets["matrix_branch"] == matrix["result_branch"]
+            and assets["topology_branch"] == topology["result_branch"]
+        ),
+        "generated_assets_synchronized": generated_sync,
+        "seven_figures_present_and_synchronized": (
+            len(figure_records) == 7
+            and all(
+                item["exists"] and item["source_hash_matches"]
+                for item in figure_records
+            )
+        ),
+        "pdf_archive_byte_identical": (
+            _sha256(FINAL_PDF) == _sha256(main_pdf)
+        ),
+        "pdf_page_count": 15 <= len(reader.pages) <= 20,
+        "pdf_title_metadata": (
+            str(metadata.get("/Title", "")) == ARTICLE_TITLE
+        ),
+        "pdf_author_metadata": (
+            "Thomas J. Wang" in str(metadata.get("/Author", ""))
+            and "OKongOYangO" in str(metadata.get("/Author", ""))
+        ),
+        "affiliations_visible": (
+            "Tsinghua University" in extracted
+            and "The Pennsylvania State University" in extracted
+        ),
+        "matrix_result_visible": (
+            "four-channel residual" in extracted
+            and "progressive Gaussianization" in extracted
+            and "finite-size operator memory" in extracted
+        ),
+        "topology_result_visible": (
+            "fixed determinantbundle topology" in extracted_lower
+            and "structured non-abelian holonomy" in extracted_lower
+        ),
+        "condensed_matter_mechanism_visible": (
+            "frustration-free" in extracted_lower
+            and "condensedmatter mechanism" in extracted_lower
+        ),
+        "scientific_scope_visible": (
+            "precise finite-size scope" in extracted
+            and "N = 6" in extracted
+            and "real-time dynamics" in extracted
+        ),
+        "code_and_data_availability_visible": (
+            "code and data availability" in extracted_lower
+            and "run quick verify v1.sh" in extracted_lower
+            and "release manifest v1.json" in extracted_lower
+        ),
+        "all_pages_rendered_180dpi": (
+            len(render_records) == len(reader.pages)
+            and all(
+                record["width"] == 1530
+                and record["height"] == 1980
+                for record in render_records
+            )
+        ),
+        **_latex_checks(ARTICLE / "main.log"),
+    }
+    existing_timestamp = None
+    if AUDIT_JSON.is_file():
+        existing_timestamp = _load(AUDIT_JSON).get("generated_utc")
+    result = {
+        "version": "v3",
+        "generated_utc": (
+            existing_timestamp or datetime.now(timezone.utc).isoformat()
+        ),
+        "passed": all(checks.values()),
+        "checks": checks,
+        "matrix_branch": matrix["result_branch"],
+        "topology_branch": topology["result_branch"],
+        "page_count": len(reader.pages),
+        "main_pdf_sha256": _sha256(main_pdf),
+        "archived_pdf_sha256": _sha256(FINAL_PDF),
+        "figures": figure_records,
+        "rendered_pages": render_records,
+        "source_hashes": {
+            str(path.relative_to(REPO_ROOT)): _sha256(path)
+            for path in (
+                ARTICLE / "main.tex",
+                ARTICLE / "sections" / "08-matrix-elements-topology.tex",
+                ARTICLE
+                / "appendices"
+                / "matrix-element-topology-v3.tex",
+                ARTICLE / "references.bib",
+            )
+        },
+    }
+    if not result["passed"]:
+        raise RuntimeError(f"v3 article audit failed: {checks}")
+    temporary = AUDIT_JSON.with_suffix(".json.tmp")
+    temporary.write_text(
+        json.dumps(result, indent=2, sort_keys=True),
+        encoding="utf-8",
+    )
+    temporary.replace(AUDIT_JSON)
+    return result
+
+
+def main() -> None:
+    result = run_audit()
+    print(json.dumps(
+        {
+            "passed": result["passed"],
+            "checks": result["checks"],
+            "page_count": result["page_count"],
+            "main_pdf_sha256": result["main_pdf_sha256"],
+        },
+        indent=2,
+        sort_keys=True,
+    ))
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/verify_large_scale_article_v1.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/verify_large_scale_article_v1.py
new file mode 100644
index 000000000..323e66481
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/verify_large_scale_article_v1.py
@@ -0,0 +1,360 @@
+#!/usr/bin/env python3
+"""Fail-closed delivery audit for the large-scale Geometric-ETH article."""
+
+from __future__ import annotations
+
+import argparse
+import hashlib
+import json
+import re
+import subprocess
+import tempfile
+from pathlib import Path
+from typing import Any
+
+from PIL import Image
+from pypdf import PdfReader
+
+
+SCRIPT_DIR = Path(__file__).resolve().parent
+TASK_DIR = SCRIPT_DIR.parent
+REPO_ROOT = TASK_DIR.parents[1]
+OUTPUT = SCRIPT_DIR / "output"
+ARTICLE = REPO_ROOT / "overleaf_sync" / "geometric_eth_large_scale"
+REGISTERED_CASES = (
+    (8, 16, 80, 2_000),
+    (10, 50, 140, 2_000),
+    (12, 112, 216, 2_000),
+    (14, 210, 308, 1_000),
+    (16, 352, 416, 1_000),
+    (18, 546, 540, 500),
+    (20, 800, 680, 250),
+)
+REGISTERED_ARCHIVE_SHA256 = (
+    "aae68de7569aae83c7ff500718ab0e3635595f050f5b7afc0d60a0e63db55417"
+)
+
+
+def _sha256(path: Path) -> str:
+    digest = hashlib.sha256()
+    with path.open("rb") as handle:
+        for chunk in iter(lambda: handle.read(1024 * 1024), b""):
+            digest.update(chunk)
+    return digest.hexdigest()
+
+
+def _load(path: Path) -> dict[str, Any]:
+    return json.loads(path.read_text(encoding="utf-8"))
+
+
+def _bibtex_keys(path: Path) -> set[str]:
+    return set(
+        re.findall(
+            r"@\w+\s*\{\s*([^,\s]+)",
+            path.read_text(encoding="utf-8"),
+        )
+    )
+
+
+def _cited_keys() -> set[str]:
+    keys: set[str] = set()
+    sources = [
+        ARTICLE / "main.tex",
+        *sorted((ARTICLE / "sections").glob("*.tex")),
+        *sorted((ARTICLE / "appendices").glob("*.tex")),
+    ]
+    for source in sources:
+        text = source.read_text(encoding="utf-8")
+        for content in re.findall(r"\\cite\w*\{([^}]+)\}", text):
+            keys.update(key.strip() for key in content.split(","))
+    return keys
+
+
+def _render_pdf(pdf: Path) -> list[dict[str, Any]]:
+    with tempfile.TemporaryDirectory(prefix="task05_render_") as directory:
+        root = Path(directory)
+        subprocess.run(
+            [
+                "pdftoppm",
+                "-png",
+                "-r",
+                "150",
+                str(pdf),
+                str(root / "page"),
+            ],
+            check=True,
+            stdout=subprocess.DEVNULL,
+            stderr=subprocess.DEVNULL,
+        )
+        records = []
+        for index, path in enumerate(sorted(root.glob("page-*.png")), 1):
+            with Image.open(path) as image:
+                records.append(
+                    {
+                        "page": index,
+                        "width": image.width,
+                        "height": image.height,
+                        "sha256": _sha256(path),
+                    }
+                )
+        return records
+
+
+def _latex_log_checks(log_path: Path) -> dict[str, bool]:
+    text = log_path.read_text(encoding="utf-8", errors="replace")
+    lowered = text.lower()
+    return {
+        "no_undefined_control_sequence": (
+            "undefined control sequence" not in lowered
+        ),
+        "no_undefined_references": (
+            "there were undefined references" not in lowered
+            and "reference `" not in lowered
+        ),
+        "no_undefined_citations": (
+            "undefined citations" not in lowered
+            and not re.search(r"citation [`'][^\\n]+ undefined", lowered)
+        ),
+        "no_overfull_boxes": "overfull \\hbox" not in lowered,
+        "no_stuck_floats": "float is stuck" not in lowered,
+    }
+
+
+def run(output_json: Path) -> dict[str, Any]:
+    physical = _load(OUTPUT / "physical_ensemble_v1.json")
+    covariance = _load(OUTPUT / "covariance_model_v1.json")
+    scaling = _load(OUTPUT / "rank_scaling_v1.json")
+    statistics = _load(OUTPUT / "statistical_analysis_v1.json")
+    manifest = _load(OUTPUT / "figure_manifest_v1.json")
+    citations = _load(OUTPUT / "citation_audit_v1.json")
+
+    expected_cases = [
+        {"n": n, "D": D, "M": M, "samples": samples}
+        for n, D, M, samples in REGISTERED_CASES
+    ]
+    observed_cases = [
+        {
+            "n": case["n"],
+            "D": case["D"],
+            "M": case["M"],
+            "samples": case["samples"],
+        }
+        for case in scaling["cases"]
+    ]
+    largest = scaling["cases"][-1]
+    inference_methods = [
+        content[metric]["method"]
+        for content in statistics["ensemble_inference"].values()
+        for metric in content
+    ]
+
+    input_hashes_match = True
+    for raw_path, expected_hash in manifest["inputs"].items():
+        path = SCRIPT_DIR / raw_path
+        input_hashes_match &= path.exists() and _sha256(path) == expected_hash
+    figure_hashes_match = True
+    synchronized_figures = True
+    for figure in manifest["figures"].values():
+        pdf = SCRIPT_DIR / figure["pdf"]
+        png = SCRIPT_DIR / figure["png"]
+        figure_hashes_match &= (
+            pdf.exists()
+            and png.exists()
+            and _sha256(pdf) == figure["pdf_sha256"]
+            and _sha256(png) == figure["png_sha256"]
+        )
+        overleaf_pdf = ARTICLE / "figures" / pdf.name
+        synchronized_figures &= (
+            overleaf_pdf.exists()
+            and _sha256(overleaf_pdf) == _sha256(pdf)
+        )
+    generated_sync = all(
+        (
+            ARTICLE / "generated" / name
+        ).exists()
+        and _sha256(ARTICLE / "generated" / name)
+        == _sha256(OUTPUT / name)
+        for name in ("generated_numbers_v1.tex", "generated_tables_v1.tex")
+    )
+
+    archived_pdf = (
+        OUTPUT / "from_local_repulsion_to_global_geometry_v1.pdf"
+    )
+    # The live Overleaf tree is allowed to advance to v2.  Audit the immutable
+    # v1 archive by its registered delivery hash rather than requiring the
+    # moving ``main.pdf`` to remain byte-identical to the earlier article.
+    main_pdf = archived_pdf
+    reader = PdfReader(str(main_pdf))
+    metadata = reader.metadata or {}
+    title = str(metadata.get("/Title", ""))
+    author = str(metadata.get("/Author", ""))
+    extracted = "\n".join(
+        page.extract_text() or "" for page in reader.pages
+    )
+    render_records = _render_pdf(main_pdf)
+    bib_keys = _bibtex_keys(ARTICLE / "references.bib")
+    cited_keys = _cited_keys()
+    pytest_path = OUTPUT / "pytest_v1.txt"
+    pytest_text = (
+        pytest_path.read_text(encoding="utf-8")
+        if pytest_path.exists()
+        else ""
+    )
+    match = re.search(r"(\d+) passed", pytest_text)
+    pytest_passed = int(match.group(1)) if match else None
+
+    checks = {
+        "physical_registered_scale": (
+            physical["sample_count"] == 20_000
+            and physical["split"]
+            == {
+                "train": 12_000,
+                "validation": 4_000,
+                "test": 4_000,
+                "split_seed": physical["seed"] + 1,
+            }
+            and physical["seed_blocks"] == 8
+            and physical["physical_case"]["D"] == 50
+            and physical["all_checks_pass"]
+        ),
+        "covariance_registered_scale": (
+            covariance["diagnostic_training_rows"] >= 1_024
+            and covariance["haar_samples"] == 10_000
+            and covariance["deformed_samples"] == 10_000
+            and covariance["held_out_test"]["result_branch"]
+            == "leading_covariance_capture"
+            and covariance["all_checks_pass"]
+        ),
+        "rank_cases_and_samples_exact": observed_cases == expected_cases,
+        "largest_rank_present": largest["D"] == 800,
+        "exact_atom_counts": (
+            scaling["cases"][-2]["plus_atoms_per_matrix"] == 6
+            and scaling["cases"][-2]["minus_atoms_per_matrix"] == 6
+            and largest["plus_atoms_per_matrix"] == 120
+            and largest["minus_atoms_per_matrix"] == 120
+        ),
+        "interior_statistics_strip_atoms": all(
+            case["interior_dimension"]
+            == case["D"]
+            - case["plus_atoms_per_matrix"]
+            - case["minus_atoms_per_matrix"]
+            for case in scaling["cases"]
+        ),
+        "matrix_level_inference_only": (
+            statistics["bootstrap_replicates"] == 10_000
+            and all(
+                method
+                in {
+                    "hierarchical_seed_block_bootstrap",
+                    "matrix_gaussian_multiplier_bootstrap",
+                    "matrix_bootstrap",
+                }
+                for method in inference_methods
+            )
+            and all(
+                "eigenvalue" not in method for method in inference_methods
+            )
+        ),
+        "statistics_checks_pass": statistics["all_checks_pass"],
+        "figure_inputs_hashed": input_hashes_match,
+        "figure_outputs_hashed": figure_hashes_match,
+        "figures_synchronized": synchronized_figures,
+        "generated_inputs_synchronized": generated_sync,
+        "citation_metadata_verified": (
+            citations["all_checks_pass"]
+            and citations["registered_records"] >= 29
+        ),
+        "all_citation_keys_resolve": cited_keys <= bib_keys,
+        "chen_seed_is_cited": "chen2026" in cited_keys,
+        "article_pdf_archived": (
+            archived_pdf.exists()
+            and _sha256(archived_pdf) == REGISTERED_ARCHIVE_SHA256
+        ),
+        "pdf_page_count_in_contract": 10 <= len(reader.pages) <= 14,
+        "pdf_title_metadata": (
+            title
+            == (
+                "From Local Repulsion to Global Geometry: "
+                "Large-Scale Tests of Geometric ETH"
+            )
+        ),
+        "pdf_author_metadata": (
+            "Thomas J. Wang" in author and "OKongOYangO" in author
+        ),
+        "pdf_affiliations_visible": (
+            "Tsinghua University" in extracted
+            and "The Pennsylvania State University" in extracted
+        ),
+        "all_pdf_pages_rendered": (
+            len(render_records) == len(reader.pages)
+            and all(
+                record["width"] > 0 and record["height"] > 0
+                for record in render_records
+            )
+        ),
+        **_latex_log_checks(ARTICLE / "main.log"),
+        "pytest_complete_if_recorded": (
+            pytest_passed is None or pytest_passed >= 1
+        ),
+    }
+    audit = {
+        "schema_version": 1,
+        "article": (
+            "From Local Repulsion to Global Geometry: "
+            "Large-Scale Tests of Geometric ETH"
+        ),
+        "checks": checks,
+        "all_checks_pass": bool(all(checks.values())),
+        "pdf": {
+            "path": str(main_pdf.relative_to(REPO_ROOT)),
+            "sha256": _sha256(main_pdf),
+            "pages": len(reader.pages),
+            "title": title,
+            "author": author,
+        },
+        "rendered_pages": render_records,
+        "pytest_passed": pytest_passed,
+        "registered_scale": {
+            "physical_matrices": physical["sample_count"],
+            "haar_matrices": covariance["haar_samples"],
+            "deformed_matrices": covariance["deformed_samples"],
+            "root_matrices": sum(
+                case["samples"] for case in scaling["cases"]
+            ),
+            "maximum_rank": largest["D"],
+        },
+    }
+    output_json.parent.mkdir(parents=True, exist_ok=True)
+    output_json.write_text(
+        json.dumps(audit, indent=2) + "\n",
+        encoding="utf-8",
+    )
+    if not audit["all_checks_pass"]:
+        failed = [key for key, value in checks.items() if not value]
+        raise RuntimeError(f"large-scale delivery audit failed: {failed}")
+    return audit
+
+
+def main() -> None:
+    parser = argparse.ArgumentParser()
+    parser.add_argument(
+        "--output-json",
+        type=Path,
+        default=OUTPUT / "large_scale_delivery_audit_v1.json",
+    )
+    args = parser.parse_args()
+    audit = run(args.output_json)
+    print(
+        json.dumps(
+            {
+                "all_checks_pass": audit["all_checks_pass"],
+                "pdf": audit["pdf"],
+                "pytest_passed": audit["pytest_passed"],
+            },
+            indent=2,
+        )
+    )
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/verify_matrix_element_geometric_eth_v3.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/verify_matrix_element_geometric_eth_v3.py
new file mode 100644
index 000000000..0a07cd1e3
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/verify_matrix_element_geometric_eth_v3.py
@@ -0,0 +1,203 @@
+#!/usr/bin/env python3
+"""Fail-closed audit for matrix-element Geometric ETH artifacts."""
+
+from __future__ import annotations
+
+import ast
+import hashlib
+import json
+from datetime import datetime, timezone
+from pathlib import Path
+from typing import Any
+
+from run_matrix_element_geometric_eth_v3 import (
+    CHECKPOINT_ROOT,
+    OUTPUT_JSON,
+    OUTPUT_NPZ,
+    SCRIPT_ROOT,
+    select_result_branch,
+)
+
+
+OUTPUT_ROOT = SCRIPT_ROOT / "output"
+FIGURE_MANIFEST = OUTPUT_ROOT / "figure_manifest_v3.json"
+FIGURE_PDF = OUTPUT_ROOT / "figure_6_wick_factorization_v3.pdf"
+FIGURE_PNG = OUTPUT_ROOT / "figure_6_wick_factorization_v3.png"
+AUDIT_JSON = OUTPUT_ROOT / "matrix_element_delivery_audit_v3.json"
+RELEASE_MANIFEST = OUTPUT_ROOT / "release_manifest_v1.json"
+
+
+def _sha256(path: Path) -> str:
+    return hashlib.sha256(path.read_bytes()).hexdigest()
+
+
+def _isolated_task_sources() -> bool:
+    for source in SCRIPT_ROOT.rglob("*.py"):
+        tree = ast.parse(source.read_text(encoding="utf-8"))
+        for node in ast.walk(tree):
+            if isinstance(node, ast.Import):
+                modules = [alias.name for alias in node.names]
+            elif isinstance(node, ast.ImportFrom):
+                modules = [node.module or ""]
+            else:
+                continue
+            if any(
+                "task_03" in module
+                or "task_04" in module
+                or "qgeom" in module
+                or "gaccess" in module
+                for module in modules
+            ):
+                return False
+    return True
+
+
+def audit_payload(payload: dict[str, Any]) -> dict[str, bool]:
+    """Recompute every scientific gate from a loaded result payload."""
+
+    cases = payload["cases"]
+    expected = [(3, 8, 16), (4, 10, 25), (5, 12, 36)]
+    observed = [
+        (case["N"], case["n_flux"], case["rank"])
+        for case in cases
+    ]
+    checks = {
+        "registered_sequence": observed == expected,
+        "fixed_two_quasiholes": all(
+            case["n_flux"] == 2 * case["N"] + 2
+            for case in cases
+        ),
+        "all_runner_checks": all(payload["checks"].values()),
+        "all_case_checks": all(
+            all(case["checks"].values()) for case in cases
+        ),
+        "reference_counts": (
+            payload["configuration"]["gaussian_samples"] == 2_000
+        ),
+        "panel_counts": payload["configuration"]["panels"] == 24,
+        "panel_size": payload["configuration"]["panel_size"] == 8,
+        "kernel_residuals": all(
+            case["kernel_residual_norm"]
+            < (1e-8 if case["kernel_method"] == "dense" else 5e-7)
+            for case in cases
+        ),
+        "resolvent_residuals": all(
+            case["maximum_relative_residual"] < 2e-3
+            for case in cases
+        ),
+        "gauge_invariance": all(
+            case["gauge_invariance_error"] < 2e-9
+            for case in cases
+        ),
+        "branch_recomputed": (
+            payload["result_branch"] == select_result_branch(payload)
+        ),
+        "n2_exclusion": (
+            payload["excluded_small_case"]["expected_rank"] == 9
+            and payload["excluded_small_case"]["observed_rank"] == 12
+            and payload["excluded_small_case"]["accepted"] is False
+        ),
+    }
+    if not all(checks.values()):
+        raise AssertionError(f"matrix-element payload audit failed: {checks}")
+    return checks
+
+
+def run_audit() -> dict[str, Any]:
+    payload = json.loads(OUTPUT_JSON.read_text(encoding="utf-8"))
+    checks = audit_payload(payload)
+    manifest = json.loads(FIGURE_MANIFEST.read_text(encoding="utf-8"))
+    figure = manifest["figure_6_wick_factorization_v3"]
+    checkpoint_files = sorted(CHECKPOINT_ROOT.glob("N*_site_response_v3.*"))
+    previous_audit = (
+        json.loads(AUDIT_JSON.read_text(encoding="utf-8"))
+        if AUDIT_JSON.exists()
+        else {}
+    )
+    if len(checkpoint_files) == 6:
+        checkpoint_hashes = {
+            str(path.relative_to(SCRIPT_ROOT)): _sha256(path)
+            for path in checkpoint_files
+        }
+        checkpoint_provenance = True
+    else:
+        checkpoint_hashes = previous_audit.get("checkpoint_hashes", {})
+        release = json.loads(RELEASE_MANIFEST.read_text(encoding="utf-8"))
+        external_hashes = {
+            Path(record["path"]).name: record["sha256"]
+            for record in release["external_artifacts"]
+            if "matrix_element_v3_checkpoints" in record["path"]
+        }
+        archived_npz_hashes = {
+            Path(path).name: digest
+            for path, digest in checkpoint_hashes.items()
+            if path.endswith(".npz")
+        }
+        checkpoint_provenance = (
+            len(checkpoint_hashes) == 6
+            and external_hashes == archived_npz_hashes
+        )
+    checks.update(
+        {
+            "npz_hash": payload["npz_sha256"] == _sha256(OUTPUT_NPZ),
+            "figure_source_hash": (
+                figure["source_sha256"] == _sha256(OUTPUT_JSON)
+            ),
+            "figure_pdf_hash": (
+                figure["pdf_sha256"] == _sha256(FIGURE_PDF)
+            ),
+            "figure_png_hash": (
+                figure["png_sha256"] == _sha256(FIGURE_PNG)
+            ),
+            "checkpoint_provenance": checkpoint_provenance,
+            "task_isolation": _isolated_task_sources(),
+        }
+    )
+    result = {
+        "version": "v3",
+        "generated_utc": previous_audit.get(
+            "generated_utc", datetime.now(timezone.utc).isoformat()
+        ),
+        "passed": all(checks.values()),
+        "checks": checks,
+        "result_branch": payload["result_branch"],
+        "registered_cases": [
+            [case["N"], case["n_flux"], case["rank"]]
+            for case in payload["cases"]
+        ],
+        "result_sha256": _sha256(OUTPUT_JSON),
+        "arrays_sha256": _sha256(OUTPUT_NPZ),
+        "checkpoint_hashes": checkpoint_hashes,
+        "figure": {
+            "pdf": str(FIGURE_PDF.relative_to(SCRIPT_ROOT)),
+            "pdf_sha256": _sha256(FIGURE_PDF),
+            "png": str(FIGURE_PNG.relative_to(SCRIPT_ROOT)),
+            "png_sha256": _sha256(FIGURE_PNG),
+        },
+    }
+    if not result["passed"]:
+        raise RuntimeError(f"matrix-element delivery audit failed: {checks}")
+    temporary = AUDIT_JSON.with_suffix(".json.tmp")
+    temporary.write_text(
+        json.dumps(result, indent=2, sort_keys=True),
+        encoding="utf-8",
+    )
+    temporary.replace(AUDIT_JSON)
+    return result
+
+
+def main() -> None:
+    result = run_audit()
+    print(json.dumps(
+        {
+            "passed": result["passed"],
+            "checks": result["checks"],
+            "result_branch": result["result_branch"],
+        },
+        indent=2,
+        sort_keys=True,
+    ))
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/verify_matrix_element_topology_theory_v3.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/verify_matrix_element_topology_theory_v3.py
new file mode 100644
index 000000000..db5a4ab6f
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/verify_matrix_element_topology_theory_v3.py
@@ -0,0 +1,220 @@
+#!/usr/bin/env python3
+"""Executable checks for the v3 Wick and topology derivations."""
+
+from __future__ import annotations
+
+import json
+from datetime import datetime, timezone
+from pathlib import Path
+from typing import Any
+
+import numpy as np
+from scipy.linalg import expm
+
+from lgeth.bundle_geometry import analyze_ambient_frame_mesh
+from lgeth.wick_channels import covariance_matched_wick
+
+
+SCRIPT_ROOT = Path(__file__).resolve().parent
+OUTPUT = SCRIPT_ROOT / "output" / "matrix_element_topology_theory_v3.json"
+
+
+def _seeded_unitary(dimension: int, rng: np.random.Generator) -> np.ndarray:
+    matrix = rng.normal(size=(dimension, dimension))
+    matrix = matrix + 1j * rng.normal(size=matrix.shape)
+    q, r = np.linalg.qr(matrix)
+    phases = np.diag(r)
+    return q * (phases / np.abs(phases)).conj()[None, :]
+
+
+def wick_identity_check(
+    D: int = 4,
+    M: int = 7,
+    channels: int = 4,
+    samples: int = 20_000,
+    seed: int = 20260729500,
+) -> dict[str, float]:
+    """Compare the two analytic Wick contractions with direct sampling."""
+
+    rng = np.random.default_rng(seed)
+    left = np.linspace(0.7, 1.6, D)
+    right = np.linspace(0.5, 1.7, M)
+    right *= D / (np.sum(left) * np.sum(right))
+    A_left = D * np.sum(left**2) / np.sum(left) ** 2
+    B_right = D * np.sum(right**2) / np.sum(right) ** 2
+    identity = np.eye(channels)
+    expected = (
+        A_left * np.einsum("mn,rs->mnrs", identity, identity)
+        + B_right * np.einsum("ms,rn->mnrs", identity, identity)
+    )
+    accumulated = np.zeros_like(expected, dtype=complex)
+    batch = 250
+    completed = 0
+    while completed < samples:
+        count = min(batch, samples - completed)
+        gaussian = (
+            rng.normal(size=(count, channels, M, D))
+            + 1j * rng.normal(size=(count, channels, M, D))
+        ) / np.sqrt(2.0)
+        values = (
+            np.sqrt(right)[None, None, :, None]
+            * gaussian
+            * np.sqrt(left)[None, None, None, :]
+        )
+        pair = np.einsum(
+            "zmai,znaj->zmnij",
+            values.conj(),
+            values,
+            optimize=True,
+        )
+        tensor = np.einsum(
+            "zmnij,zrsji->zmnrs",
+            pair,
+            pair,
+            optimize=True,
+        ) / D
+        accumulated += np.sum(tensor, axis=0)
+        completed += count
+    observed = accumulated / samples
+    return {
+        "A_left": float(A_left),
+        "B_right": float(B_right),
+        "relative_error": float(
+            np.linalg.norm(observed - expected) / np.linalg.norm(expected)
+        ),
+        "maximum_absolute_error": float(
+            np.max(np.abs(observed - expected))
+        ),
+    }
+
+
+def gauge_and_gram_check(
+    seed: int = 20260729501,
+) -> dict[str, float]:
+    """Check gauge invariance and the nonzero Gram-spectrum reduction."""
+
+    rng = np.random.default_rng(seed)
+    channels = (
+        rng.normal(size=(5, 9, 4))
+        + 1j * rng.normal(size=(5, 9, 4))
+    ) / np.sqrt(18.0)
+    original = covariance_matched_wick(channels)
+    external = _seeded_unitary(9, rng)
+    target = _seeded_unitary(4, rng)
+    transformed = np.einsum(
+        "ab,mbi,ij->maj",
+        external.conj().T,
+        channels,
+        target,
+        optimize=True,
+    )
+    gauged = covariance_matched_wick(transformed)
+    matrix = channels.transpose(1, 0, 2).reshape(9, -1)
+    R = matrix @ matrix.conj().T / channels.shape[0]
+    G = matrix.conj().T @ matrix / channels.shape[0]
+    eigen_R = np.linalg.eigvalsh(0.5 * (R + R.conj().T))
+    eigen_G = np.linalg.eigvalsh(0.5 * (G + G.conj().T))
+    nonzero_R = eigen_R[eigen_R > 1e-12 * eigen_R[-1]]
+    nonzero_G = eigen_G[eigen_G > 1e-12 * eigen_G[-1]]
+    return {
+        "R4_error": abs(original.R4 - gauged.R4),
+        "tensor_error": float(
+            np.max(np.abs(original.tensor - gauged.tensor))
+        ),
+        "gram_spectrum_error": float(
+            np.max(np.abs(nonzero_R - nonzero_G))
+        ),
+    }
+
+
+def _qiwuzhang_mesh(mesh: int, mass: float = -1.0) -> np.ndarray:
+    frames = np.empty((mesh, mesh, 2, 1), dtype=complex)
+    momenta = 2.0 * np.pi * np.arange(mesh) / mesh
+    for ix, kx in enumerate(momenta):
+        for iy, ky in enumerate(momenta):
+            hamiltonian = np.array(
+                [
+                    [
+                        mass + np.cos(kx) + np.cos(ky),
+                        np.sin(kx) - 1j * np.sin(ky),
+                    ],
+                    [
+                        np.sin(kx) + 1j * np.sin(ky),
+                        -mass - np.cos(kx) - np.cos(ky),
+                    ],
+                ],
+                dtype=complex,
+            )
+            _, vectors = np.linalg.eigh(hamiltonian)
+            frames[ix, iy, :, 0] = vectors[:, 0]
+    return frames
+
+
+def periodic_unitary_chern_check(mesh: int = 24) -> dict[str, float]:
+    """Check Chern invariance under a smooth periodic ambient unitary."""
+
+    frames = _qiwuzhang_mesh(mesh)
+    deformed = np.empty_like(frames)
+    sigma_x = np.array([[0.0, 1.0], [1.0, 0.0]], dtype=complex)
+    sigma_z = np.diag([1.0, -1.0]).astype(complex)
+    angles = 2.0 * np.pi * np.arange(mesh) / mesh
+    for ix, theta_x in enumerate(angles):
+        for iy, theta_y in enumerate(angles):
+            unitary = expm(0.7j * np.sin(theta_x) * sigma_x)
+            unitary = unitary @ expm(
+                0.5j * np.sin(theta_y) * sigma_z
+            )
+            deformed[ix, iy] = unitary @ frames[ix, iy]
+    before = analyze_ambient_frame_mesh(frames)
+    after = analyze_ambient_frame_mesh(deformed)
+    return {
+        "chern_before": before.chern_determinant,
+        "chern_after": after.chern_determinant,
+        "chern_error": abs(
+            before.chern_determinant - after.chern_determinant
+        ),
+        "minimum_branch_margin": min(
+            before.determinant_branch_margin,
+            after.determinant_branch_margin,
+        ),
+    }
+
+
+def run_checks() -> dict[str, Any]:
+    wick = wick_identity_check()
+    gauge = gauge_and_gram_check()
+    topology = periodic_unitary_chern_check()
+    checks = {
+        "wick_monte_carlo": wick["relative_error"] < 0.04,
+        "gauge_tensor": gauge["tensor_error"] < 1e-10,
+        "gauge_R4": gauge["R4_error"] < 1e-10,
+        "gram_reduction": gauge["gram_spectrum_error"] < 1e-10,
+        "chern_isomorphism": topology["chern_error"] < 1e-10,
+        "chern_branch": topology["minimum_branch_margin"] > 0.0,
+    }
+    result = {
+        "version": "v3",
+        "generated_utc": datetime.now(timezone.utc).isoformat(),
+        "passed": all(checks.values()),
+        "checks": checks,
+        "wick": wick,
+        "gauge_and_gram": gauge,
+        "topology": topology,
+    }
+    if not result["passed"]:
+        raise RuntimeError(f"v3 theory checks failed: {result}")
+    temporary = OUTPUT.with_suffix(".json.tmp")
+    temporary.write_text(
+        json.dumps(result, indent=2, sort_keys=True),
+        encoding="utf-8",
+    )
+    temporary.replace(OUTPUT)
+    return result
+
+
+def main() -> None:
+    print(json.dumps(run_checks(), indent=2, sort_keys=True))
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/verify_release_contract_v1.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/verify_release_contract_v1.py
new file mode 100644
index 000000000..1b7cf212f
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/verify_release_contract_v1.py
@@ -0,0 +1,218 @@
+#!/usr/bin/env python3
+"""Fail-closed verification of the task-05 public release contract."""
+
+from __future__ import annotations
+
+import argparse
+import ast
+import hashlib
+import json
+import os
+import re
+import subprocess
+from pathlib import Path
+from typing import Any
+
+import yaml
+
+
+SCRIPT_ROOT = Path(__file__).resolve().parent
+DEFAULT_REPO_ROOT = SCRIPT_ROOT.parents[2]
+DEFAULT_MANIFEST = SCRIPT_ROOT / "output" / "release_manifest_v1.json"
+REGISTERED_BRANCHES = {
+    "matrix_element": "deformed_geometric_eth",
+    "topology": "fixed_chern_deformed_holonomy",
+}
+FORBIDDEN_IMPORTS = {"task_03", "task_04", "qgeom", "gaccess"}
+CACHE_PARTS = {"__pycache__", ".pytest_cache", ".DS_Store"}
+
+
+def _sha256(path: Path) -> str:
+    digest = hashlib.sha256()
+    with path.open("rb") as handle:
+        for block in iter(lambda: handle.read(1024 * 1024), b""):
+            digest.update(block)
+    return digest.hexdigest()
+
+
+def _record_matches(record: dict[str, Any], repo_root: Path) -> bool:
+    path = repo_root / record.get("path", "")
+    return (
+        path.is_file()
+        and path.stat().st_size == record.get("size_bytes")
+        and _sha256(path) == record.get("sha256")
+    )
+
+
+def _tracked_files(repo_root: Path) -> list[Path]:
+    result = subprocess.run(
+        ["git", "ls-files", "-z"],
+        cwd=repo_root,
+        check=True,
+        capture_output=True,
+    )
+    return [
+        repo_root / item.decode("utf-8")
+        for item in result.stdout.split(b"\0")
+        if item
+    ]
+
+
+def _task_isolated(repo_root: Path) -> bool:
+    source = repo_root / "01_task_folder" / "task_05" / "script"
+    for path in source.rglob("*.py"):
+        tree = ast.parse(path.read_text(encoding="utf-8"))
+        for node in ast.walk(tree):
+            if isinstance(node, ast.Import):
+                for alias in node.names:
+                    if alias.name.split(".", 1)[0] in FORBIDDEN_IMPORTS:
+                        return False
+            elif isinstance(node, ast.ImportFrom):
+                module = node.module or ""
+                if module.split(".", 1)[0] in FORBIDDEN_IMPORTS:
+                    return False
+    return True
+
+
+def _local_links_valid(path: Path) -> bool:
+    text = path.read_text(encoding="utf-8")
+    for target in re.findall(r"\[[^\]]*\]\(([^)]+)\)", text):
+        if target.startswith(("http://", "https://", "#")):
+            continue
+        local = target.split("#", 1)[0]
+        if local and not (path.parent / local).resolve().exists():
+            return False
+    return True
+
+
+def _citation_valid(repo_root: Path) -> bool:
+    path = repo_root / "CITATION.cff"
+    if not path.is_file():
+        return False
+    data = yaml.safe_load(path.read_text(encoding="utf-8"))
+    return (
+        data.get("cff-version") == "1.2.0"
+        and data.get("title")
+        == (
+            "Spectral Silence and Geometric Chaos in an Exactly "
+            "Degenerate Topological Manifold"
+        )
+        and data.get("license") == "GPL-3.0-only"
+        and len(data.get("authors", [])) == 2
+    )
+
+
+def verify_manifest(path: Path, *, repo_root: Path) -> dict[str, Any]:
+    repo_root = repo_root.resolve()
+    manifest = json.loads(path.read_text(encoding="utf-8"))
+    tracked = _tracked_files(repo_root)
+    release_tracked = [
+        item
+        for item in tracked
+        if item.relative_to(repo_root).as_posix().startswith(
+            (
+                "01_task_folder/task_05/",
+                "overleaf_sync/geometric_eth_large_scale/",
+            )
+        )
+    ]
+    max_bytes = int(
+        os.environ.get("TASK05_RELEASE_MAX_TRACKED_BYTES", 10 * 1024 * 1024)
+    )
+    figures = manifest.get("figures", [])
+    compact = manifest.get("compact_artifacts", [])
+    external = manifest.get("external_artifacts", [])
+
+    checks = {
+        "schema_version": manifest.get("schema_version") == 1,
+        "release_id": (
+            manifest.get("release_id") == "task05-geometric-chaos-v1"
+        ),
+        "registered_result_branches": (
+            manifest.get("result_branches") == REGISTERED_BRANCHES
+        ),
+        "paper_record": (
+            manifest.get("paper", {}).get("page_count") == 17
+            and _record_matches(manifest.get("paper", {}), repo_root)
+        ),
+        "seven_figures": (
+            len(figures) == 7
+            and all(_record_matches(item, repo_root) for item in figures)
+        ),
+        "compact_artifacts": (
+            bool(compact)
+            and all(_record_matches(item, repo_root) for item in compact)
+        ),
+        "external_records": (
+            len(external) == 25
+            and all(
+                item.get("storage_class") == "recompute_or_release_asset"
+                and isinstance(item.get("size_bytes"), int)
+                and item["size_bytes"] > 0
+                and len(item.get("sha256", "")) == 64
+                and bool(item.get("producer"))
+                for item in external
+            )
+        ),
+        "verification_commands": (
+            manifest.get("verification", {}).get("quick")
+            == "bash run_quick_verify_v1.sh"
+            and manifest.get("verification", {}).get("full")
+            == "bash run_full_recompute_v1.sh"
+        ),
+        "tracked_blob_limit": all(
+            not item.is_file() or item.stat().st_size <= max_bytes
+            for item in release_tracked
+        ),
+        "no_tracked_caches": all(
+            not CACHE_PARTS.intersection(item.parts) for item in tracked
+        ),
+        "task_runtime_isolated": _task_isolated(repo_root),
+        "public_readmes": (
+            _local_links_valid(repo_root / "README.md")
+            and _local_links_valid(
+                repo_root / "01_task_folder" / "task_05" / "README.md"
+            )
+        ),
+        "citation_metadata": _citation_valid(repo_root),
+        "release_notes": (
+            repo_root / "docs" / "2026-07-30-task05-release-notes.md"
+        ).is_file(),
+        "technical_report": (
+            repo_root / "docs" / "2026-07-30-task05-technical-report.md"
+        ).is_file(),
+        "pr_handoff": all(
+            (
+                repo_root / "docs" / name
+            ).is_file()
+            for name in (
+                "2026-07-30-task05-pr-body.md",
+                "2026-07-30-task05-pr-review-comment.md",
+                "2026-07-30-task05-public-release-checklist.md",
+            )
+        ),
+        "challenge_handoff": (
+            repo_root
+            / "docs"
+            / "2026-07-30-quantum-geometry-harness-challenge-draft.md"
+        ).is_file(),
+    }
+    return {"passed": all(checks.values()), "checks": checks}
+
+
+def main() -> None:
+    parser = argparse.ArgumentParser()
+    parser.add_argument(
+        "manifest", type=Path, nargs="?", default=DEFAULT_MANIFEST
+    )
+    parser.add_argument("--repo-root", type=Path, default=DEFAULT_REPO_ROOT)
+    args = parser.parse_args()
+
+    report = verify_manifest(args.manifest, repo_root=args.repo_root)
+    print(json.dumps(report, indent=2, sort_keys=True))
+    if not report["passed"]:
+        raise SystemExit(1)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/verify_spectral_silence_article_v2.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/verify_spectral_silence_article_v2.py
new file mode 100755
index 000000000..8ad316e0d
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/verify_spectral_silence_article_v2.py
@@ -0,0 +1,474 @@
+#!/usr/bin/env python3
+"""Fail-closed audit for the spectral-silence/geometric-chaos article."""
+
+from __future__ import annotations
+
+import argparse
+import hashlib
+import json
+import re
+import subprocess
+import tempfile
+from pathlib import Path
+from typing import Any
+
+import numpy as np
+from PIL import Image
+from pypdf import PdfReader
+
+
+SCRIPT_DIR = Path(__file__).resolve().parent
+TASK_DIR = SCRIPT_DIR.parent
+REPO_ROOT = TASK_DIR.parents[1]
+OUTPUT = SCRIPT_DIR / "output"
+ARTICLE = REPO_ROOT / "overleaf_sync" / "geometric_eth_large_scale"
+ARTICLE_TITLE = (
+    "Spectral Silence and Geometric Chaos in an Exactly Degenerate "
+    "Topological Manifold"
+)
+ARCHIVED_PDF = OUTPUT / "spectral_silence_and_geometric_chaos_v2.pdf"
+REGISTERED_ARCHIVE_SHA256 = (
+    "5d51ad4997a8cc95fa60fdafa02ef5aa13ad86cd31f10764b61a8f8903c2895c"
+)
+V2_SOURCES = (
+    SCRIPT_DIR / "lgeth" / "form_factors.py",
+    SCRIPT_DIR / "lgeth" / "controls.py",
+    SCRIPT_DIR / "run_spectral_silence_v2.py",
+    SCRIPT_DIR / "run_spectral_silence_statistics_v2.py",
+    SCRIPT_DIR / "make_spectral_silence_figures_v2.py",
+    Path(__file__).resolve(),
+)
+
+
+def _sha256(path: Path) -> str:
+    digest = hashlib.sha256()
+    with path.open("rb") as handle:
+        for block in iter(lambda: handle.read(1024 * 1024), b""):
+            digest.update(block)
+    return digest.hexdigest()
+
+
+def _load(path: Path) -> dict[str, Any]:
+    return json.loads(path.read_text(encoding="utf-8"))
+
+
+def _bibtex_keys(path: Path) -> set[str]:
+    return set(
+        re.findall(
+            r"@\w+\s*\{\s*([^,\s]+)",
+            path.read_text(encoding="utf-8"),
+        )
+    )
+
+
+def _tex_sources() -> list[Path]:
+    return [
+        ARTICLE / "main.tex",
+        *sorted((ARTICLE / "sections").glob("*.tex")),
+        *sorted((ARTICLE / "appendices").glob("*.tex")),
+    ]
+
+
+def _cited_keys() -> set[str]:
+    keys: set[str] = set()
+    for source in _tex_sources():
+        text = source.read_text(encoding="utf-8")
+        for content in re.findall(r"\\cite\w*\{([^}]+)\}", text):
+            keys.update(key.strip() for key in content.split(","))
+    return keys
+
+
+def _render_pdf(pdf: Path) -> list[dict[str, Any]]:
+    with tempfile.TemporaryDirectory(
+        prefix="task05_spectral_silence_render_"
+    ) as directory:
+        root = Path(directory)
+        subprocess.run(
+            [
+                "pdftoppm",
+                "-png",
+                "-r",
+                "150",
+                str(pdf),
+                str(root / "page"),
+            ],
+            check=True,
+            stdout=subprocess.DEVNULL,
+            stderr=subprocess.DEVNULL,
+        )
+        records: list[dict[str, Any]] = []
+        for index, path in enumerate(sorted(root.glob("page-*.png")), 1):
+            with Image.open(path) as image:
+                records.append(
+                    {
+                        "page": index,
+                        "width": image.width,
+                        "height": image.height,
+                        "sha256": _sha256(path),
+                    }
+                )
+        return records
+
+
+def _latex_log_checks(log_path: Path) -> dict[str, bool]:
+    text = log_path.read_text(encoding="utf-8", errors="replace")
+    lowered = text.lower()
+    return {
+        "no_undefined_control_sequence": (
+            "undefined control sequence" not in lowered
+        ),
+        "no_undefined_references": (
+            "there were undefined references" not in lowered
+            and not re.search(r"reference [`'][^\n]+ undefined", lowered)
+        ),
+        "no_undefined_citations": (
+            "undefined citations" not in lowered
+            and not re.search(r"citation [`'][^\n]+ undefined", lowered)
+        ),
+        "no_overfull_boxes": "overfull \\hbox" not in lowered,
+        "no_stuck_floats": "float is stuck" not in lowered,
+    }
+
+
+def _manifest_checks(
+    manifest: dict[str, Any],
+) -> tuple[bool, bool, bool]:
+    input_hashes = all(
+        Path(raw_path).is_file()
+        and _sha256(Path(raw_path)) == expected_hash
+        for raw_path, expected_hash in manifest["inputs"].items()
+    )
+    figure_hashes = True
+    figure_sync = True
+    for figure in manifest["figures"].values():
+        pdf = Path(figure["pdf"])
+        png = Path(figure["png"])
+        figure_hashes &= bool(
+            pdf.is_file()
+            and png.is_file()
+            and _sha256(pdf) == figure["pdf_sha256"]
+            and _sha256(png) == figure["png_sha256"]
+        )
+        target = ARTICLE / "figures" / pdf.name
+        figure_sync &= bool(
+            target.is_file() and _sha256(target) == _sha256(pdf)
+        )
+    return input_hashes, figure_hashes, figure_sync
+
+
+def _new_reference_metadata_passes(bib_text: str) -> bool:
+    required_fragments = (
+        "@article{pandey2020",
+        "10.1103/PhysRevX.10.041017",
+        "2004.05043",
+        "@misc{sharipov2024",
+        "2411.11968",
+        "@article{chenludwig2018",
+        "10.1103/PhysRevB.98.064309",
+        "1710.02686",
+        "@misc{chen2026",
+        "2604.23287",
+    )
+    return all(fragment in bib_text for fragment in required_fragments)
+
+
+def run(output_json: Path) -> dict[str, Any]:
+    source_json = _load(OUTPUT / "spectral_silence_v2.json")
+    statistics_json = _load(
+        OUTPUT / "spectral_silence_statistics_v2.json"
+    )
+    manifest = _load(OUTPUT / "figure_manifest_v2.json")
+    physical_v1 = _load(OUTPUT / "physical_ensemble_v1.json")
+    covariance_v1 = _load(OUTPUT / "covariance_model_v1.json")
+    scaling_v1 = _load(OUTPUT / "rank_scaling_v1.json")
+    with (
+        np.load(
+            OUTPUT / "spectral_silence_v2.npz",
+            allow_pickle=False,
+        ) as source,
+        np.load(
+            OUTPUT / "spectral_silence_statistics_v2.npz",
+            allow_pickle=False,
+        ) as statistics,
+    ):
+        energy_exact = bool(
+            np.array_equal(source["energy_raw"], np.full(121, 50.0))
+            and np.array_equal(source["energy_connected"], np.zeros(121))
+        )
+        structured_control = bool(
+            source["structured_spectra"].shape == (24, 50)
+            and np.all(source["structured_active_ranks"] == 50)
+            and int(np.max(source["structured_unique_counts"])) <= 10
+            and np.unique(source["structured_orbit_id"]).size == 12
+        )
+        geometry_axis = bool(
+            source["g_spectra"].shape == (7, 4000, 50)
+            and np.all(source["g_active_ranks"] == 50)
+            and np.allclose(
+                source["g_values"],
+                [0.02, 0.05, 0.10, 0.20, 0.40, 0.70, 1.00],
+            )
+        )
+        spectral_axis = bool(
+            source["energy_spectra_alpha"].shape == (8, 4000, 50)
+            and np.allclose(
+                source["alpha_values"],
+                [0.0, 0.10, 0.20, 0.35, 0.50, 0.70, 0.85, 1.00],
+            )
+            and float(np.max(source["projector_distance_alpha"])) < 1e-12
+            and float(np.max(source["curvature_error_alpha"])) < 1e-12
+        )
+        atom_data = bool(
+            int(source["rank_D"][-1]) == 800
+            and int(source["rank_interior"][-1]) == 560
+            and int(source["rank_atom_each"][-1]) == 120
+            and abs(
+                float(source["rank_interior"][-1])
+                / float(source["rank_D"][-1])
+                - 0.7
+            )
+            < 1e-12
+        )
+        statistics_arrays = bool(
+            statistics["g_form_mean"].shape == (7, 121)
+            and statistics["energy_gap_ratio_mean"].shape == (8,)
+            and statistics["rank_physical_connected_full"].shape
+            == (7, 121)
+        )
+
+    input_hashes, figure_hashes, figure_sync = _manifest_checks(manifest)
+    generated_sync = all(
+        (ARTICLE / "generated" / name).is_file()
+        and _sha256(ARTICLE / "generated" / name)
+        == _sha256(OUTPUT / name)
+        for name in (
+            "generated_numbers_v2.tex",
+            "generated_tables_v2.tex",
+        )
+    )
+
+    # v2 is an immutable archived delivery.  The live Overleaf tree may advance
+    # to later article versions without invalidating this historical audit.
+    main_pdf = ARCHIVED_PDF
+    reader = PdfReader(str(main_pdf))
+    metadata = reader.metadata or {}
+    title = str(metadata.get("/Title", ""))
+    author = str(metadata.get("/Author", ""))
+    extracted = "\n".join(
+        page.extract_text() or "" for page in reader.pages
+    )
+    render_records = _render_pdf(main_pdf)
+    source_text = "\n".join(
+        path.read_text(encoding="utf-8") for path in _tex_sources()
+    )
+    bib_path = ARTICLE / "references.bib"
+    bib_text = bib_path.read_text(encoding="utf-8")
+    bib_keys = _bibtex_keys(bib_path)
+    cited_keys = _cited_keys()
+    forbidden_task_import = any(
+        re.search(r"task_0[0-46-9]", path.read_text(encoding="utf-8"))
+        for path in V2_SOURCES
+    )
+
+    outcomes = statistics_json["outcomes"]
+    physics_hierarchy = bool(
+        abs(outcomes["physical_tau_compatibility_onset"] - 0.25) < 1e-12
+        and abs(
+            outcomes["first_g_with_haar_gap_ratio_interval"] - 0.20
+        )
+        < 1e-7
+        and abs(
+            outcomes["first_g_with_registered_jacobi_window"] - 0.40
+        )
+        < 1e-7
+        and abs(
+            outcomes["number_variance_compatibility_extent"] - 1.0
+        )
+        < 1e-12
+        and outcomes["number_variance_L8_residual"]["lower"] > 0.0
+    )
+    endpoint_separation = bool(
+        outcomes["energy_gap_ratio_endpoints"]["poisson_upper"]
+        < outcomes["energy_gap_ratio_endpoints"]["gue_lower"]
+    )
+    v1_retained = bool(
+        physical_v1["all_checks_pass"]
+        and physical_v1["sample_count"] == 20_000
+        and covariance_v1["all_checks_pass"]
+        and covariance_v1["held_out_test"]["result_branch"]
+        == "leading_covariance_capture"
+        and scaling_v1["all_checks_pass"]
+        and scaling_v1["cases"][-1]["D"] == 800
+    )
+
+    pytest_path = OUTPUT / "pytest_v2.txt"
+    pytest_text = (
+        pytest_path.read_text(encoding="utf-8")
+        if pytest_path.exists()
+        else ""
+    )
+    match = re.search(r"(\d+) passed", pytest_text)
+    pytest_passed = int(match.group(1)) if match else None
+
+    checks = {
+        "source_artifact_passes": bool(source_json["all_checks_pass"]),
+        "statistical_artifact_passes": bool(
+            statistics_json["all_checks_pass"]
+        ),
+        "figure_manifest_passes": bool(manifest["all_checks_pass"]),
+        "exact_energy_silence": energy_exact,
+        "same_rank_structured_control": structured_control,
+        "registered_geometry_axis": geometry_axis,
+        "registered_spectral_axis": spectral_axis,
+        "spectral_endpoint_confidence_separated": endpoint_separation,
+        "finite_jacobi_numerics_pass": bool(
+            source_json["finite_jacobi"]["mass_error"] < 1e-10
+            and source_json["finite_jacobi"]["orthogonality_error"] < 1e-10
+            and source_json["finite_jacobi"]["atom_relation_error"] < 1e-12
+            and source_json["finite_jacobi"]["raw_atom_closure_error"] < 1e-10
+        ),
+        "atom_plateau_data_exact": atom_data,
+        "registered_hierarchy_resolved": physics_hierarchy,
+        "statistical_arrays_complete": statistics_arrays,
+        "bootstrap_replicates_exact": (
+            statistics_json["bootstrap_replicates"] == 10_000
+        ),
+        "v1_large_scale_evidence_retained": v1_retained,
+        "figure_inputs_hashed": input_hashes,
+        "figure_outputs_hashed": figure_hashes,
+        "figures_synchronized": figure_sync,
+        "generated_inputs_synchronized": generated_sync,
+        "all_citation_keys_resolve": cited_keys <= bib_keys,
+        "new_reference_metadata_registered": (
+            _new_reference_metadata_passes(bib_text)
+        ),
+        "chen_program_positioned": (
+            "chen2026" in cited_keys
+            and "pandey2020" in cited_keys
+            and "sharipov2024" in cited_keys
+            and "chenludwig2018" in cited_keys
+        ),
+        "no_cross_task_v2_runtime_dependency": not forbidden_task_import,
+        "article_pdf_archived": bool(
+            ARCHIVED_PDF.is_file()
+            and _sha256(ARCHIVED_PDF) == REGISTERED_ARCHIVE_SHA256
+        ),
+        "pdf_page_count_in_contract": 10 <= len(reader.pages) <= 15,
+        "pdf_title_metadata": title == ARTICLE_TITLE,
+        "pdf_author_metadata": (
+            "Thomas J. Wang" in author and "OKongOYangO" in author
+        ),
+        "pdf_affiliations_visible": (
+            "Tsinghua University" in extracted
+            and "The Pennsylvania State University" in extracted
+        ),
+        "headline_claim_visible": (
+            "Exact degeneracy makes the energy spectrum silent"
+            in source_text
+            and "projector geometry retains" in source_text
+        ),
+        "time_caveat_visible": (
+            "not physical time" in source_text
+            and "not an out-of-time-order correlator" in source_text
+        ),
+        "non_susy_scope_visible": (
+            "no SUSY cohomology" in extracted
+            and "no gravitational interpretation" in extracted
+        ),
+        "all_pdf_pages_rendered": (
+            len(render_records) == len(reader.pages)
+            and all(
+                record["width"] == 1275 and record["height"] == 1650
+                for record in render_records
+            )
+        ),
+        **_latex_log_checks(ARTICLE / "main.log"),
+        "pytest_complete_if_recorded": (
+            pytest_passed is None or pytest_passed >= 1
+        ),
+    }
+    audit = {
+        "schema_version": 2,
+        "article": ARTICLE_TITLE,
+        "checks": checks,
+        "all_checks_pass": bool(all(checks.values())),
+        "pdf": {
+            "path": str(main_pdf.relative_to(REPO_ROOT)),
+            "archived_path": str(ARCHIVED_PDF.relative_to(REPO_ROOT)),
+            "sha256": _sha256(main_pdf),
+            "pages": len(reader.pages),
+            "title": title,
+            "author": author,
+        },
+        "rendered_pages": render_records,
+        "pytest_passed": pytest_passed,
+        "registered_scale": {
+            "physical_matrices": physical_v1["sample_count"],
+            "physical_test_matrices": 4_000,
+            "structured_momenta": 24,
+            "structured_orbits": 12,
+            "geometric_interpolation_matrices": 7 * 4_000,
+            "spectral_interpolation_matrices": 8 * 4_000,
+            "haar_matrices": covariance_v1["haar_samples"],
+            "root_matrices": sum(
+                case["samples"] for case in scaling_v1["cases"]
+            ),
+            "maximum_rank": scaling_v1["cases"][-1]["D"],
+            "bootstrap_replicates": (
+                statistics_json["bootstrap_replicates"]
+            ),
+        },
+        "supported_conclusion": {
+            "energy_connected_sff": 0.0,
+            "physical_jacobi_tau_onset": (
+                outcomes["physical_tau_compatibility_onset"]
+            ),
+            "geometric_local_onset": (
+                outcomes["first_g_with_haar_gap_ratio_interval"]
+            ),
+            "geometric_ramp_onset": (
+                outcomes["first_g_with_registered_jacobi_window"]
+            ),
+            "number_variance_compatibility_extent": (
+                outcomes["number_variance_compatibility_extent"]
+            ),
+            "D800_connected_plateau": 0.7,
+        },
+    }
+    output_json.parent.mkdir(parents=True, exist_ok=True)
+    output_json.write_text(
+        json.dumps(audit, indent=2) + "\n",
+        encoding="utf-8",
+    )
+    if not audit["all_checks_pass"]:
+        failed = [key for key, value in checks.items() if not value]
+        raise RuntimeError(
+            f"spectral-silence delivery audit failed: {failed}"
+        )
+    return audit
+
+
+def main() -> None:
+    parser = argparse.ArgumentParser()
+    parser.add_argument(
+        "--output-json",
+        type=Path,
+        default=OUTPUT / "spectral_silence_delivery_audit_v2.json",
+    )
+    args = parser.parse_args()
+    audit = run(args.output_json)
+    print(
+        json.dumps(
+            {
+                "all_checks_pass": audit["all_checks_pass"],
+                "pdf": audit["pdf"],
+                "pytest_passed": audit["pytest_passed"],
+                "registered_scale": audit["registered_scale"],
+            },
+            indent=2,
+        )
+    )
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/verify_topological_holonomy_v3.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/verify_topological_holonomy_v3.py
new file mode 100644
index 000000000..ca665873d
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/verify_topological_holonomy_v3.py
@@ -0,0 +1,272 @@
+#!/usr/bin/env python3
+"""Fail-closed audit for fixed-Chern Wilson-holonomy artifacts."""
+
+from __future__ import annotations
+
+import hashlib
+import json
+from datetime import datetime, timezone
+from pathlib import Path
+from typing import Any
+
+import numpy as np
+
+from run_topological_holonomy_v3 import (
+    MESH_ALIAS_AUDIT_JSON,
+    MESH_ALIAS_AUDIT_NPZ,
+    OUTPUT_JSON,
+    OUTPUT_NPZ,
+    REGISTERED_CONVERGENCE_MESH,
+    REGISTERED_CUE_SAMPLES,
+    REGISTERED_G,
+    REGISTERED_GENERATOR_SEEDS,
+    REGISTERED_PRIMARY_MESH,
+    REGISTERED_SIZES,
+    SCRIPT_ROOT,
+    select_topology_branch,
+)
+
+
+OUTPUT_ROOT = SCRIPT_ROOT / "output"
+FIGURE_MANIFEST = OUTPUT_ROOT / "figure_manifest_v3.json"
+FIGURE_PDF = OUTPUT_ROOT / "figure_7_topological_holonomy_v3.pdf"
+FIGURE_PNG = OUTPUT_ROOT / "figure_7_topological_holonomy_v3.png"
+AUDIT_JSON = OUTPUT_ROOT / "topological_holonomy_delivery_audit_v3.json"
+
+
+def _sha256(path: Path) -> str:
+    return hashlib.sha256(path.read_bytes()).hexdigest()
+
+
+def audit_topology_payload(
+    payload: dict[str, Any],
+) -> dict[str, bool]:
+    """Recompute the registered topology gates from serialized metrics."""
+
+    configuration = payload["configuration"]
+    sizes = payload["sizes"]
+    observed_sizes = [
+        (size["N"], size["n_flux"], size["rank"]) for size in sizes
+    ]
+    expected_chern = {3: 6, 4: 10}
+    checks = {
+        "registered_sizes": observed_sizes == list(REGISTERED_SIZES),
+        "registered_meshes": (
+            configuration["primary_mesh"] == REGISTERED_PRIMARY_MESH
+            and configuration["convergence_mesh"]
+            == REGISTERED_CONVERGENCE_MESH
+        ),
+        "registered_g_grid": (
+            configuration["g_values"] == list(REGISTERED_G)
+        ),
+        "registered_generator_seeds": (
+            configuration["generator_seeds"]
+            == list(REGISTERED_GENERATOR_SEEDS)
+        ),
+        "cue_reference_count": (
+            configuration["cue_samples"] == REGISTERED_CUE_SAMPLES
+        ),
+        "runner_checks": all(payload["checks"].values()),
+        "branch_recomputed": (
+            payload["result_branch"] == select_topology_branch(payload)
+        ),
+        "supported_branch": (
+            payload["result_branch"] == "fixed_chern_deformed_holonomy"
+        ),
+        "chern_fixed": all(
+            abs(size["base_chern_integer"] - expected_chern[size["N"]])
+            < 1e-12
+            and max(size["primary_chern_range"])
+            - min(size["primary_chern_range"])
+            < 1e-8
+            and max(size["convergence_endpoint_chern_range"])
+            - min(size["convergence_endpoint_chern_range"])
+            < 1e-8
+            for size in sizes
+        ),
+        "mesh_agreement": all(
+            abs(
+                size["base_chern_primary"]
+                - size["base_chern_convergence"]
+            )
+            < 1e-8
+            for size in sizes
+        ),
+        "determinant_trace_agreement": all(
+            size["maximum_determinant_trace_difference"] < 1e-8
+            for size in sizes
+        ),
+        "positive_gap_branch_overlap": all(
+            size["minimum_external_gap"] > 0.0
+            and size["minimum_branch_margin"] > 0.0
+            and size["minimum_overlap_singular_value"] > 5e-2
+            for size in sizes
+        ),
+        "exact_isospectral_construction": all(
+            size["maximum_energy_spectrum_error"] < 1e-13
+            and size["maximum_gap_error"] < 1e-13
+            and size["isospectrality_mode"]
+            == (
+                "exact_coordinate_identity_under_periodic_ambient_"
+                "conjugation"
+            )
+            for size in sizes
+        ),
+        "gauge_invariance": (
+            payload["random_gauge_errors"]["chern_error"] < 1e-9
+            and payload["random_gauge_errors"]["wilson_phase_error"]
+            < 1e-8
+        ),
+        "deformed_but_non_cue": all(
+            size["holonomy_change_significant"]
+            and not size["cue_compatible_at_largest_g"]
+            for size in sizes
+        ),
+    }
+    if not all(checks.values()):
+        raise AssertionError(f"topology payload audit failed: {checks}")
+    return checks
+
+
+def _array_checks(payload: dict[str, Any]) -> dict[str, bool]:
+    configuration = payload["configuration"]
+    seeds = len(configuration["generator_seeds"])
+    g_count = len(configuration["g_values"])
+    checks: dict[str, bool] = {}
+    with np.load(OUTPUT_NPZ, allow_pickle=False) as arrays:
+        checks["result_npz_hash"] = (
+            payload["npz_sha256"] == _sha256(OUTPUT_NPZ)
+        )
+        for index, size in enumerate(payload["sizes"]):
+            rank = size["rank"]
+            primary_mesh = size["primary_mesh"]
+            convergence_mesh = size["convergence_mesh"]
+            checks[f"size_{index}_seed_shapes"] = (
+                arrays[f"size_{index}_gap_mean"].shape
+                == (seeds, g_count)
+                and arrays[f"size_{index}_form_mean"].shape
+                == (seeds, g_count, rank)
+            )
+            checks[f"size_{index}_loop_shapes"] = (
+                arrays[f"size_{index}_gap_loops"].shape
+                == (seeds, g_count, 2 * primary_mesh)
+                and arrays[f"size_{index}_form_loops"].shape
+                == (seeds, g_count, 2 * primary_mesh, rank)
+                and arrays[f"size_{index}_endpoint_gap_loops"].shape
+                == (seeds, 2 * convergence_mesh)
+            )
+            checks[f"size_{index}_commuting_control"] = (
+                arrays[f"size_{index}_commuting_gap"].shape
+                == (g_count,)
+                and arrays[f"size_{index}_commuting_form"].shape
+                == (g_count, rank)
+            )
+            checks[f"size_{index}_cue_count"] = (
+                arrays[f"size_{index}_cue_gap"].shape[0]
+                == REGISTERED_CUE_SAMPLES
+                and arrays[f"size_{index}_cue_form"].shape
+                == (REGISTERED_CUE_SAMPLES, rank)
+            )
+    return checks
+
+
+def run_audit() -> dict[str, Any]:
+    payload = json.loads(OUTPUT_JSON.read_text(encoding="utf-8"))
+    checks = audit_topology_payload(payload)
+    checks.update(_array_checks(payload))
+    alias = json.loads(MESH_ALIAS_AUDIT_JSON.read_text(encoding="utf-8"))
+    checks.update(
+        {
+            "alias_artifacts_present": (
+                MESH_ALIAS_AUDIT_JSON.exists()
+                and MESH_ALIAS_AUDIT_NPZ.exists()
+            ),
+            "alias_failure_retained": (
+                alias["result_branch"] == "topology_mesh_unresolved"
+                and alias["checks"]["mesh_chern_integer"] is False
+                and alias["checks"]["branch_margin"] is False
+                and min(alias["sizes"][1]["primary_chern_range"]) < 9.0
+            ),
+            "alias_hashes": (
+                payload["mesh_alias_audit"]["json_sha256"]
+                == _sha256(MESH_ALIAS_AUDIT_JSON)
+                and payload["mesh_alias_audit"]["npz_sha256"]
+                == _sha256(MESH_ALIAS_AUDIT_NPZ)
+            ),
+        }
+    )
+    for relative, expected_hash in payload["checkpoint_hashes"].items():
+        checks[f"checkpoint:{relative}"] = (
+            _sha256(SCRIPT_ROOT / relative) == expected_hash
+        )
+    manifest = json.loads(FIGURE_MANIFEST.read_text(encoding="utf-8"))
+    figure = manifest["figure_7_topological_holonomy_v3"]
+    checks.update(
+        {
+            "figure_source_json_hash": (
+                figure["source_json_sha256"] == _sha256(OUTPUT_JSON)
+            ),
+            "figure_source_npz_hash": (
+                figure["source_npz_sha256"] == _sha256(OUTPUT_NPZ)
+            ),
+            "figure_pdf_hash": (
+                figure["pdf_sha256"] == _sha256(FIGURE_PDF)
+            ),
+            "figure_png_hash": (
+                figure["png_sha256"] == _sha256(FIGURE_PNG)
+            ),
+        }
+    )
+    result = {
+        "version": "v3",
+        "generated_utc": datetime.now(timezone.utc).isoformat(),
+        "passed": all(checks.values()),
+        "checks": checks,
+        "result_branch": payload["result_branch"],
+        "registered_sizes": [
+            [size["N"], size["n_flux"], size["rank"]]
+            for size in payload["sizes"]
+        ],
+        "registered_meshes": [
+            configuration_mesh
+            for configuration_mesh in (
+                payload["configuration"]["primary_mesh"],
+                payload["configuration"]["convergence_mesh"],
+            )
+        ],
+        "result_sha256": _sha256(OUTPUT_JSON),
+        "arrays_sha256": _sha256(OUTPUT_NPZ),
+        "alias_audit_sha256": _sha256(MESH_ALIAS_AUDIT_JSON),
+        "figure": {
+            "pdf": str(FIGURE_PDF.relative_to(SCRIPT_ROOT)),
+            "pdf_sha256": _sha256(FIGURE_PDF),
+            "png": str(FIGURE_PNG.relative_to(SCRIPT_ROOT)),
+            "png_sha256": _sha256(FIGURE_PNG),
+        },
+    }
+    if not result["passed"]:
+        raise RuntimeError(f"topology delivery audit failed: {checks}")
+    temporary = AUDIT_JSON.with_suffix(".json.tmp")
+    temporary.write_text(
+        json.dumps(result, indent=2, sort_keys=True),
+        encoding="utf-8",
+    )
+    temporary.replace(AUDIT_JSON)
+    return result
+
+
+def main() -> None:
+    result = run_audit()
+    print(json.dumps(
+        {
+            "passed": result["passed"],
+            "checks": result["checks"],
+            "result_branch": result["result_branch"],
+        },
+        indent=2,
+        sort_keys=True,
+    ))
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/task_05_dashboard.md b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/task_05_dashboard.md
new file mode 100644
index 000000000..a1929430f
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/task_05_dashboard.md
@@ -0,0 +1,407 @@
+# task_05: Spectral Silence and Geometric Chaos
+Status: 🟡 Ongoing
+Last Updated: 2026-07-30 (v35) [Codex]
+
+Provenance: `docs/plans/2026-07-28-large-scale-geometric-eth-companion-design.md`
+Primary execution zone: `01_task_folder/task_05/script/`
+Article target: `overleaf_sync/geometric_eth_large_scale/`
+Main outputs: `script/output/spectral_silence_v2.{json,npz}`, `script/output/matrix_element_geometric_eth_v3.{json,npz}`, `script/output/topological_holonomy_v3.{json,npz}`, `script/output/geometric_eth_topology_delivery_audit_v3.json`, plus the immutable v1/v2 artifacts
+Article: `script/output/spectral_silence_and_geometric_chaos_v3.pdf`
+Verdict: Exact degeneracy turns projector geometry into the operative chaos signal. The v3 extension resolves a shrinking gauge-invariant connected four-channel component (`deformed_geometric_eth`) and a fixed-Chern, exactly isospectral twist bundle with tunably deformed Wilson holonomy (`fixed_chern_deformed_holonomy`). Both results, their analytic derivations, seven figures, and forward scaling program are integrated into an audited 17-page article and a tiered public release.
+
+## Objective
+
+Create an independent large-scale numerical companion, *From Local Repulsion to Global Geometry: Large-Scale Tests of Geometric ETH*. Expand the physical ensemble to 20000 tangent pairs, extend exact root-response calculations through \(D=800\) across the Jacobi boundary-atom transition, replace rough histograms and sparse bars with uncertainty-aware publication graphics, and deliver a separately audited PDF without importing task-04 executables or artifacts.
+
+**Scope addendum (2026-07-28) [Human/Codex]:** Expand the same article around *Spectral Silence and Geometric Chaos in an Exactly Degenerate Topological Manifold*: contrast the identically trivial energy SFF with the nontrivial curvature SFF, add a same-parent structured tangent control, vary intrafiber spectral and projector-geometric chaos independently, derive the finite-Jacobi/atom form factor analytically, and retain explicit non-SUSY and nondynamical claim boundaries.
+
+**Scope addendum (2026-07-28) [Human/Codex]:** Extend the delivered article with both approved post-delivery programs: a gauge-invariant four-channel Wick-factorization test on a genuine fixed-two-quasihole particle-number sequence, and a closed twist-torus calculation that separates fixed \(U(1)\) Chern topology from tunable \(SU(D)\) Wilson-loop holonomy.
+
+## Version Log
+
+**v1 (2026-07-28) [Codex]:** Created task_05 from the human's request for substantially larger calculations, improved figures, and a separate PDF. Froze the independent-workspace rule, physical \(20000\)-pair train/validation/test design, fixed-eigenvalue-budget rank sequence through \(D=800\), exact atom handling, hierarchical inference, five-figure visual contract, manuscript architecture, and completion gates.
+
+**v2 (2026-07-28) [Codex]:** Saved the eight-task implementation plan `docs/plans/2026-07-28-large-scale-geometric-eth-companion-implementation-plan.md`. It specifies task-local module interfaces, test-driven physical/covariance/scaling runners, exact atom labels, matrix-level statistical estimators, five figure contracts, a separate REVTeX source tree, and a fail-closed one-command delivery audit. Execution is inline because unrequested subagents are prohibited.
+
+**v3 (2026-07-28) [Codex]:** Built the independent `lgeth` numerical package. Task 05 now owns its combinatorics, Kapit--Mueller lattice, channel, Jacobi, Grassmannian, root-operator, and statistics algorithms; an AST import audit forbids task-04 dependencies. Four focused tests verify \(D(3,20)=800\), \(M(3,20)=680\), \(120\) exact atoms on each boundary when \(r=800,M=680\), algebraic atom removal, and \(YY^\dagger=I\).
+
+**v4 (2026-07-28) [Codex]:** Generated the preregistered \(20000\)-pair Kapit--Mueller physical ensemble in eight independently seeded blocks and 104.33 s. The fixed split is \(12000/4000/4000\); every sample has active and curvature rank \(50\), the parent kernel width is \(5.78\times10^{-16}\), the external gap is \(0.106672\), and no exact \(\pm1\) atoms occur. The reduced deterministic runner test passes.
+
+**v5 (2026-07-28) [Codex]:** Fit the covariance model on \(1024\) training row spaces, selected the eigenvalue floor \(0.05\) from five candidates using validation data only, and generated \(10000\) Haar plus \(10000\) covariance-deformed spectra. On the untouched \(4000\)-matrix test set, the deformed model reduces density \(L^1\) error from \(0.290988\) to \(0.123720\) (\(57.48\%\)) while matching the mean gap ratio within \(6.06\times10^{-4}\). The registered outcome is `leading_covariance_capture`; six focused tests pass.
+
+**v6 (2026-07-28) [Codex]:** Completed all seven root-response cases with no sample-count reduction: \(2000,2000,2000,1000,1000,500,250\) matrices at \(D=16,50,112,210,352,546,800\). Interior density error falls \(0.43375\to0.05226\), participation rises \(0.77394\to0.97000\), and the exact atom transition produces \(6+6\) atoms at \(D=546\) and \(120+120\) at \(D=800\). All checkpoint files are resumable, all six scaling gates pass, and the nine accumulated focused tests pass.
+
+**v7 (2026-07-28) [Codex]:** Added \(10000\)-replicate seed-block/matrix-level simultaneous bands for density, \(P(r)\), number variance, rigidity, form factor, and moments through eighth order. Covariance improvement holds at every registered KDE bandwidth; local ratios are stable under bulk-window, unfolding, and binning choices. Finite-size fits favor a free density exponent \(p=0.5929\), \(D^{-1}\) for the gap-ratio difference, and \(D^{-1/2}\) for participation deficit, but are explicitly treated as finite-range evidence rather than a thermodynamic theorem. All six inference gates and three analytic statistics tests pass.
+
+**v8 (2026-07-28) [Codex]:** Generated and visually audited five \(7.0\)-inch vector figures with \(2100\)-pixel, \(300\)-dpi previews: physical density/residuals/moments; the local-to-global hierarchy; continuous-spectrum/atom crossover; confidence-aware size fits; and the covariance mechanism. Removed two data-label collisions after original-resolution inspection. The figure manifest hashes all seven numerical inputs and every output, and generated LaTeX macros/tables carry the exact registered values.
+
+**v9 (2026-07-28) [Codex]:** Wrote and compiled the independent REVTeX PRB-style article *From Local Repulsion to Global Geometry: Large-Scale Tests of Geometric ETH*. The 10-page PDF has correct authors and affiliations, five vector figures, an analytic signature-compression/Jacobi derivation, the exact \(r-M\) atom theorem, a covariance-deformed ETH ansatz, held-out physical results, finite-size limitations, and a numerical appendix. The final log has no undefined citations/references, overfull boxes, or stuck floats; PDF SHA-256 is `004a8615aa293e121b3cc20b5b2b9f80b19e10adbcecdafa91913b7feae1781f`.
+
+**v10 (2026-07-28) [Codex]:** Clarified the random-matrix/ETH claim boundary. The project already contains exact finite-rank Haar--Jacobi theory, independent Wishart--Jacobi and covariance-deformed ensembles, and local-to-long-range spectral tests. Its ETH content is presently an operational covariance-deformed Geometric-ETH ansatz, not the conventional energy-resolved ETH matrix-element law or a thermodynamic theorem. The next priority is a gauge-invariant tangent-channel Wick-factorization test on a genuine many-body sequence, followed by a controlled comparison with intramultiplet spectral chaos and dynamics.
+
+**v11 (2026-07-28) [Codex]:** Completed the fail-closed delivery workflow. The one-command runner regenerated \(20000\) physical matrices, \(10000\) Haar matrices, \(10000\) covariance-deformed matrices, \(8750\) rank-sequence matrices through \(D=800\), \(10000\)-replicate matrix-level confidence bands, all five vector figures, and the independent article. Twenty-nine bibliography records resolve online, 14 tests and all 27 delivery gates pass, and all 10 final PDF pages were rendered and visually inspected. The synchronized manuscript/archive SHA-256 is `aae68de7569aae83c7ff500718ab0e3635595f050f5b7afc0d60a0e63db55417`.
+
+**v12 (2026-07-28) [Codex]:** Repositioned the proposed SFF expansion after a literature and falsification audit. The new recommended spine is “spectral silence versus geometric ramp,” but only with a same-rank/same-gap structured curvature control and independent \(PHP\) versus \(P(\partial H)Q\) interventions. Registered an A+B target: causal channel separation plus a finite-\(D\) Jacobi form-factor derivation, including exact boundary-atom terms. Saved the clickable research memo at `docs/2026-07-28-curvature-sff-research-positioning.md`; no implementation is approved yet.
+
+**v13 (2026-07-28) [Codex]:** The human approved the recommended A+B expansion with “做吧.” Saved the frozen design at `docs/plans/2026-07-28-spectral-silence-geometric-ramp-design.md`. The primary structured control uses momentum-resolved cosine/sine tangent quadratures on the same Kapit--Mueller zero-mode projector; an exploratory audit finds full active rank \(50\) but only \(10\) distinct curvature eigenvalues. The approved analytic target is the unfolded finite-\(D\) Jacobi determinantal-kernel SFF plus the exact \(K_{c}^{\rm full}=(k/D)K_{c}^{\rm cont}\) boundary-atom theorem.
+
+**v14 (2026-07-28) [Codex]:** Saved the eight-task test-driven implementation plan at `docs/plans/2026-07-28-spectral-silence-geometric-ramp-implementation-plan.md`. It freezes task-local v2 interfaces, registered control grids and sample counts, finite-Jacobi quadrature tests, simultaneous-band crossover rules, five argument-ordered figures, the retitled REVTeX article, and a fail-closed one-command delivery audit. Inline execution begins with the exact form-factor module.
+
+**v15 (2026-07-28) [Codex]:** Implemented the exact form-factor core. A single \(1/D\)-normalized decomposition now returns raw, disconnected, and connected parts; the exactly degenerate energy band gives \(K_{E,\mathrm{raw}}=D\) and \(K_{E,c}=0\) to machine precision. The finite complex-Jacobi connected SFF is evaluated from the unfolded Gauss--Jacobi determinantal kernel, agrees with an independent rank-\(16\) Monte Carlo curve within the preregistered tolerance, and is stable at rank \(50\) between quadrature orders 384 and 512. The \(D>M\) theorem \(K_{c}^{\rm full}=(k/D)K_{c}^{\rm cont}\) and raw atom decomposition are executable and tested; 15 focused/regression tests pass.
+
+**v16 (2026-07-28) [Codex]:** Implemented the two causal controls. All 24 nonzero \(5\times5\) Fourier tangent quadratures preserve the physical active rank \(D=50\) but have at most 10 distinct metric-normalized curvature eigenvalues, giving a full-rank structured negative control. The independent fixed-\(P\) interpolation moves the mean energy gap ratio from \(0.392116\) to \(0.598531\), while the numerically reconstructed target projector changes by at most \(1.13\times10^{-14}\) and the repeated curvature spectrum is invariant exactly. Thirteen focused/control regressions pass.
+
+**v17 (2026-07-28) [Codex]:** Generated the registered `spectral_silence_v2` artifact in 113.03 s: 24 exact Fourier controls in 12 momentum-inversion orbits, \(7\times4000\) positive-\(g\) geometric-scrambling spectra, \(8\times4000\) fixed-projector energy spectra, the \(4000\)-matrix physical test set, \(10000\) independent Haar spectra, and form factors for all seven rank cases. At \(\tau=0.5\), \(K_{F,c}=4.476\) for the structured control, \(0.502\) for the physical ensemble, and \(0.501\) for the finite-\(D\) Jacobi kernel. The fixed-\(P\) energy ratio moves \(0.385645\to0.598677\); all ten production gates pass.
+
+**v18 (2026-07-28) [Codex]:** Completed \(10000\)-replicate simultaneous-band inference. The physical curvature SFF is compatible with the exact finite-\(D\) Jacobi curve throughout the registered \(\tau\in[0.25,1.5]\) window, whereas the structured control is decisively rejected. Along geometric scrambling, the gap-ratio interval first overlaps Haar at \(g=0.20\), but a registered Jacobi SFF window first appears at \(g=0.40\). Number-variance compatibility ends at \(L=1\); at \(L=8\) the physical excess is \(0.12582\) with simultaneous interval \([0.11428,0.13736]\). All nine inference gates pass.
+
+**v19 (2026-07-28) [Codex]:** Generated and visually audited the five-figure v2 package: spectral silence versus geometric ramp; the structured/physical/Jacobi falsification triangle; independent \(PHP\) and \(P(\partial H)Q\) channels; the controlled geometric correlation hierarchy; and the exact Jacobi boundary-atom form factor. Every figure is a 7-inch vector PDF with a 2100-pixel/300-dpi preview, synchronized hashes, generated TeX inputs, and exact scientific annotations. Both figure tests pass after replacing a nonmonotonic onset plot by the monotone RMS SFF residual.
+
+**v20 (2026-07-28) [Codex]:** Rewrote the article as *Spectral Silence and Geometric Chaos in an Exactly Degenerate Topological Manifold*. The 12-page REVTeX manuscript now begins from the exact \(K_{E,\mathrm{raw}}=D,\ K_{E,c}=0\) theorem, derives the metric-normalized signature compression and unfolded finite-Jacobi determinantal-kernel SFF, proves \(K_{J,c}^{\mathrm{full}}=(k/D)K_{J,c}^{(k)}\) with exact boundary atoms, and organizes all five v2 figures as falsification and causal controls. Added verified AGP, Hilbert-space-geometry, and non-energy-SFF references; clean compilation has no undefined citations/references, overfull boxes, or stuck floats, and all 12 pages pass original-render visual inspection. A new fail-closed audit and delivery test pass on the current PDF.
+
+**v21 (2026-07-28) [Codex]:** Executed the complete v2 one-command delivery at full registered scale: regenerated 24 Fourier controls, \(7\times4000\) geometric-interpolation matrices, \(8\times4000\) fixed-projector spectral matrices, all seven rank form factors, \(10000\)-replicate simultaneous bands, five vector figures, and the 12-page PDF. Both immutable v1 and live v2 delivery tests now coexist; 34/34 tests and 37/37 final gates pass. The final manuscript/archive SHA-256 is `5d51ad4997a8cc95fa60fdafa02ef5aa13ad86cd31f10764b61a8f8903c2895c`, and the newly rendered pages are pixel-identical to the manually inspected audit set.
+
+**v22 (2026-07-28) [Codex]:** Triaged the post-delivery research program. The recommended next extension is no longer another curvature-spectrum statistic, but a covariance-whitened, gauge-invariant four-channel Wick-factorization test on a genuine many-body sequence. A closed two-cycle topology/holonomy calculation is the second priority, and a lifted-band dynamical comparison is retained only as external validation. This is a discussion-stage recommendation; no new implementation or numerical claim is approved.
+
+**v23 (2026-07-28) [Codex]:** The human approved both post-delivery programs. Froze the joint design at `docs/plans/2026-07-28-matrix-element-geometric-eth-and-topology-design.md`: the Wick test uses fixed local operators rather than tautological Gaussian tangent combinations, the true many-body sequence is \(N=3,4,5\) at \(n_\phi=2N+2\), and the topology test uses a smooth periodic quasi-local ambient unitary orbit over the twist torus so exact degeneracy, the full energy spectrum, the gap, and \(C_1\) remain fixed while traceless Wilson holonomy can change. Preliminary feasibility checks validate the three registered kernel ranks and open gaps; no production result is yet claimed.
+
+**v24 (2026-07-28) [Codex]:** Saved three test-driven implementation plans: `docs/plans/2026-07-28-matrix-element-geometric-eth-implementation-plan.md`, `docs/plans/2026-07-28-topological-holonomy-implementation-plan.md`, and `docs/plans/2026-07-28-geometric-eth-topology-article-integration-plan.md`. They define task-local module interfaces, exact sequence and mesh gates, covariance-matched finite-size references, isospectral topology controls, seven-figure manuscript integration, and fail-closed delivery. Execution is inline because unrequested subagents are prohibited.
+
+**v25 (2026-07-28) [Codex]:** Completed the registered matrix-element production calculation on the genuine fixed-two-quasihole sequence \((N,n_\phi,D)=(3,8,16),(4,10,25),(5,12,36)\). All exact-kernel, open-gap, resolvent, support, gauge, and reference gates pass. The physical median \(R_4\) decreases \(0.37093\to0.24715\to0.20906\), but remains above the covariance-matched Gaussian medians \(0.21708\to0.14638\to0.12723\); the non-Gaussian excess decreases \(0.15385\to0.10078\to0.08183\). The registered branch is `deformed_geometric_eth`, not finite-size Wick compatibility.
+
+**v26 (2026-07-28) [Codex]:** Generated and visually audited `figure_6_wick_factorization_v3` as a 7-inch vector PDF with a 2100-pixel preview. The four-panel figure exposes the exact many-body/gap sequence, finite-size Gaussian reference bands, physical and Fourier four-channel residuals, shrinking non-Gaussian excess, and covariance effective dimension. The independent matrix-element delivery audit passes all 18 scientific, provenance, isolation, reference-count, checkpoint, and figure-hash gates.
+
+**v27 (2026-07-29) [Codex]:** Completed the closed-twist-torus Chern/Wilson production calculation for \((N,n_\phi,D)=(3,8,16),(4,10,25)\). A retained \(12\times12\) audit exposed one \(N=4,g=1\) plaquette-phase alias; upgrading the accepted convergence pair to \(16\times16\) and \(20\times20\) restores \(C_1=6,10\) for every one of eight noncommuting seeds, all five \(g\) values, and the commuting control. All ten topology, gap, branch, overlap, determinant/trace, gauge, and isospectral gates pass. Wilson gap ratios change significantly under the periodic ambient conjugation but remain far below CUE, selecting `fixed_chern_deformed_holonomy`.
+
+**v28 (2026-07-29) [Codex]:** Generated and visually audited `figure_7_topological_holonomy_v3` as a 7-inch vector PDF with a 2100-pixel preview. Its four panels show fixed \(C_1\) and gap, fixed determinant winding with deformed local spectral flow, significant Wilson gap-ratio changes that remain outside CUE, and a structured Wilson SFF. The independent topology delivery audit preserves the coarse-mesh failure and passes every production, per-loop shape, checkpoint-hash, alias, figure, branch-recomputation, and negative-corruption gate; 21 focused tests pass.
+
+**v29 (2026-07-29) [Codex]:** Integrated the matrix-element and topology results into the REVTeX article, including the gauge-covariant four-channel tensor, separable complex-Gaussian Wick law, Gram-spectrum reduction, periodic bundle-isomorphism proof for fixed \(C_1\), and connection-shift explanation for changing Wilson holonomy. The one-command v3 build now synchronizes Figures 6/7, validates 35 references, compiles and archives a clean 17-page PDF, passes all 24 delivery gates and 89 task-local tests, and survives original-resolution inspection of all pages. A fixed source-date epoch makes Figures 6/7 and the article byte-reproducible across consecutive clean builds; the final PDF SHA-256 is `68f565e7152d910e78ffb9c42e17e753f497fde1849dda5c4be8a08c5e50c985`.
+
+**v30 (2026-07-30) [Codex]:** Designed the public Task 05 release around the innovation ladder from spectral silence to curvature statistics, gauge-invariant channel memory, and fixed-Chern holonomy. Added the public-release design and implementation plans, a reviewer-first artifact map, and tiered compact/full reproduction paths.
+
+**v31 (2026-07-30) [Codex]:** Added the machine-readable release contract, quick and full runners, compact-checkout support, external-artifact provenance, citation metadata, and release tests. The manifest registers 14 compact artifacts, seven figures, 25 production records, exact result branches, and executable verification commands.
+
+**v32 (2026-07-30) [Codex]:** Reframed the repository, Task 05 entry point, article, release notes, and technical report around the condensed-matter advance and the four new algorithms. Added the challenge draft, PR body, reviewer comment with `@OkongOyangO`, and public-release checklist. Figure 6 now presents the measured quantity directly as connected channel memory.
+
+**v33 (2026-07-30) [Codex]:** Completed the PR-ready delivery audit. The quick path passes 17 release checks and 38 focused tests; the full compact suite reports 86 passing tests plus six manifest-activated production tests; the article audit passes 25/25 gates across 17 pages and seven synchronized figures. The final PDF SHA-256 is `a75377f76acd78eb3354e186a57933abdf11abbbe5e9a8abd43482ca8c4e05ad`. Task 05 remains 🟡 Ongoing for Issue-linked review and PR discussion.
+
+**v34 (2026-07-30) [Codex]:** Reconciled the public landing page, citation metadata, and PR body with the repository's GNU GPL v3.0 license, then revalidated the quick release path before the final remote push.
+
+**v35 (2026-07-30) [Codex]:** Linked the release to `QuantumBFS/quantum.harness#276` and sharpened the PR's direct answer: non-Abelian projector geometry over coupling space is the chaos probe that remains operative inside an exactly degenerate eigenspace. Synchronized the PR body, collaborator review comment, and public checklist for draft-PR submission.
+
+## Canvas
+
+### Central numerical question
+
+When the active rank and Monte Carlo resolution grow, do local correlations, smooth density, channel covariance, and higher Grassmannian cumulants approach the Jacobi law at the same scale?
+
+The new paper tests a hierarchy rather than a single yes/no random-matrix gate:
+
+$$\text{local repulsion}\ \longrightarrow\ \text{global density}\ \longrightarrow\ \text{higher Grassmannian cumulants}.$$
+
+The \(D=546\) and \(D=800\) cases additionally cross the exact \(r=M\) boundary and expose forced \(\pm1\) atoms. This converts a previously rough finite-size extension into a qualitatively new geometric regime.
+
+### Independent-core checkpoint
+
+The executable namespace is now fully task-local. The first completion gate passes with `4 passed`: no task-05 Python source imports `task_04` or `gaccess`, the registered largest root space has \((D,M)=(800,680)\), the Jacobi intersection theorem fixes \(120\) eigenvalues at each of \(\lambda=\pm1\), and the normalized-curvature rows satisfy the numerical isometry identity.
+
+### Physical high-statistics checkpoint
+
+The physical anchor is now \((N,n,D,M)=(3,10,50,170)\), with one million normalized curvature eigenvalues. All \(20000\) tangent pairs are retained together with the tangent coefficients and eight seed-block labels. The train, validation, and test sets are disjoint, so covariance learning, hyperparameter choice, and the final density comparison cannot leak into one another.
+
+### Held-out Geometric-ETH checkpoint
+
+The physical row spaces are manifestly non-Haar: their mean-projector relative anisotropy is \(0.86743\), coordinate participation is \(0.62494\), mean frame overlap is \(12.8384\) versus the exact Haar value \(7.35294\), and the entry fourth ratio is \(3.32657\). Nevertheless, local eigenvalue repulsion is already Jacobi-like:
+
+$$\langle r\rangle_{\rm phys}=0.599806,\qquad \langle r\rangle_{\rm Haar}=0.599395,\qquad \langle r\rangle_{\rm cov}=0.599200.$$
+
+The covariance deformation explains most of the global one-point discrepancy and closely tracks moments through eighth order. The supported statement is therefore a hierarchical Geometric ETH: local correlations forget microscopic tangent structure before the global density and Grassmannian frame statistics do.
+
+### Rank and boundary-atom checkpoint
+
+The increasing-rank result separates two effects. Before the capacity crossing, the continuous root-response spectrum approaches the exact Jacobi law:
+
+| \(D\) | \(M\) | matrices | \(\Delta\langle r\rangle\) | interior density \(L^1\) | participation |
+|---:|---:|---:|---:|---:|---:|
+| 16 | 80 | 2000 | 0.03023 | 0.43375 | 0.77394 |
+| 50 | 140 | 2000 | 0.00767 | 0.22916 | 0.85413 |
+| 112 | 216 | 2000 | 0.00403 | 0.14094 | 0.89476 |
+| 210 | 308 | 1000 | 0.00173 | 0.09624 | 0.92125 |
+| 352 | 416 | 1000 | 0.00290 | 0.06866 | 0.94097 |
+
+After \(D>M\), the intersection theorem forces \((D-M)\) eigenvalues at each boundary while the algebraically stripped interior remains random-matrix-like:
+
+| \(D\) | \(M\) | interior dimension | atoms at each boundary | \(\Delta\langle r\rangle_{\rm int}\) | interior density \(L^1\) |
+|---:|---:|---:|---:|---:|---:|
+| 546 | 540 | 534 | 6 | 0.00024 | 0.05149 |
+| 800 | 680 | 560 | 120 | 0.00423 | 0.05226 |
+
+Thus exact geometric modes at \(\lambda=\pm1\) do not destroy chaos in the complementary continuous sector. This coexistence is the companion paper's new structural result.
+
+### Matrix-level inference checkpoint
+
+Every visual confidence band is now based on independent matrices or the eight physical seed blocks. At the longest displayed scale \(L=8\), the number variance retains a measurable physical excess,
+
+$$\Sigma^2_{\rm phys}(8)=0.696,\qquad \Sigma^2_{\rm Haar}(8)=0.570,\qquad \Sigma^2_{\rm cov}(8)=0.570,$$
+
+while the connected form-factor ramp is already close at \(\tau=0.5\),
+
+$$K_{c,\rm phys}(0.5)=0.502,\qquad K_{c,\rm Haar}(0.5)=0.495,\qquad K_{c,\rm cov}(0.5)=0.502.$$
+
+This refines the hierarchy: short-range repulsion and the ramp are nearly universal, the one-point density is largely covariance controlled, and number variance at the largest available windows still resolves physical memory. Across bandwidths \(h=0.015\) to \(0.05\), the covariance model's density error remains \(0.105\)–\(0.119\), compared with \(0.280\)–\(0.290\) for Haar.
+
+### Principal result figure
+
+![Spectral silence and geometric ramp](script/output/figure_1_spectral_silence_v2.png)
+
+The v2 argument-ordered figure package is:
+
+- [Structured/physical/Jacobi falsification triangle](script/output/figure_2_falsification_triangle_v2.png)
+- [Independent spectral and geometric chaos channels](script/output/figure_3_independent_channels_v2.png)
+- [Controlled geometric correlation hierarchy](script/output/figure_4_geometric_hierarchy_v2.png)
+- [Finite-Jacobi and exact boundary-atom SFF](script/output/figure_5_jacobi_atoms_v2.png)
+
+The v1 high-statistics density, covariance, rigidity, and finite-size figures remain immutable provenance and will be retained as supporting material rather than discarded.
+
+### Independent article
+
+[Spectral Silence and Geometric Chaos in an Exactly Degenerate Topological Manifold](script/output/spectral_silence_and_geometric_chaos_v2.pdf)
+
+The article is deliberately positioned as a non-supersymmetric condensed-matter extension of Chen \emph{et al.}: exact degeneracy is supplied by a frustration-free fractional topological zero-mode manifold, not SUSY cohomology. The sharpened central result is that exact degeneracy removes the energy ramp while projector geometry retains a finite-Jacobi correlation ramp independent of intrafiber spectral chaos. For \(r>M\), exact \(\pm1\) atoms have multiplicity \(r-M\) per boundary and suppress the full connected plateau to \((2M-r)/r\), while the continuous complement remains Jacobi correlated.
+
+### Random-matrix and ETH claim boundary
+
+Random matrices have already been computed at three distinct levels:
+
+1. The exact null model is the finite-\((D,M)\) complex Jacobi ensemble obtained by Haar compression of the signature matrix \(J\).
+2. Independent Wishart--Jacobi samples provide \(10000\) Haar reference matrices at the physical anchor and matched references for every rank from \(D=16\) through \(D=800\).
+3. A second \(10000\)-matrix ensemble uses the training-only channel covariance and tests a covariance-deformed random-plane law on an untouched physical test set.
+
+The present Geometric-ETH statement is correspondingly specific. It decomposes the tangent-channel distribution into a deterministic two-point covariance envelope and a locally Gaussian random residual. The observed hierarchy is
+
+$$\text{Jacobi local repulsion}\ \prec\ \text{covariance-controlled one-point law}\ \prec\ \text{non-Haar higher cumulants}.$$
+
+This is not yet the conventional energy-resolved ETH ansatz, because all states in the target manifold are exactly degenerate and there is no internal frequency variable. It is also not yet a microscopic or thermodynamic Geometric-ETH theorem.
+
+### Next decisive extension
+
+The next calculation should test an invariant matrix-element form of Geometric ETH before adding more curvature histograms. For tangent channels
+
+$$X_\mu=P(\partial_\mu H)Q\,[Q(H-E_0)Q]^{-1},$$
+
+the target statement is that, after removing a smooth channel covariance, connected invariant cumulants approach their Gaussian Wick contractions along a many-body sequence:
+
+$$\mathcal{K}^{(4)}_{\mu\nu\rho\sigma}=\operatorname{Tr}(X_\mu X_\nu^\dagger X_\rho X_\sigma^\dagger)-\operatorname{Wick}_{\mu\nu\rho\sigma}\longrightarrow0.$$
+
+The implementation priority is:
+
+1. Derive the two- and four-channel invariant contractions, their finite-\((D,M)\) Gaussian predictions, and the expected scaling of the connected residual.
+2. Replace the fixed-\(N=3\) dilution sequence by a genuine many-body Laughlin/FCI sequence with increasing particle number, a fixed physical scaling prescription, an open external gap, and a growing exact multiplet.
+3. Measure covariance-whitened channel cumulants, multi-curvature correlators, quantum-metric statistics, and the joint metric--curvature law rather than only eigenvalue statistics of one curvature matrix.
+4. Add an independent intramultiplet perturbation \(PHP\) that crosses Poisson to GUE while leaving the full projector \(P\) fixed. This separates conventional spectral chaos from external geometric scrambling \(P(\partial_\mu H)Q\).
+5. Compare the resulting geometric crossover with projected-operator ETH, entanglement, fidelity susceptibility, and, where feasible, an OTOC or dynamical structure factor. Berry curvature is decisive only if it detects chaos in the exactly degenerate limit where the internal spectrum remains silent.
+
+The immediate paper-level target is therefore not “more RMT.” It is a falsifiable matrix-element Geometric-ETH law: two-point covariance sets the smooth envelope, Wick factorization controls the universal residual, and connected higher cumulants vanish with a script-derived finite-size exponent.
+
+### SFF expansion: revised positioning
+
+The curvature SFF is scientifically useful only if it survives the following objection: an arbitrary generic Hermitian matrix can display a ramp after unfolding. The revised design therefore does not treat the existing \(K_{F,c}(\tau)\) curve as a standalone chaos proof.
+
+For the exactly degenerate target energies \(E_a=E_0\),
+
+$$K_{E,\mathrm{raw}}(t)=D,\qquad K_{E,c}(t)=0,$$
+
+under the task's \(1/D\) normalization. This analytic spectral silence should be placed beside the nontrivial connected curvature ramp, while displaying raw and connected conventions for both objects so that the comparison is statistically fair.
+
+The decisive control is a three-way comparison at fixed rank, exact target bandwidth, external-gap condition, and topology:
+
+$$\text{structured tangent geometry}\ \longleftrightarrow\ \text{physical scrambled geometry}\ \longleftrightarrow\ \text{Haar--Jacobi}.$$
+
+The paper must then separate two independent mechanisms. An internal \(PHP\) intervention changes intramultiplet Poisson/GUE statistics at fixed projector \(P\), whereas an external \(P(\partial_\mu H)Q\) intervention changes the projector geometry while the target energy spectrum remains exactly degenerate. A \(2\times2\) quadrant figure—neither chaotic, spectral only, geometric only, both chaotic—would make Berry curvature's nonredundant role explicit.
+
+Three routes were compared:
+
+1. **A: spectral silence versus geometric ramp.** Best narrative and shortest causal test.
+2. **B: exact finite-\(D\) Jacobi SFF and boundary-atom decomposition.** Best immediate analytic upgrade, but insufficient by itself to establish physical meaning.
+3. **C: covariance-whitened matrix-element Geometric ETH and Wick factorization on a genuine many-body sequence.** Strongest ultimate theory, but most expensive and not required before repairing the main story.
+
+The recommended synthesis is A+B now, with the first invariant four-channel cumulant from C as a final or supplemental result. The proposed main figures are: (1) exact energy silence versus geometric ramp; (2) structured/physical/Jacobi falsification triangle; (3) independent spectral and geometric chaos axes; (4) confidence-defined geometric correlation scale; (5) exact full versus atom-stripped Jacobi SFF across \(D=M\); and optionally (6) covariance-whitened Wick-factorization residuals. The current spectral-rigidity panel should move to the supplement.
+
+The complete literature position, equations, figure contracts, acceptance gates, and overclaim boundaries are recorded in [the curvature-SFF research memo](../../docs/2026-07-28-curvature-sff-research-positioning.md). This remains a discussion-stage design pending human choice between Route A alone and the recommended A+B synthesis.
+
+The human subsequently approved the A+B synthesis. The implementation ground truth is now [the spectral-silence/geometric-ramp design](../../docs/plans/2026-07-28-spectral-silence-geometric-ramp-design.md). Existing v1 scripts and artifacts remain immutable provenance; all extension code and results will use v2 names.
+
+The structured control is now concrete rather than schematic. Its momentum quadratures are local site-potential operators evaluated through the same physical channel cache as the random-local ensemble. Because they remain full active rank but organize into only ten curvature eigenvalues, failure of RMT cannot be dismissed as an accessibility-rank artifact.
+
+The fixed-projector control separately establishes the algebraic mechanism: \(PHP\) can develop GUE energy correlations while the complete fiber projector and its curvature do not move. This control is effective rather than a microscopic local path and will be labeled as such in the manuscript.
+
+### Spectral-silence production checkpoint
+
+The primary v2 artifact contains three genuinely different objects rather than three relabelings of one random ensemble:
+
+1. the structured momentum-resolved curvature spectra, with exact magnetic-translation multiplets;
+2. the physical random-local-potential curvature spectra and their continuous \(g\)-interpolation from the structured endpoint;
+3. the independent finite-\(D\) Haar--Jacobi reference, including the exact boundary-atom normalization.
+
+At the headline Fourier scale,
+
+$$K_{F,c}^{\rm structured}(0.5)=4.476,\qquad K_{F,c}^{\rm physical}(0.5)=0.502,\qquad K_{J,c}^{(50,170)}(0.5)=0.501.$$
+
+The structured control therefore fails in the opposite direction from a weak finite-size deviation: its unresolved symmetry multiplets create a large coherent form-factor excess despite full active rank. Along the geometric-scrambling axis, the mean gap ratio is already \(0.577596\) at \(g=0.02\) and approaches \(0.600307\) at \(g=1\). Whether the SFF residual is statistically compatible with Jacobi over a registered non-plateau interval is deferred to the simultaneous-band analysis rather than inferred from these point values.
+
+The exact-parent checks remain unchanged throughout this axis:
+
+$$\operatorname{bandwidth}(PHP)=5.78\times10^{-16},\qquad \Delta_{\rm ext}=0.106672.$$
+
+The independent spectral axis gives
+
+$$\langle r\rangle_{\alpha=0}=0.385645,\qquad \langle r\rangle_{\alpha=1}=0.598677,$$
+
+with maximum reconstructed-projector distance \(1.15\times10^{-14}\) and zero repeated-curvature-spectrum error. Thus the two axes already realize the four logical quadrants required by the approved design; the next stage assigns confidence bands and registered crossover sets.
+
+### Registered correlation hierarchy
+
+The simultaneous-band analysis separates three correlation scales on the geometric-scrambling axis:
+
+$$g_{\rm local}=0.20<g_{\rm ramp}=0.40,$$
+
+where \(g_{\rm local}\) is the first coupling at which the mean adjacent-gap-ratio simultaneous interval overlaps the independent Haar interval, and \(g_{\rm ramp}\) is the first coupling with a nontrivial registered interval that remains compatible with the exact finite-\(D\) Jacobi form factor through \(\tau=1.5\). This ordering is not inferred from visual curve proximity; both endpoints are confidence-defined.
+
+At the final physical ensemble, the exact Jacobi compatibility onset lies at the lower registered boundary,
+
+$$\tau_{\rm geo}=0.25,\qquad 0.25\le\tau\le1.5,$$
+
+while the long-range number-variance agreement survives only through
+
+$$L_{\rm universal}=1.0.$$
+
+The residual at the longest measured window is
+
+$$\Sigma_{\rm phys}^{2}(8)-\Sigma_{\rm Haar}^{2}(8)=0.12582,\qquad \mathrm{CI}_{\rm simultaneous}=[0.11428,0.13736].$$
+
+Thus the supported hierarchy is now causal and confidence-aware:
+
+$$\text{local repulsion}\ \longrightarrow\ \text{finite-window ramp}\ \longrightarrow\ \text{unresolved long-range rigidity}.$$
+
+No dynamical Thouless time is claimed. The extracted quantities are correlation scales in the unfolded curvature spectrum.
+
+### Final delivery audit
+
+The v2 task-local one-command pipeline now reproduces the entire numerical and manuscript chain. The authoritative audit records:
+
+- \(20000\) original physical matrices with an exact \(12000/4000/4000\) train/validation/test split and a \(4000\)-matrix untouched physical SFF test set.
+- \(24\) Fourier tangents in \(12\) independent momentum-inversion orbits, all at active rank \(50\) and with at most ten distinct curvature eigenvalues.
+- \(28000\) positive-\(g\) geometric-interpolation matrices and \(32000\) fixed-projector spectral-interpolation matrices.
+- \(10000\) independent Haar--Jacobi matrices, \(8750\) root-response matrices through \(D=800\), and \(10000\) simultaneous-band replicates.
+- Five synchronized 7-inch vector figures with 2100-pixel, 300-dpi previews and exact scientific annotations.
+- Thirty-four passing tests and 37/37 scientific, source, figure, citation, metadata, compilation, rendering, and archive gates.
+- A 12-page PDF with the correct title, Thomas J. Wang and OKongOYangO authorship, Tsinghua University and The Pennsylvania State University affiliations, no undefined citations/references, no overfull boxes, and no stuck floats.
+- All 12 final page-render hashes exactly match the manually inspected audit set.
+
+The supported conclusion is deliberately bounded: \(K_{E,c}=0\) under exact degeneracy; the physical curvature SFF is finite-Jacobi compatible over \(0.25\leq\tau\leq1.5\); local and ramp onsets satisfy \(g_{\rm local}=0.20<g_{\rm ramp}=0.40\); number-variance universality ends at \(L=1\); and the \(D=800\) exact-atom plateau is \(0.7\). No physical time, full-Haar, conventional-ETH, or thermodynamic theorem is claimed.
+
+The final PDF and archived deliverable are byte-identical with SHA-256 `5d51ad4997a8cc95fa60fdafa02ef5aa13ad86cd31f10764b61a8f8903c2895c`.
+
+### Post-delivery next-step triage
+
+The highest-value extension is to explain why the curvature ramp occurs, rather than to add another spectral statistic. Introduce the resolvent-dressed tangent-response channels
+
+$$X_\mu=Q(H-E_0)^{-1}Q\,(\partial_\mu H)P,$$
+
+remove their learned smooth two-point covariance, and test the connected gauge-invariant four-channel tensor
+
+$$\mathcal C_{\mu\nu\rho\sigma}^{(4)}=\operatorname{Tr}\!\left(X_\mu^\dagger X_\nu X_\rho^\dagger X_\sigma\right)-\operatorname{Wick}_{\mu\nu\rho\sigma}.$$
+
+The decisive numerical object should be a normalized residual \(R_4\) versus a genuine many-body size parameter, with the structured Fourier control, physical local tangents, and covariance-matched random channels shown together. If \(R_4\) decreases while the exact kernel and external gap survive, the curvature ramp acquires a microscopic Geometric-ETH mechanism: it is the spectral shadow of Wick factorization in projector-response channels. If \(R_4\) remains nonzero but stable, the result instead identifies a non-Gaussian or deformed Geometric ETH. Either branch is more informative than another fixed-\(D\) form-factor curve.
+
+The second route is topology/holonomy. Construct a closed two-dimensional coupling surface, separate the central \(U(1)\) curvature from the traceless \(SU(D)\) fluctuations, and compare Chern number and Wilson-loop statistics while geometric scrambling is varied. Its sharp question is whether a fixed topological class can coexist with locally random non-Abelian curvature. This is closest to the moduli-space topology program of the BPS-microstate work, but it requires branch-stable discretization and a clean central/traceless decomposition.
+
+The third route is a dynamics bridge: weakly lift the degenerate band or apply a controlled drive and compare the geometric diagnostic with adiabatic-gauge-potential norms, projected-operator ETH, or an OTOC-like response. This can test physical consequences, but it should follow the channel-cumulant calculation because lifting the band weakens the article's exact-degeneracy paradox.
+
+Recommended order:
+
+1. Gauge-invariant four-channel Wick factorization plus true many-body scaling.
+2. Closed-cycle Chern/holonomy calculation.
+3. Dynamical validation after the geometric mechanism is established.
+
+More fixed-rank Monte Carlo, additional SFF normalizations, or another random-matrix ensemble are not current priorities. The design remains pending human choice between the matrix-element mechanism and the topology-first route.
+
+### Approved matrix-element and topology extension
+
+The human approved both routes. The implementation ground truth is [the joint design](../../docs/plans/2026-07-28-matrix-element-geometric-eth-and-topology-design.md).
+
+The main conceptual correction is that random Gaussian linear combinations of tangent potentials cannot test Wick factorization: because the response is linear in the tangent, Gaussian coefficients make the response Gaussian by construction. The approved observable instead uses eight fixed simple local density operators, whitens only their measured channel-label covariance, and tests the gauge-invariant four-channel trace tensor against a covariance-matched finite-size Gaussian reference.
+
+The true many-body axis is fixed before result inspection:
+
+$$N=3,4,5,\qquad n_\phi=2N+2,\qquad D=16,25,36.$$
+
+The topology axis is the closed twist torus. A periodic quasi-local ambient unitary conjugation preserves every energy eigenvalue, the exact kernel, the external gap, and the Chern class by construction, while its parameter dependence can modify local non-Abelian curvature and Wilson holonomy. The decisive comparison is therefore
+
+$$\text{fixed }C_1\text{ and fixed spectrum}\qquad\text{versus}\qquad\text{structured or CUE-like }SU(D)\text{ Wilson statistics}.$$
+
+The work now moves from approved design to two independently testable implementation plans.
+
+The test-driven execution is split into [matrix-element numerics](../../docs/plans/2026-07-28-matrix-element-geometric-eth-implementation-plan.md), [topological holonomy](../../docs/plans/2026-07-28-topological-holonomy-implementation-plan.md), and [article integration](../../docs/plans/2026-07-28-geometric-eth-topology-article-integration-plan.md). The two scientific subprojects produce independent artifacts and audits before either can enter the manuscript.
+
+### Matrix-element Geometric-ETH result
+
+![Four-channel Wick factorization on a genuine many-body sequence](script/output/figure_6_wick_factorization_v3.png)
+
+The genuine many-body sequence passes every mandatory numerical gate:
+
+| \(N\) | \(n_\phi\) | \(D\) | \(\dim\mathcal H\) | external gap | median \(R_4\) | Gaussian median | excess |
+|---:|---:|---:|---:|---:|---:|---:|---:|
+| 3 | 8 | 16 | 120 | 0.055872 | 0.37093 | 0.21708 | 0.15385 |
+| 4 | 10 | 25 | 715 | 0.103502 | 0.24715 | 0.14638 | 0.10078 |
+| 5 | 12 | 36 | 4368 | 0.093593 | 0.20906 | 0.12723 | 0.08183 |
+
+The \(N=5\) zero-mode frame is obtained by a complete block sparse solve with kernel residual \(3.59\times10^{-9}\). Its two-shift extrapolated site responses have maximum relative residual \(2.75\times10^{-7}\), maximum shift difference \(3.94\times10^{-4}\), and gauge-invariance error \(6.11\times10^{-16}\). Thus the persistent four-channel excess cannot be assigned to a missed degenerate direction or an unstable resolvent.
+
+The supported branch is `deformed_geometric_eth`: the connected four-channel residual decreases along a true particle-number sequence, but the largest size remains outside the finite-size covariance-matched Gaussian interval \([0.12657,0.12797]\). The current evidence therefore supports progressive Gaussianization with a resolvable non-Gaussian operator-channel memory, not completed Wick factorization or a thermodynamic theorem.
+
+The vector source is [Figure 6](script/output/figure_6_wick_factorization_v3.pdf), and the fail-closed evidence is [the matrix-element delivery audit](script/output/matrix_element_delivery_audit_v3.json).
+
+### Fixed-Chern Wilson-holonomy result
+
+![Fixed Chern topology with deformed non-Abelian Wilson holonomy](script/output/figure_7_topological_holonomy_v3.png)
+
+The physical closed surface is the complete twist torus, not an open parameter patch. The accepted \(16\times16\) and \(20\times20\) meshes give
+
+| \(N\) | \(D\) | \(C_1\) | minimum external gap | minimum branch margin | minimum overlap | base \(\langle r_W\rangle\) | final seed interval | CUE interval |
+|---:|---:|---:|---:|---:|---:|---:|---:|---:|
+| 3 | 16 | 6 | 0.051741 | 2.06643 | 0.85325 | 0.28849 | [0.30837, 0.35754] | [0.45932, 0.73219] |
+| 4 | 25 | 10 | 0.094695 | 1.17980 | 0.83693 | 0.30998 | [0.32379, 0.34411] | [0.48664, 0.70911] |
+
+The \(N=3\) seed-cluster bootstrap interval for the change in the Wilson circular gap ratio is \([0.02777,0.05068]\); for \(N=4\) it is \([0.01805,0.02835]\). Both exclude zero, so the parameter-dependent ambient unitary changes the non-Abelian holonomy reproducibly. Neither final interval overlaps the corresponding CUE interval, and the Wilson SFF also fails the simultaneous CUE gate. The supported result is therefore a fixed topological class with a tunably deformed, still structured Wilson sector—not complete circular-unitary randomness.
+
+The complete energy spectrum and external gap are unchanged exactly because \(H_g(\theta)=\mathcal U_g(\theta)H_0(\theta)\mathcal U_g^\dagger(\theta)\). The bundle Chern class is unchanged because the globally defined periodic \(\mathcal U_g\) is a bundle isomorphism. Numerically, determinant and trace-log Chern estimators agree to better than \(10^{-13}\), all accepted plaquette branch margins are positive, and a random local frame gauge changes Chern by \(1.42\times10^{-14}\) and Wilson eigenphases by \(6.85\times10^{-15}\).
+
+The failed coarse calculation is preserved at [the mesh-12 alias audit](script/output/topological_holonomy_mesh12_alias_audit_v3.json), while [the accepted production artifact](script/output/topological_holonomy_v3.json) hashes the \(16/20\) checkpoints and all raw per-loop/per-seed arrays. The vector source is [Figure 7](script/output/figure_7_topological_holonomy_v3.pdf), and the fail-closed evidence is [the topology delivery audit](script/output/topological_holonomy_delivery_audit_v3.json).
+
+### Integrated v3 article and analytic result
+
+The manuscript now gives the matrix-element statement in a frame-independent form. For complement-to-fiber response maps \(X_\mu\), independent frame changes act as \(X_\mu\mapsto U_Q^\dagger X_\mu U_P\), so the channel covariance and the four-channel trace tensor are gauge invariant. After whitening the channel labels, the separable complex-Gaussian null has two Wick contractions with coefficients fixed by the measured left and right covariances. The reported \(R_4\) is the normalized distance from that finite-\((D,M)\), covariance-matched prediction; it is not a fit to the same physical four-point data. The nonzero \(N=5\) excess is therefore a measured connected operator-channel cumulant.
+
+The topology statement is likewise analytic rather than solely numerical. A globally defined periodic ambient unitary \(\mathcal U_g:T^2\to U(\mathcal H)\) gives a vector-bundle isomorphism \(E_g\simeq E_0\), hence \(c_1(E_g)=c_1(E_0)\). However, the pulled-back connection acquires the projected one-form
+
+$$A_g=A_0+i\Phi_0^\dagger\mathcal U_g^\dagger d\mathcal U_g\Phi_0,$$
+
+which is generally not an internal periodic pure gauge. Thus fixed spectrum and fixed \(C_1\) do not imply fixed non-Abelian Wilson holonomy. The accepted \(16/20\) mesh pair implements this separation with positive overlap and determinant-branch margins.
+
+The final article deliberately stops at the two supported negative boundaries:
+
+1. the shrinking four-channel residual does not establish completed Wick factorization or a thermodynamic exponent;
+2. the deformed Wilson sector remains outside CUE, and the ambient orbit is a controlled isospectral construction rather than a generic microscopic phase diagram.
+
+The archived [17-page v3 article](script/output/spectral_silence_and_geometric_chaos_v3.pdf) is byte-identical to the live compiled manuscript. [The combined delivery audit](script/output/geometric_eth_topology_delivery_audit_v3.json) records all 17 rendered-page hashes, the seven synchronized figures, exact result branches, author metadata, affiliations, claim-boundary text, and clean LaTeX gates. The task remains 🟡 Ongoing for human/external scientific review rather than because an approved computational deliverable is missing.
+
+### Public-release and PR handoff
+
+![Geometric chaos under exact degeneracy](script/output/figure_1_spectral_silence_v2.png)
+
+The public release presents one continuous advance: the energy connected SFF becomes exactly silent in the degenerate Laughlin manifold, while metric-normalized curvature develops finite-Jacobi local correlations; the invariant four-channel tensor then measures the remaining connected operator memory, and periodic ambient conjugation separates fixed Chern class from tunable non-Abelian holonomy.
+
+The reviewer-facing package consists of the [Task 05 guide](README.md), [technical report](../../docs/2026-07-30-task05-technical-report.md), [release notes](../../docs/2026-07-30-task05-release-notes.md), [PR body](../../docs/2026-07-30-task05-pr-body.md), [review comment](../../docs/2026-07-30-task05-pr-review-comment.md), [public-release checklist](../../docs/2026-07-30-task05-public-release-checklist.md), and [challenge draft](../../docs/2026-07-30-quantum-geometry-harness-challenge-draft.md). The intended sequence is Issue publication, replacement of `ISSUE_NUMBER` in the PR body, PR submission from `codex/task-05-geometric-chaos-baseline`, and collaborator review through the prepared `@OkongOyangO` comment.
+
+The release has three evidence layers. The compact checkout stores the article, seven public PNG figures, small JSON/TeX audits, and code. The manifest records 25 production-scale arrays and checkpoints with exact hashes and producers. `bash run_quick_verify_v1.sh` verifies the public contract and analytic core in under one minute, while `bash run_full_recompute_v1.sh` regenerates the production chain.
diff --git a/tracks/mps/solutions/Wander-276/research/CITATION.cff b/tracks/mps/solutions/Wander-276/research/CITATION.cff
new file mode 100644
index 000000000..c05ba8f40
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/CITATION.cff
@@ -0,0 +1,29 @@
+cff-version: 1.2.0
+message: "If you use this code or dataset, please cite the article and this software release."
+title: "Spectral Silence and Geometric Chaos in an Exactly Degenerate Topological Manifold"
+type: software
+authors:
+  - family-names: Wang
+    given-names: Thomas J.
+  - family-names: OKongOYangO
+repository-code: "https://github.com/JunkaiWang-TheoPhy/Chaos-of-Quantum-Geometry"
+url: "https://github.com/JunkaiWang-TheoPhy/Chaos-of-Quantum-Geometry"
+version: 1.0.0
+date-released: 2026-07-30
+license: GPL-3.0-only
+abstract: "A reproducible analytic and numerical baseline for non-Abelian geometric chaos under exact spectral degeneracy, including finite-Jacobi curvature correlations, gauge-invariant four-channel response tests, and fixed-Chern Wilson holonomy."
+keywords:
+  - quantum chaos
+  - non-Abelian Berry curvature
+  - geometric ETH
+  - fractional quantum Hall effect
+  - Chern number
+  - Wilson holonomy
+preferred-citation:
+  type: article
+  authors:
+    - family-names: Wang
+      given-names: Thomas J.
+    - family-names: OKongOYangO
+  title: "Spectral Silence and Geometric Chaos in an Exactly Degenerate Topological Manifold"
+  year: 2026
diff --git a/tracks/mps/solutions/Wander-276/research/LICENSE b/tracks/mps/solutions/Wander-276/research/LICENSE
new file mode 100644
index 000000000..f288702d2
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/LICENSE
@@ -0,0 +1,674 @@
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diff --git a/tracks/mps/solutions/Wander-276/research/README.md b/tracks/mps/solutions/Wander-276/research/README.md
new file mode 100644
index 000000000..62e85b34f
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/README.md
@@ -0,0 +1,69 @@
+# Chaos of Quantum Geometry
+
+> **Exact degeneracy turns quantum geometry into the signal.**
+
+![Exact spectral flatness and an emergent geometric ramp](01_task_folder/task_05/script/output/figure_1_spectral_silence_v2.png)
+
+An exactly degenerate quantum manifold carries a flat internal energy spectrum. This project shows that its state-space geometry remains richly informative: non-Abelian Berry curvature, the quantum metric, response-channel cumulants, Chern numbers, and Wilson holonomy resolve a hierarchy of correlations hidden from energy spacings.
+
+The project begins with Chen, Colin-Ellerin, Mamroud, and Papadodimas, [“Chaos of Berry curvature for BPS microstates”](https://arxiv.org/abs/2604.23287), and builds a complementary condensed-matter realization in an exactly degenerate bosonic Laughlin manifold.
+
+## Featured Advance
+
+The task-05 release, [*Spectral Silence and Geometric Chaos in an Exactly Degenerate Topological Manifold*](01_task_folder/task_05/script/output/spectral_silence_and_geometric_chaos_v3.pdf), establishes three geometric scales inside one protected manifold:
+
+| Scale | New capability | Result |
+|---|---|---|
+| Exact spectrum | Separate degeneracy from state-space complexity | \(K_{E,\mathrm{raw}}=D\), \(K_{E,c}=0\) exactly |
+| Local geometry | Compare curvature directly with a finite-rank analytic law | Jacobi-like level repulsion and a registered curvature ramp |
+| Higher/global geometry | Resolve operator memory and topological transport | A persistent four-channel cumulant and fixed-Chern, deformable Wilson holonomy |
+
+```mermaid
+flowchart LR
+    A["Exactly degenerate Laughlin manifold"] --> B["Exact energy identity"]
+    A --> C["Projector response P(dH)Q"]
+    C --> D["Finite-rank Jacobi curvature law"]
+    C --> E["Gauge-invariant four-channel Geometric ETH"]
+    C --> F["Fixed C1 with tunable Wilson holonomy"]
+```
+
+## What Is New
+
+| Foundation | Advance delivered here |
+|---|---|
+| Berry curvature as a BPS chaos probe | A local, frustration-free fractional-topological parent with an exact, gapped zero-mode manifold |
+| Random-matrix comparison | A parameter-free finite-\(D\) complex-Jacobi kernel, connected form factor, and exact boundary-atom plateau theorem |
+| Curvature eigenvalue statistics | A covariance-whitened, gauge-invariant four-channel matrix-element test on the genuine \(N=3,4,5\) sequence |
+| Integrated Chern data | A closed-torus construction that preserves the complete spectrum and \(C_1\) while continuously tuning relative Wilson holonomy |
+| Numerical evidence | A hash-complete release contract connecting source, figures, compact artifacts, external production arrays, and the final PDF |
+
+These advances become possible by combining exact parent-Hamiltonian kernels with metric-normalized signature compression. The resulting algorithm turns a large projector-response problem into a finite-rank Jacobi process, while gauge-invariant trace tensors and discrete Wilson transport capture structure beyond eigenvalue statistics.
+
+## Reproduce
+
+The review path checks analytic identities, task isolation, release hashes, registered result branches, and 38 focused tests:
+
+```bash
+cd 01_task_folder/task_05/script
+python -m pip install -r requirements.txt
+bash run_quick_verify_v1.sh
+```
+
+The task-level [release guide](01_task_folder/task_05/README.md) documents the article build, full numerical recomputation, artifact classes, exact commands, and growth roadmap. Machine-readable provenance lives in the [release manifest](01_task_folder/task_05/script/output/release_manifest_v1.json).
+
+## Start Here
+
+| Deliverable | Purpose |
+|---|---|
+| [Technical report](docs/2026-07-30-task05-technical-report.md) | Innovation, algorithm, equations, evidence, and research outlook |
+| [17-page PDF](01_task_folder/task_05/script/output/spectral_silence_and_geometric_chaos_v3.pdf) | Complete analytic and numerical article |
+| [Task release guide](01_task_folder/task_05/README.md) | Reproduction tiers and figure-by-figure map |
+| [Release notes](docs/2026-07-30-task05-release-notes.md) | Reviewer-facing summary |
+| [Quantum Harness challenge](docs/2026-07-30-quantum-geometry-harness-challenge-draft.md) | Public next-stage benchmark |
+| [Main dashboard](00_main/main_dashboard.md) | Global task ledger and provenance log |
+
+## Research Horizon
+
+The current release establishes a finite-size geometric-chaos baseline with exact algebraic identities, high-statistics curvature results, a genuine many-body response sequence, and closed-surface topology. The next phase extends the sequence to \(N=6\), transfers the invariant test to a second exact-degeneracy mechanism, and derives the observed four-channel scaling from locality.
+
+The code is released under the [GNU General Public License v3.0](LICENSE). Citation metadata are provided in [CITATION.cff](CITATION.cff).
diff --git a/tracks/mps/solutions/Wander-276/research/docs/2026-07-30-quantum-geometry-harness-challenge-draft.md b/tracks/mps/solutions/Wander-276/research/docs/2026-07-30-quantum-geometry-harness-challenge-draft.md
new file mode 100644
index 000000000..6510a4588
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/docs/2026-07-30-quantum-geometry-harness-challenge-draft.md
@@ -0,0 +1,94 @@
+# Quantum Harness Challenge Draft: Geometry Speaks Under Exact Degeneracy
+
+## Form Fields
+
+**Title**
+
+`[challenge] Can non-Abelian quantum geometry reveal chaos inside an exactly degenerate manifold?`
+
+**Released by**
+
+Thomas J. Wang, Tsinghua University
+
+**Public contact**
+
+[@JunkaiWang-TheoPhy](https://github.com/JunkaiWang-TheoPhy); the issue form can carry the preferred public email.
+
+**Method**
+
+Exact Diagonalization
+
+## Challenge Issue
+
+**Difficulty:** ★★★
+
+### Background
+
+An exactly degenerate multiplet has identical internal energies, while its projector can trace a rich path through Hilbert space. Chen, Colin-Ellerin, Mamroud, and Papadodimas proposed non-Abelian Berry curvature as an intrinsic chaos diagnostic for degenerate BPS microstates in [arXiv:2604.23287](https://arxiv.org/abs/2604.23287). The public task-05 baseline turns that idea into a gauge-invariant many-body matrix-element program with exact analytic references and machine-checkable outcomes.
+
+For a degenerate projector \(P(\lambda)\), \(Q=1-P\), and zero-mode energy \(E_0\), define the resolvent-dressed tangent response
+
+$$X_\mu=P(\partial_\mu H)Q[Q(H-E_0)Q]^{-1}.$$
+
+After whitening by a preregistered two-point channel covariance, evaluate the gauge-invariant tensor
+
+$$T_{\mu\nu\rho\sigma}=\frac{1}{D}\operatorname{Tr}(\widetilde X_\mu\widetilde X_\nu^\dagger\widetilde X_\rho\widetilde X_\sigma^\dagger)$$
+
+against its finite-size covariance-matched complex-Gaussian Wick reference.
+
+The baseline establishes feasibility for a bosonic Laughlin sequence at \(N=3,4,5\): local curvature correlations follow the finite-Jacobi law, the connected four-channel component decreases monotonically, and fixed-Chern Wilson holonomy occupies a structured tunable regime. The challenge begins at the next scaling frontier.
+
+### Research Objective
+
+Complete at least one branch:
+
+1. extend the fixed-two-quasihole Laughlin sequence through \(N=6\) and issue a preregistered matrix-element verdict;
+2. repeat the full gauge-invariant test in a second local exact-degeneracy mechanism;
+3. derive and verify the asymptotic scaling of the connected four-channel component from locality or constraint algebra.
+
+The verifier selects exactly one outcome:
+
+- `emergent_wick_geometric_eth`;
+- `deformed_geometric_eth`;
+- `structured_geometry_regime`;
+- `scaling_frontier`.
+
+Every branch carries scientific value and maps a distinct universality structure.
+
+### Mandatory Gates
+
+**Gate 0: exact kernel and gap.** Match the target rank to independent counting, resolve internal bandwidth below \(10^{-8}\) times the external gap, publish eigensolver/resolvent residuals, and retain every preregistered size.
+
+**Gate 1: gauge and mesh invariance.** Curvature spectra, the four-channel residual, Chern number, and Wilson eigenphases must remain stable under independently sampled local \(U(D)\) frame rotations. Two meshes must agree on the integer Chern number with positive determinant-branch margin and stable Wilson statistics.
+
+**Gate 2: independent chaos axes.** Tune unfolded intramultiplet statistics through \(PHP\) while preserving \(P\) and its geometry; tune \(P(\partial_\mu H)Q\) while preserving the complete energy spectrum.
+
+**Gate 3: matrix-element verdict.** Freeze sizes, local-operator panels, covariance cutoff, random seeds, reference count, compatibility bands, and solver tolerances before the largest run. Emit the result branch from raw artifacts through a public script.
+
+**Gate 4: topology.** On a closed two-parameter surface, separate determinant \(U(1)\) topology from relative \(SU(D)\) holonomy and report both the fixed \(C_1\) sector and the Wilson universality class.
+
+### Deliverables
+
+- source and environment lock;
+- raw spectra, overlaps, seeds, and solver checkpoints or a DOI-backed data archive;
+- machine-readable result schema and one-command verifier;
+- gauge-randomization and mesh-convergence reports;
+- compact figures showing the three-ensemble comparison, four-channel scaling, and fixed-Chern holonomy;
+- a research report that explains the selected outcome as a distinct universality statement.
+
+### Why This Can Produce Research
+
+Wick compatibility would establish a microscopic matrix-element Geometric-ETH law in an exactly degenerate many-body manifold. A stable connected component would establish a deformed fixed tensor with operator memory. Independent spectral and geometric axes reveal how multiple notions of chaos coexist, while the topology gate connects local universality to the global structure of parameter space.
+
+The baseline contributes new finite-rank algorithms, a gauge-invariant tensor law, and an isospectral topology control, so every submission begins from an executable research platform rather than a conceptual prompt.
+
+### References
+
+1. Y. Chen, S. Colin-Ellerin, O. Mamroud, and K. Papadodimas, [“Chaos of Berry curvature for BPS microstates”](https://arxiv.org/abs/2604.23287).
+2. M. Kolodrubetz, D. Sels, P. Mehta, and A. Polkovnikov, [“Geometry and non-adiabatic response in quantum and classical systems”](https://arxiv.org/abs/1602.01062).
+3. T. Fukui, Y. Hatsugai, and H. Suzuki, [“Chern Numbers in Discretized Brillouin Zone”](https://doi.org/10.1143/JPSJ.74.1674).
+4. Quantum Harness [issue 73](https://github.com/QuantumBFS/quantum.harness/issues/73), an Abelian Berry-phase benchmark complementary to this non-Abelian challenge.
+
+## Submission Note
+
+An authorized repository member can paste this draft into the issue form, add the preferred public email, and attach the release DOI when available.
diff --git a/tracks/mps/solutions/Wander-276/research/docs/2026-07-30-task05-pr-body.md b/tracks/mps/solutions/Wander-276/research/docs/2026-07-30-task05-pr-body.md
new file mode 100644
index 000000000..01d80bbef
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/docs/2026-07-30-task05-pr-body.md
@@ -0,0 +1,90 @@
+# PR Title
+
+`Geometric chaos under exact degeneracy: reproducible task-05 release`
+
+# PR Body
+
+Related research challenge: [QuantumBFS/quantum.harness#276 — What is the Probe of Quantum Chaos for Degenerate Eigenstate Subspace?](https://github.com/QuantumBFS/quantum.harness/issues/276)
+
+## Exact degeneracy turns quantum geometry into the signal
+
+<img src="https://raw.githubusercontent.com/JunkaiWang-TheoPhy/Chaos-of-Quantum-Geometry/codex/task-05-geometric-chaos-baseline/01_task_folder/task_05/script/output/figure_1_spectral_silence_v2.png" alt="Exact spectral flatness and geometric ramp" width="900">
+
+This PR gives an executable answer to Issue #276: the chaos probe for a degenerate eigenspace is the non-Abelian quantum geometry of its projector over coupling space. In an exactly degenerate bosonic Laughlin manifold, the energy sector obeys the exact identities \(K_{E,\mathrm{raw}}=D\) and \(K_{E,c}=0\), while the projector geometry resolves local finite-Jacobi correlations, a gauge-invariant connected response cumulant, and tunable Wilson holonomy at fixed Chern class.
+
+## Scientific Advance
+
+| Layer | New capability | Registered result |
+|---|---|---|
+| Exact spectrum | Clean spectral-flatness reference | \(K_{E,c}=0\) identically |
+| Local geometry | Parameter-free finite-\(D\) Jacobi kernel and SFF | Physical curvature tracks the registered Jacobi ramp |
+| Matrix elements | Covariance-whitened four-channel tensor | `deformed_geometric_eth` |
+| Global topology | Isospectral, fixed-Chern Wilson control | `fixed_chern_deformed_holonomy` |
+
+## Four Innovations
+
+1. **Metric-normalized signature compression.** The projector response becomes a compression of a fixed signature matrix, turning a model-specific many-body problem into an exact finite-rank complex-Jacobi process.
+2. **Boundary-atom form-factor theorem.** The implementation treats exact \(\lambda=\pm1\) modes algebraically and proves \(K_{J,c}^{\mathrm{full}}=(k/D)K_{J,c}^{(k)}\), including the \(D=800\) plateau.
+3. **Matrix-element Geometric ETH.** A gauge-invariant four-channel tensor, evaluated on the genuine \(N=3,4,5\) sequence, promotes the analysis beyond curvature eigenvalues and reveals progressive Gaussianization with a resolved connected component.
+4. **Fixed-Chern holonomy engineering.** A periodic ambient unitary preserves every energy, the external gap, and \(C_1\), while continuously tuning relative Wilson transport.
+
+These advances build directly on the Berry-curvature chaos program of Chen, Colin-Ellerin, Mamroud, and Papadodimas and add a local frustration-free condensed-matter realization, exact finite-rank algorithms, causal spectral/geometric interventions, an operator-level law, and global topology control.
+
+## Quantitative Highlights
+
+- 20000 physical tangent pairs with a frozen `12000/4000/4000` train/validation/test split.
+- At \(\tau=0.5\), physical \(K_{F,c}=0.502\) and finite-Jacobi \(K_{J,c}=0.501\).
+- Four-channel connected excess: \(0.15385\to0.10078\to0.08183\) across \(N=3,4,5\).
+- Fixed Chern numbers \(C_1=6,10\) with reproducibly shifted Wilson statistics.
+- Exact rank sequence through \(D=800\), including 120 atoms at each boundary and connected plateau \(0.7\).
+- Seven synchronized publication figures and an audited 17-page article.
+
+## Delivery Package
+
+- innovation-first [project landing page](https://github.com/JunkaiWang-TheoPhy/Chaos-of-Quantum-Geometry/tree/codex/task-05-geometric-chaos-baseline);
+- task-level [reproduction guide](https://github.com/JunkaiWang-TheoPhy/Chaos-of-Quantum-Geometry/blob/codex/task-05-geometric-chaos-baseline/01_task_folder/task_05/README.md);
+- [Markdown technical report](https://github.com/JunkaiWang-TheoPhy/Chaos-of-Quantum-Geometry/blob/codex/task-05-geometric-chaos-baseline/docs/2026-07-30-task05-technical-report.md);
+- [17-page PDF](https://github.com/JunkaiWang-TheoPhy/Chaos-of-Quantum-Geometry/blob/codex/task-05-geometric-chaos-baseline/01_task_folder/task_05/script/output/spectral_silence_and_geometric_chaos_v3.pdf);
+- `CITATION.cff`, pinned Python dependencies, and GPL-3.0 licensing;
+- quick and full recomputation runners;
+- machine-readable release manifest covering 7 figures, 14 compact artifacts, and 25 production arrays;
+- issue-ready [Quantum Harness challenge](https://github.com/JunkaiWang-TheoPhy/Chaos-of-Quantum-Geometry/blob/codex/task-05-geometric-chaos-baseline/docs/2026-07-30-quantum-geometry-harness-challenge-draft.md).
+
+## Verification
+
+```bash
+cd 01_task_folder/task_05/script
+python -m pip install -r requirements.txt
+bash run_quick_verify_v1.sh
+```
+
+Verified release state:
+
+- 38 focused quick-path tests;
+- 86 passing compact-checkout tests plus 6 production-data tests that activate with the manifest-listed arrays;
+- 25 article-delivery checks across all 17 rendered pages;
+- synchronized paper/archive SHA-256 recorded in `release_manifest_v1.json`;
+- task-local runtime isolation and a 10 MiB tracked-blob policy.
+
+## Reviewer Route
+
+1. Read the [technical report](https://github.com/JunkaiWang-TheoPhy/Chaos-of-Quantum-Geometry/blob/codex/task-05-geometric-chaos-baseline/docs/2026-07-30-task05-technical-report.md).
+2. Inspect Figures 1, 6, and 7.
+3. Run `bash run_quick_verify_v1.sh`.
+4. Check the two registered result branches in the manifest and JSON artifacts.
+5. Review the \(N=6\)/second-model growth program in the challenge draft.
+
+## Growth Horizon
+
+The public baseline makes three next steps immediately executable: \(N=6\) matrix-element scaling, transfer to a second exact-degeneracy mechanism, and a locality-based derivation of the four-channel law. The associated Quantum Harness issue turns these directions into a community benchmark with machine-verifiable outcomes.
+
+## Checklist
+
+- [x] Scientific source and task isolation
+- [x] Seven publication figures
+- [x] 17-page article and Markdown technical report
+- [x] Quick and full reproduction paths
+- [x] Compact/external artifact manifest
+- [x] Citation metadata and public landing pages
+- [x] Issue-ready follow-on challenge
+- [x] Clean-checkout verification
diff --git a/tracks/mps/solutions/Wander-276/research/docs/2026-07-30-task05-pr-review-comment.md b/tracks/mps/solutions/Wander-276/research/docs/2026-07-30-task05-pr-review-comment.md
new file mode 100644
index 000000000..139bb6469
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/docs/2026-07-30-task05-pr-review-comment.md
@@ -0,0 +1,25 @@
+# PR Review Comment
+
+Paste this comment after opening the PR:
+
+---
+
+@OkongOyangO This release provides the executable answer to [QuantumBFS/quantum.harness#276](https://github.com/QuantumBFS/quantum.harness/issues/276) and is ready for a focused scientific review. The most valuable review path is:
+
+1. **Core claim:** exact spectral flatness \(K_{E,c}=0\) together with finite-Jacobi local curvature correlations.
+2. **New matrix-element law:** gauge invariance of \(T_{\mu\nu\rho\sigma}\), covariance matching, and the \(N=3,4,5\) decrease of the connected excess.
+3. **Topology result:** the bundle-isomorphism proof for fixed \(C_1\) and the independent deformation of relative Wilson holonomy.
+4. **Release contract:** `bash run_quick_verify_v1.sh`, the 17-page PDF audit, and the compact/external artifact manifest.
+
+The quickest entry points are the [technical report](https://github.com/JunkaiWang-TheoPhy/Chaos-of-Quantum-Geometry/blob/codex/task-05-geometric-chaos-baseline/docs/2026-07-30-task05-technical-report.md), Figures 1/6/7, and `01_task_folder/task_05/script/output/release_manifest_v1.json`.
+
+The central innovation is the combination of exact parent-Hamiltonian kernels, metric-normalized signature compression, a gauge-invariant four-channel Geometric-ETH test, and fixed-Chern holonomy engineering. This creates a calculable bridge from the BPS Berry-curvature program to fractional topological matter and opens a concrete \(N=6\)/second-model scaling program.
+
+Verification command:
+
+```bash
+cd 01_task_folder/task_05/script
+bash run_quick_verify_v1.sh
+```
+
+---
diff --git a/tracks/mps/solutions/Wander-276/research/docs/2026-07-30-task05-public-release-checklist.md b/tracks/mps/solutions/Wander-276/research/docs/2026-07-30-task05-public-release-checklist.md
new file mode 100644
index 000000000..e9c4fd3be
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/docs/2026-07-30-task05-public-release-checklist.md
@@ -0,0 +1,59 @@
+# Task 05 Public Release Checklist
+
+## 1. Research Issue Submitted
+
+- Issue: [QuantumBFS/quantum.harness#276](https://github.com/QuantumBFS/quantum.harness/issues/276).
+- Title: `What is the Probe of Quantum Chaos for Degenerate Eigenstate Subspace?`
+- The PR body now links the issue and supplies the executable geometric answer.
+
+## 2. Open the PR
+
+- Base: `main`
+- Head: `codex/task-05-geometric-chaos-baseline`
+- Title: `Geometric chaos under exact degeneracy: reproducible task-05 release`
+- Body: paste [the prepared PR body](2026-07-30-task05-pr-body.md).
+- Suggested mode: Draft during the first scientific review, then Ready for Review after author sign-off.
+
+## 3. Add the Review Comment
+
+- Paste [the prepared review comment](2026-07-30-task05-pr-review-comment.md).
+- Keep `@OkongOyangO` in the first line so GitHub sends the review notification.
+- Request review from the same collaborator in the PR sidebar.
+
+## 4. Review the Public Landing Page
+
+- Confirm the hero figure renders on the repository front page.
+- Open the Markdown technical report and 17-page PDF.
+- Check `CITATION.cff` rendering in GitHub's citation panel.
+- Confirm every link in the task release guide resolves.
+
+## 5. Run the Release Gate
+
+```bash
+cd 01_task_folder/task_05/script
+bash run_quick_verify_v1.sh
+```
+
+Expected compact release state:
+
+- 38 focused tests;
+- 86 passing complete-suite tests;
+- 6 production-data tests activated by the manifest-listed arrays;
+- 17 rendered article pages;
+- 7 synchronized main figures;
+- 14 Git-resident compact artifacts;
+- 25 production arrays recorded with SHA-256 and byte size.
+
+## 6. Publish the Data Layer
+
+- Create a DOI-backed archive for the 25 production arrays when desired.
+- Attach the DOI to the GitHub release, technical report, and challenge issue.
+- Regenerate `release_manifest_v1.json` with the archived artifacts present and confirm identical hashes.
+
+## 7. Convert the PR to Ready for Review
+
+- Confirm author names and public contact details.
+- Confirm the issue link.
+- Confirm the final article hash.
+- Publish the prepared review comment.
+- Select **Ready for Review**.
diff --git a/tracks/mps/solutions/Wander-276/research/docs/2026-07-30-task05-release-notes.md b/tracks/mps/solutions/Wander-276/research/docs/2026-07-30-task05-release-notes.md
new file mode 100644
index 000000000..2e256398c
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/docs/2026-07-30-task05-release-notes.md
@@ -0,0 +1,39 @@
+# Task 05 Research Release Notes
+
+**Release ID:** `task05-geometric-chaos-v1`
+
+## Headline
+
+**Exact degeneracy turns quantum geometry into the signal.**
+
+This release transforms the completed task-05 calculation into a public, independently reviewable baseline. It includes the task-local numerical package, compact evidence, seven publication figures, a 17-page REVTeX article, a Markdown technical report, quick and full verification paths, and a machine-readable artifact manifest.
+
+## Four Research Advances
+
+1. **An exact geometric-chaos setting.** A local Kapit–Mueller parent supplies a gapped bosonic Laughlin kernel with exact many-body degeneracy.
+2. **A finite-rank analytic algorithm.** Metric-normalized curvature reduces to a complex-Jacobi signature compression with an executable determinantal-kernel form factor and boundary-atom theorem.
+3. **A matrix-element Geometric-ETH test.** A covariance-whitened, gauge-invariant four-channel tensor exposes progressive Gaussianization plus a resolved connected component across \(N=3,4,5\).
+4. **A topology/holonomy separation.** A closed twist-torus family preserves the complete spectrum and \(C_1\) while tuning relative Wilson transport.
+
+## Evidence Layers
+
+| Evidence class | Public result | Authoritative artifact |
+|---|---|---|
+| Exact | \(K_{E,\mathrm{raw}}=D\) and \(K_{E,c}=0\) in the degenerate manifold | Article Eq. (1), Figure 1 |
+| Statistical | Metric-normalized curvature follows finite-Jacobi local correlations and a registered ramp | Figures 1–5, `spectral_silence_delivery_audit_v2.json` |
+| Matrix element | The four-channel connected excess decreases \(0.15385\to0.10078\to0.08183\) | Figure 6, `matrix_element_geometric_eth_v3.json` |
+| Topological | \(C_1=6,10\) stays fixed while Wilson statistics shift reproducibly | Figure 7, `topological_holonomy_v3.json` |
+
+The registered outcome labels are `deformed_geometric_eth` and `fixed_chern_deformed_holonomy`. Numerical gates generate both labels directly from the frozen artifacts.
+
+## Reproduction Contract
+
+- Quick verification: 38 focused tests plus release hashes, result labels, task isolation, analytic identities, documentation links, and citation metadata.
+- Complete compact suite: 86 passing tests and 6 production-data tests that activate upon restoration of the manifest-listed arrays.
+- Article verification: seven synchronized figures, clean REVTeX compilation, PDF metadata, 17 rendered pages, citation records, and scientific-scope checks.
+- Full reproduction: staged v1, v2, and v3 numerical pipelines with resumable checkpoints.
+- Data manifest: 14 compact artifacts in Git and 25 production arrays with exact paths, sizes, SHA-256 hashes, and producer commands.
+
+## Growth Horizon
+
+The completed \(N=3,4,5\) sequence is the public reference baseline. The Quantum Harness challenge advances to \(N=6\), a second exact-degeneracy mechanism, and a derivation of the four-channel scaling from locality. Each registered outcome contributes a publishable statement about the emergence and structure of Geometric ETH.
diff --git a/tracks/mps/solutions/Wander-276/research/docs/2026-07-30-task05-technical-report.md b/tracks/mps/solutions/Wander-276/research/docs/2026-07-30-task05-technical-report.md
new file mode 100644
index 000000000..025eb6557
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/docs/2026-07-30-task05-technical-report.md
@@ -0,0 +1,148 @@
+# Technical Report: Geometry Speaks Under Exact Degeneracy
+
+**Release:** `task05-geometric-chaos-v1`
+**Article:** *Spectral Silence and Geometric Chaos in an Exactly Degenerate Topological Manifold*
+**Authors:** Thomas J. Wang and OKongOYangO
+**Date:** 2026-07-30
+
+## Executive Signal
+
+This project establishes a new route to diagnosing quantum chaos when an entire many-body manifold is exactly degenerate. Instead of introducing an artificial energy splitting, it measures how the protected subspace moves over coupling space. The result is a hierarchy of geometric information: finite-Jacobi curvature correlations at local scales, a gauge-invariant connected response cumulant at the operator level, and tunable Wilson holonomy inside a fixed Chern class.
+
+The central scientific advance is therefore stronger than a new statistic. It is a complete architecture for **geometric chaos under exact spectral flatness**:
+
+$$\text{exact parent kernel}\longrightarrow\text{projector response}\longrightarrow\text{metric normalization}\longrightarrow\text{finite-rank RMT}\longrightarrow\text{global bundle topology}.$$
+
+## Relation to the Starting Point
+
+Chen, Colin-Ellerin, Mamroud, and Papadodimas introduced non-Abelian Berry curvature as an intrinsic chaos diagnostic for exactly degenerate BPS sectors. Their work supplies the conceptual starting point: energy degeneracy elevates quantum geometry from an auxiliary observable to the primary carrier of chaos information.
+
+This release adds a complementary condensed-matter realization and four new layers:
+
+| Starting capability | Innovation in this project | Why it matters |
+|---|---|---|
+| Curvature as a BPS chaos diagnostic | Exact bosonic Laughlin zero modes of a local Kapit–Mueller parent | Demonstrates the geometric principle in a frustration-free fractional-topological system |
+| Random-matrix-like curvature | Exact finite-\(D\) complex-Jacobi kernel and connected form factor | Supplies a parameter-free benchmark at the dimensions used numerically |
+| Curvature eigenvalue evidence | Gauge-invariant four-channel response tensor | Promotes Geometric ETH from eigenvalue statistics to a matrix-element statement |
+| Moduli-space Chern topology | Fixed-spectrum, fixed-Chern, tunable Wilson holonomy | Separates integrated topology from relative non-Abelian transport |
+| Numerical demonstration | Cryptographic release manifest and tiered verification | Makes every public claim traceable to source, figure, compact artifact, or regenerable array |
+
+## Why the New Algorithms Make This Possible
+
+### Exact parent-Hamiltonian geometry
+
+The bosonic contact parent is positive semidefinite, and its Laughlin quasihole manifold is the exact kernel. The Kapit–Mueller lattice supplies an exactly flat Chern band and a clean boundary-twist torus. Together they provide exact degeneracy, an open external gap, a growing multiplet rank, and local response channels in one calculable model.
+
+### Signature-compression reduction
+
+Let \(P\) project onto the exact zero-mode manifold and \(Q=1-P\). The resolvent-dressed response map for a deformation \(\lambda^\mu\) is
+
+$$X_\mu=P(\partial_\mu H)Q\,[Q(H-E_0)Q]^{-1}.$$
+
+After whitening by the quantum metric, the curvature becomes a compression of a fixed signature matrix by the row space of the response channel. When that row space is Haar distributed, the curvature eigenvalues form an exact complex-Jacobi process. The algorithm therefore replaces a large, model-specific matrix comparison with a finite-rank analytic law containing the correct rank, support, and boundary atoms.
+
+### Determinantal-kernel form factor
+
+The connected curvature form factor is evaluated directly from the unfolded finite-Jacobi determinantal kernel. For \(D>M\), the signature compression produces exact atoms at \(\lambda=\pm1\). Separating their algebraic multiplicities yields
+
+$$K_{J,c}^{\mathrm{full}}(\tau)=\frac{k}{D}K_{J,c}^{(k)}(\tau),\qquad k=2M-D.$$
+
+At \(D=800\), the calculation resolves 120 atoms on each boundary and a connected plateau of \(0.7\). This finite-rank correction is available analytically and is implemented as an executable theorem.
+
+### Gauge-invariant four-channel law
+
+The whitened response tensor
+
+$$T_{\mu\nu\rho\sigma}=\frac{1}{D}\operatorname{Tr}(\widetilde X_\mu\widetilde X_\nu^\dagger\widetilde X_\rho\widetilde X_\sigma^\dagger)$$
+
+is invariant under independent changes of basis in the zero-mode and complementary subspaces. Its complex-Gaussian reference is generated from measured two-point covariances and independent samples, so the normalized residual \(R_4\) measures a genuine connected four-channel component.
+
+### Bundle-isomorphism control of holonomy
+
+For a smooth periodic ambient unitary \(\mathcal U_g(\theta)\),
+
+$$H_g(\theta)=\mathcal U_g(\theta)H_0(\theta)\mathcal U_g^\dagger(\theta)$$
+
+preserves every energy, the external gap, and the vector-bundle isomorphism class. The Berry connection gains the projected one-form
+
+$$A_g=A_0+i\Phi_0^\dagger\mathcal U_g^\dagger d\mathcal U_g\Phi_0,$$
+
+which tunes relative Wilson transport while \(C_1\) stays fixed. This provides a clean causal separation of determinant topology and non-Abelian holonomy.
+
+## Quantitative Results
+
+### Exact spectral-flatness identity
+
+For a \(D\)-fold degenerate zero-mode manifold,
+
+$$K_{E,\mathrm{raw}}=D,\qquad K_{E,c}=0.$$
+
+This exact identity fixes the baseline and motivates the geometric channel.
+
+### Local curvature universality
+
+The physical ensemble contains 20000 independent Kapit–Mueller tangent pairs. At \(\tau=0.5\), the connected curvature form factor is \(0.502\), compared with \(0.501\) from the exact finite-\(D\) Jacobi kernel. A full-rank Fourier tangent family produces \(4.476\), cleanly resolving microscopic structure at the same active rank.
+
+### Matrix-element Geometric ETH
+
+| \(N\) | \(D\) | Physical median \(R_4\) | Matched Gaussian median | Connected excess |
+|---:|---:|---:|---:|---:|
+| 3 | 16 | 0.37093 | 0.21708 | 0.15385 |
+| 4 | 25 | 0.24715 | 0.14638 | 0.10078 |
+| 5 | 36 | 0.20906 | 0.12723 | 0.08183 |
+
+The monotone decrease reveals progressive Gaussianization, while the resolved connected component defines the registered `deformed_geometric_eth` branch.
+
+### Fixed-Chern holonomy
+
+| \(N\) | \(D\) | \(C_1\) | Minimum external gap | Base Wilson \(\langle r\rangle\) | Deformed seed interval |
+|---:|---:|---:|---:|---:|---:|
+| 3 | 16 | 6 | 0.051741 | 0.28849 | [0.30837, 0.35754] |
+| 4 | 25 | 10 | 0.094695 | 0.30998 | [0.32379, 0.34411] |
+
+The complete spectrum and \(C_1\) stay fixed across the family. The Wilson shift is reproducible across seeds and occupies a structured regime distinct from CUE, establishing `fixed_chern_deformed_holonomy`.
+
+## Innovation-to-Evidence Matrix
+
+| Innovation | Primary evidence | Independent verification |
+|---|---|---|
+| Exact spectral-flatness baseline | Figure 1 and Eq. (1) | Analytic form-factor tests |
+| Finite-Jacobi curvature algorithm | Figures 1, 2, and 5 | Quadrature stability and Monte Carlo cross-checks |
+| Independent spectral/geometric interventions | Figure 3 | Fixed-projector and tangent-channel invariance tests |
+| Correlation hierarchy | Figure 4 | Matrix-level simultaneous confidence bands |
+| Four-channel Geometric ETH | Figure 6 | Gauge randomization and covariance-matched references |
+| Fixed-Chern Wilson engineering | Figure 7 | Mesh convergence, branch margins, and isospectral checks |
+| Reproducible public release | Release manifest | Hash, link, blob-size, isolation, PDF, and test audits |
+
+## Delivery Package
+
+- [17-page article PDF](../01_task_folder/task_05/script/output/spectral_silence_and_geometric_chaos_v3.pdf)
+- [Task release guide](../01_task_folder/task_05/README.md)
+- [Machine-readable release manifest](../01_task_folder/task_05/script/output/release_manifest_v1.json)
+- [Combined PDF/article audit](../01_task_folder/task_05/script/output/geometric_eth_topology_delivery_audit_v3.json)
+- [Matrix-element artifact](../01_task_folder/task_05/script/output/matrix_element_geometric_eth_v3.json)
+- [Topology artifact](../01_task_folder/task_05/script/output/topological_holonomy_v3.json)
+- [Seven-figure package](../01_task_folder/task_05/script/output/figure_1_spectral_silence_v2.png)
+- [Public challenge handoff](2026-07-30-quantum-geometry-harness-challenge-draft.md)
+
+## Verification
+
+The compact review path is:
+
+```bash
+cd 01_task_folder/task_05/script
+python -m pip install -r requirements.txt
+bash run_quick_verify_v1.sh
+```
+
+It checks 17 release-contract classes and 38 focused tests. The complete compact-checkout suite reports 86 passing tests plus 6 production-data tests that activate when their manifest-listed arrays are restored. The article build independently compiles and audits all 17 pages, seven figures, references, metadata, and source synchronization.
+
+## Forward Program
+
+The release opens three high-value directions:
+
+1. extend the genuine fixed-two-quasihole sequence through \(N=6\) and resolve the asymptotic four-channel law;
+2. transfer the invariant response-tensor protocol to a second exact-degeneracy mechanism;
+3. connect local curvature, operator cumulants, and Wilson transport to dynamical observables.
+
+The combined analytic reduction and reproducible numerical architecture make each direction immediately testable. The public challenge packages these goals into machine-verifiable outcomes and welcomes independent implementations.
diff --git a/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/.gitignore b/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/.gitignore
new file mode 100644
index 000000000..8c7e43ebe
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/.gitignore
@@ -0,0 +1,8 @@
+*.aux
+*.bbl
+*.blg
+*.fdb_latexmk
+*.fls
+*.log
+*.out
+*Notes.bib
diff --git a/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/appendices/matrix-element-topology-v3.tex b/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/appendices/matrix-element-topology-v3.tex
new file mode 100644
index 000000000..1567b6a7f
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/appendices/matrix-element-topology-v3.tex
@@ -0,0 +1,128 @@
+\section{Gauge-invariant response cumulants and bundle topology}
+\label{app:matrix-topology}
+
+\subsection{Response maps and gauge covariance}
+
+Let \(\Phi_P(\lambda)\) and \(\Phi_Q(\lambda)\) be orthonormal frames for the \(D\)-dimensional zero-mode fiber and its resolved complement, respectively. For a fixed local perturbation \(V_\mu\), we use the complement-to-fiber response map
+\begin{equation}
+ X_\mu=R_Q QV_\mu P,\qquad R_Q=[Q(H-E_0)Q]^{-1},
+ \label{eq:appendix-response-map}
+\end{equation}
+whose matrix in these frames has shape \(M\times D\). Independent frame changes \(\Phi_P\mapsto\Phi_PU_P\) and \(\Phi_Q\mapsto\Phi_QU_Q\) act as
+\begin{equation}
+ X_\mu\mapsto U_Q^\dagger X_\mu U_P.
+ \label{eq:response-gauge-transformation}
+\end{equation}
+Consequently the channel-label covariance
+\begin{equation}
+ C_{\mu\nu}=\frac{1}{D}\Tr(X_\mu^\dagger X_\nu)
+ \label{eq:channel-label-covariance}
+\end{equation}
+is independent of both frame gauges. On the strictly positive support of \(C\), define \(\widetilde X_\mu=(C^{-1/2})_{\mu\nu}X_\nu\). The algebraic support projection retains precisely the accessible perturbation directions. The normalized four-channel tensor
+\begin{equation}
+ T_{\mu\nu\rho\sigma}
+ =\frac{1}{D}\Tr\!\left(
+ \widetilde X_\mu^\dagger\widetilde X_\nu
+ \widetilde X_\rho^\dagger\widetilde X_\sigma\right)
+ \label{eq:invariant-four-channel-tensor}
+\end{equation}
+is therefore invariant under \(U(M)\times U(D)\) frame rotations. Label-space rotations transform all four indices covariantly, so the Frobenius norm of its connected part is label-basis independent as well.
+
+\subsection{Separable Gaussian contraction}
+
+The covariance-matched null model is a complex Gaussian response tensor satisfying
+\begin{equation}
+ \mathbb E[(X_\mu)_{ai}(X_\nu)^*_{bj}]
+ =\delta_{\mu\nu}R_{ab}L_{ij},
+ \qquad
+ \frac{\Tr R\,\Tr L}{D}=1 .
+ \label{eq:separable-gaussian-covariance}
+\end{equation}
+Here \(R\) and \(L\) are positive external- and target-space covariances; the last identity is precisely the label-whitening normalization. Expanding Eq.~\eqref{eq:invariant-four-channel-tensor} in indices gives
+\begin{equation}
+ T_{\mu\nu\rho\sigma}
+ =\frac{1}{D}\sum_{abij}
+ X_{\mu,ai}^*X_{\nu,aj}
+ X_{\rho,bj}^*X_{\sigma,bi}.
+ \label{eq:four-channel-indices}
+\end{equation}
+Complex Wick contraction permits two pairings. Pairing \((\mu,\nu)\) and \((\rho,\sigma)\) yields
+\begin{equation}
+ \frac{(\Tr R)^2\Tr L^2}{D}
+ \delta_{\mu\nu}\delta_{\rho\sigma}
+ =A_L\delta_{\mu\nu}\delta_{\rho\sigma},
+ \qquad
+ A_L=D\frac{\Tr L^2}{(\Tr L)^2}.
+ \label{eq:left-wick-pairing}
+\end{equation}
+Pairing \((\mu,\sigma)\) and \((\rho,\nu)\) instead yields
+\begin{equation}
+ \frac{\Tr R^2(\Tr L)^2}{D}
+ \delta_{\mu\sigma}\delta_{\rho\nu}
+ =B_R\delta_{\mu\sigma}\delta_{\rho\nu},
+ \qquad
+ B_R=D\frac{\Tr R^2}{(\Tr R)^2}.
+ \label{eq:right-wick-pairing}
+\end{equation}
+Thus
+\begin{equation}
+ \begin{aligned}
+ T^{\rm Wick}_{\mu\nu\rho\sigma}
+ &=A_L\delta_{\mu\nu}\delta_{\rho\sigma}
+ +B_R\delta_{\mu\sigma}\delta_{\rho\nu},\\
+ R_4&=\frac{\|T-T^{\rm Wick}\|_F}{\|T^{\rm Wick}\|_F}.
+ \end{aligned}
+ \label{eq:wick-residual-appendix}
+\end{equation}
+This defines a finite-dimensional distribution of \(R_4\). The comparison ensemble is generated with the measured spectra of \(L\) and \(R\), passed through the identical whitening map, and evaluated at the same \((D,M,m)\).
+
+\subsection{External covariance through a compact Gram space}
+
+Stack the whitened maps as \(\mathsf X=(\widetilde X_1\,\widetilde X_2\cdots\widetilde X_m)\), an \(M\times mD\) matrix. The external covariance and its Gram reduction are
+\begin{equation}
+ R=\frac{1}{m}\mathsf X\mathsf X^\dagger,\qquad
+ G=\frac{1}{m}\mathsf X^\dagger\mathsf X.
+ \label{eq:gram-reduction}
+\end{equation}
+If \(R u=\lambda u\) with \(\lambda\ne0\), then \(\mathsf X^\dagger u\ne0\) and \(G(\mathsf X^\dagger u)=\lambda(\mathsf X^\dagger u)\); the reverse implication follows by applying \(\mathsf X\). Hence \(R\) and \(G\) have identical nonzero spectra, including multiplicities. The coefficient \(B_R\) is therefore evaluated efficiently in the \(mD\)-dimensional Gram space.
+
+\subsection{Periodic ambient conjugation}
+
+Let \(E_0\to T^2\) be the base zero-mode bundle and let \(\mathcal U_g:T^2\to U(\mathcal H)\) be smooth and periodic. The deformed Hamiltonian and projector are
+\begin{equation}
+ \begin{aligned}
+ H_g(\theta)
+ &=\mathcal U_g(\theta)H_0(\theta)\mathcal U_g^\dagger(\theta),\\
+ P_g(\theta)
+ &=\mathcal U_g(\theta)P_0(\theta)\mathcal U_g^\dagger(\theta).
+ \end{aligned}
+ \label{eq:periodic-ambient-conjugation}
+\end{equation}
+Every eigenvalue, the kernel dimension, and the external gap are identical pointwise. More strongly, \((\theta,v)\mapsto(\theta,\mathcal U_g(\theta)v)\) is a globally defined vector-bundle isomorphism \(E_0\simeq E_g\). Naturality of Chern classes therefore gives
+\begin{equation}
+ c_1(E_g)=c_1(E_0).
+ \label{eq:chern-isomorphism}
+\end{equation}
+The same conclusion follows at the level of connections. For a local frame \(\Phi_g=\mathcal U_g\Phi_0\) and the convention \(A=i\Phi^\dagger\dd\Phi\),
+\begin{equation}
+ A_g=A_0+i\Phi_0^\dagger\mathcal U_g^\dagger
+ (\dd\mathcal U_g)\Phi_0
+ \equiv A_0+\mathcal A_g.
+ \label{eq:connection-shift}
+\end{equation}
+The difference \(\mathcal A_g\) is a globally defined endomorphism-valued one-form on the identified bundle. Since \(\Tr[A_\mu,A_\nu]=0\),
+\begin{equation}
+ \Tr F_g-\Tr F_0=\dd\,\Tr\mathcal A_g,\qquad
+ \frac{1}{2\pi}\int_{T^2}(\Tr F_g-\Tr F_0)=0.
+ \label{eq:chern-exact-difference}
+\end{equation}
+Equation~\eqref{eq:connection-shift} also explains the compatibility of fixed topology and variable holonomy. For a generic projected one-form \(\mathcal A_g\), the path-ordered exponential changes around a noncontractible cycle. The determinant winding remains constrained by Eq.~\eqref{eq:chern-isomorphism}, while the relative \(SU(D)\) eigenphases may deform.
+
+\subsection{Discrete links and branch control}
+
+On a periodic mesh, neighboring physical many-body frames have overlap \(M_\ell\). We use its polar unitary \(U_\ell=M_\ell(M_\ell^\dagger M_\ell)^{-1/2}\), so arbitrary local \(U(D)\) frame gauges act on links by endpoint conjugation. Plaquette products transform by similarity, and both their eigenphases and \(\arg\det W_\square\) are gauge invariant. The lattice first Chern estimator is
+\begin{equation}
+ C_1=\frac{1}{2\pi}\sum_\square\arg\det W_\square.
+ \label{eq:lattice-chern-v3}
+\end{equation}
+We require positive overlap singular-value and determinant-branch margins, agreement of determinant and trace-log estimators, and the same integer on two meshes. Directly unwrapping determinant Wilson phases can alias when the flux accumulated across an entire transverse strip exceeds \(\pi\); Fig.~\ref{fig:topological-holonomy} instead accumulates the branch-resolved plaquette flux within each strip. The retained \(12\times12\) alias preflight and accepted \(16\times16\)/\(20\times20\) pair make this distinction explicit.
diff --git a/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/appendices/numerical-methods.tex b/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/appendices/numerical-methods.tex
new file mode 100644
index 000000000..993ff4985
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/appendices/numerical-methods.tex
@@ -0,0 +1,246 @@
+\section{Numerical methods, inference, and reproducibility}
+\label{app:numerics}
+
+\subsection{Physical parent and response cache}
+
+The single-particle Kapit--Mueller hopping matrix is constructed with
+magneto-periodic boundary conditions and projected to its flat lowest band
+\cite{kapitmueller2010}.
+The many-body contact interaction is represented as a positive constraint
+factor before diagonalization.
+Its numerical null space supplies \(P\); the nonzero eigenvectors and energy
+denominators supply \(R\) in Eq.~\eqref{eq:reduced-resolvent}.
+For a site-potential coefficient vector \(v\), linearity is used to cache
+\(X[v]=PV[v]R\).
+Every sampled channel is checked against a direct many-body
+Hilbert--Schmidt norm, and every normalized curvature is audited for
+\(YY^\dagger=I_r\), Hermiticity, rank, and
+\(\operatorname{spec}\Omega\subset[-1,1]\).
+
+The random-local ensemble has \(\PhysicalMatrices\) tangent pairs in eight
+independently seeded blocks.
+A fixed permutation determines a \(12000/4000/4000\)
+training/validation/test split before any density, covariance, or form-factor
+comparison.
+The \(\PhysicalTestMatrices\)-matrix test set is used in all v2 physical
+figures.
+The Fourier reference enumerates all nonzero momenta and combines them into
+the \(\StructuredOrbits\) distinct \(\bm q\leftrightarrow-\bm q\) orbit-level
+statistical units.
+
+\subsection{Exact finite-Jacobi quadrature}
+
+Equation~\eqref{eq:finite-jacobi-sff} is evaluated directly by quadrature.
+At Gauss--Jacobi nodes \(x_i\) and weights \(\omega_i\) of order \(q=512\),
+we form the weighted orthonormal basis
+\begin{equation}
+ \Phi_{in}=\sqrt{\omega_i}\,
+ \frac{P_n^{(a,a)}(x_i)}{\sqrt{h_n^{(a)}}},
+ \qquad 0\leq n<k ,
+ \label{eq:quadrature-basis}
+\end{equation}
+where
+\begin{equation}
+ h_n^{(a)}
+ =\frac{2^{2a+1}}{2n+2a+1}
+ \frac{\Gamma(n+a+1)^2}{\Gamma(n+1)\Gamma(n+2a+1)} .
+ \label{eq:jacobi-norm}
+\end{equation}
+The discrete projection kernel is \({\cal P}=\Phi\Phi^\dagger\), its diagonal
+is the quadrature mass of \(\rho_k\), and the midpoint cumulative sum of that
+diagonal implements Eq.~\eqref{eq:finite-unfolding}.
+The registered \(D=50,M=170\) calculation has density-mass error
+\(4.19\times10^{-13}\) and basis-orthogonality error
+\(4.18\times10^{-13}\).
+Repeating the complete curve at quadrature orders \(384\) and \(512\) changes
+it by less than \(5\times10^{-5}\).
+
+As an independent test, two complex Wishart matrices generate the
+matrix-beta Jacobi ensemble.
+For rank \(16\), \(1500\) independently sampled spectra agree with the
+determinantal-kernel connected SFF within \(0.075\) over the registered test
+grid.
+For \(r>M\), exact \(\pm1\) atoms are appended algebraically.
+The identity in Eq.~\eqref{eq:atom-plateau} is satisfied to floating-point
+zero, and the raw decomposition
+Eq.~\eqref{eq:atom-raw-decomposition} closes within
+\(1.14\times10^{-13}\).
+
+\subsection{Interpolation ensembles}
+
+The geometric interpolation uses
+\[
+ g=0,\ 0.02,\ 0.05,\ 0.10,\ 0.20,\ 0.40,\ 0.70,\ 1.00 .
+\]
+At every positive \(g\), \(\GeometricSamplesPerPoint\) independent random
+local residual pairs are mixed with a registered Fourier pair through
+Eq.~\eqref{eq:geometric-interpolation}.
+All \(28000\) positive-\(g\) curvature matrices have active rank \(50\).
+The complete script-generated scalar adjacent-gap intervals are retained with
+the numerical artifacts; the Haar--Jacobi simultaneous interval is
+\(0.598440\)--\(0.600349\).
+
+The spectral interpolation uses
+\[
+ \alpha=0,\ 0.10,\ 0.20,\ 0.35,\ 0.50,\ 0.70,\ 0.85,\ 1.00
+\]
+and \(\SpectralSamplesPerPoint\) matrices per value.
+For every sample, the same Poisson and GUE endpoints are used across
+\(\alpha\), which reduces interpolation noise while different samples remain
+independent.
+The target projector is recomputed numerically from the embedded full
+Hamiltonian rather than assumed fixed.
+The maximum measured distance in
+Eq.~\eqref{eq:projector-invariance} and the zero curvature-spectrum error are
+hard delivery gates.
+
+\subsection{Connected estimators and simultaneous inference}
+
+Raw, disconnected, and connected form factors are retained separately for
+every ensemble:
+\begin{equation}
+ \widehat K_{\rm raw}
+ =\frac{1}{D N_s}\sum_{s=1}^{N_s}|Z_s|^2,\qquad
+ \widehat K_{\rm disc}
+ =\frac{1}{D}\left|\frac{1}{N_s}\sum_{s=1}^{N_s}Z_s\right|^2 .
+ \label{eq:empirical-sff}
+\end{equation}
+Their difference is the displayed connected estimator.
+This common convention is used for the exact-degenerate energy baseline,
+physical curvature, Fourier control, interpolation ensembles, and Monte Carlo
+Jacobi reference.
+At \(\tau=0\), connected values below \(5\times10^{-15}\) are set to zero
+only after raw-minus-disconnected subtraction.
+
+Complete matrices are the independent statistical units.  Physical curves are
+first averaged within eight independent seed blocks;
+Fourier curves are averaged within the twelve momentum orbits; the Haar
+reference uses complete matrices.
+We construct \(\BootstrapReplicatesVTwo\)-replicate Gaussian-multiplier or
+hierarchical-block processes and take the 95th percentile of the maximum
+studentized deviation over each registered grid.
+Thus every shaded region used for an onset or compatibility statement is a
+simultaneous confidence band across the complete registered grid.
+
+For an SFF residual band \([\ell(\tau),u(\tau)]\), the registered compatibility
+onset is the first grid point \(\tau_*\in[0.25,1.5]\) such that
+\(0\in[\ell(\tau),u(\tau)]\) for every subsequent registered point.
+An interpolation value \(g\) is said to possess a nontrivial compatibility
+window only if at least eight grid points remain.
+The number-variance compatibility extent is the largest \(L\) in the
+contiguous initial interval beginning at \(L=0.25\) whose residual band
+contains zero.
+These definitions were fixed before reading the reported onsets.
+
+\subsection{One-point covariance and finite-rank sequence}
+
+The v1 analysis retained in the present expanded article tests a distinct
+observable: the ensemble-mean ambient row-space projector
+\begin{equation}
+ \overline\Pi=\mathbb E[Y^\dagger Y].
+ \label{eq:mean-row-projector}
+\end{equation}
+A covariance-deformed Gaussian row-space ensemble learned from
+\(\TrainingRows\) training matrices and selected on validation data reduces
+the held-out density \(L^1\) error from \(\DensityHaarLone\) to
+\(\DensityCovLone\), while preserving the local gap ratio.
+The exact Jacobi SFF in v2 remains parameter free; this result explains why
+one-point and long-range observables can retain structure alongside local
+two-level agreement.
+
+For the rank sequence, cyclic \((1,2)\)-admissible root configurations and
+their one-body descendants are generated independently of the lattice cache.
+The seven registered sample counts are
+\[
+ 2000,\ 2000,\ 2000,\ 1000,\ 1000,\ 500,\ 250 .
+\]
+Atoms are labeled by Eq.~\eqref{eq:atom-count} before their numerical
+eigenvalues are inspected.
+The final \(D=800\) case therefore contains \(120+120\) exact atoms and
+\(560\) interior levels in every matrix.
+Because \(N=3\) remains fixed, changes along this sequence are described as
+finite-rank evidence only.
+
+\subsection{Many-body Wick sequence}
+
+The fixed-two-quasihole sequence uses \(n_\phi=2N+2\) and the exact cyclic
+zero-mode ranks \(D=16,25,36\).
+The \(N=3,4\) parents are diagonalized densely.
+For \(N=5\), the complete 36-column kernel frame is obtained by a block sparse
+eigensolver; its residual norm is \(3.59\times10^{-9}\).
+Complement resolvents are evaluated at two positive shifts and extrapolated
+linearly to zero shift.
+The maximum \(N=5\) relative equation residual is
+\(2.75\times10^{-7}\), and the maximum two-shift difference is
+\(3.94\times10^{-4}\).
+The physical sequence begins at \(N=3\), since the \(N=2,n_\phi=6\)
+Kapit--Mueller parent has 12 numerical zero modes compared with the cyclic
+target rank nine.
+
+\begin{table*}[t]
+ \caption{Registered matrix-element sequence. The Gaussian column is the
+ covariance-matched finite-size median; ``excess'' is the physical median
+ minus that value.}
+ \label{tab:matrix-element-v3}
+ \begin{ruledtabular}
+ \begin{tabular}{cccccccc}
+ \(N\) & \(n_\phi\) & \(D\) & \(\dim\mathcal H\) & \(\Delta\) &
+ \(R_4\) & \(R_4^{\rm G}\) & excess\\
+ \MatrixElementResultRows
+ \end{tabular}
+ \end{ruledtabular}
+\end{table*}
+
+For each size, 24 deterministic balanced local-density panels supply the
+physical resampling units.
+Each panel has eight operators.
+The finite-size null uses 2000 complete covariance-matched Gaussian response
+tensors per size.
+All target and external gauge checks are applied before the four-channel
+tensor is evaluated.
+
+\subsection{Closed twist bundle and Wilson statistics}
+
+The base twist bundles are diagonalized at every point of the periodic mesh.
+Physical many-body overlaps include the exact symmetric bosonic lift of the
+single-particle orbital overlap.
+The undeformed \(6\times6\) and \(8\times8\) meshes establish the base
+integer.  A \(12\times12\) preflight identifies a determinant-branch alias
+and a shifted \(C_1=8\) for one \(N=4,g=1\) seed.  The accepted production
+pair \(16\times16\) and \(20\times20\) resolves the full \(g\leq1\) orbit,
+with the coarse alias artifact retained for provenance.
+
+\begin{table*}[t]
+ \caption{Accepted closed-surface topology and Wilson statistics. The final
+ and CUE columns are median circular adjacent-gap ratios.}
+ \label{tab:topology-v3}
+ \begin{ruledtabular}
+ \begin{tabular}{cccccccc}
+ \(N\) & \(D\) & \(C_1\) & \(\Delta_{\min}\) &
+ branch margin & overlap minimum & \(\langle r_W\rangle_{g=1}\) &
+ \(\langle r_W\rangle_{\rm CUE}\)\\
+ \TopologyResultRows
+ \end{tabular}
+ \end{ruledtabular}
+\end{table*}
+
+Eight independently seeded noncommuting generator pairs and one commuting
+control are evaluated at \(g=0,0.25,0.5,0.75,1\).
+Generator seeds are the cluster units in the bootstrap.
+The CUE reference contains 10000 independent matrices per rank.
+Per-loop arrays are retained within their generator-seed clusters for
+bootstrap inference.
+
+\subsection{Reproducibility gates}
+
+The task-local delivery requires regenerated hashes for every source artifact;
+exact registered sample counts, ranks, and interpolation points; disjoint
+training, validation, and test indices; matrix-level confidence calculations;
+finite-Jacobi mass, orthogonality, Monte Carlo, atom, and raw-closure checks;
+fixed-projector error below \(10^{-12}\); synchronized figure hashes; resolved
+LaTeX references; and a render record for every compiled page.  Task isolation
+keeps the v3 implementation fully self-contained.  Additional gates require
+both independent v3 audits, the registered \(16/20\) topology pair, the
+retained coarse-mesh alias preflight, exact result branches, executable Wick
+and Chern identities, and source hashes for
+Figs.~\ref{fig:wick-factorization} and~\ref{fig:topological-holonomy}.
diff --git a/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/figures/figure_1_physical_law_v1.pdf b/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/figures/figure_1_physical_law_v1.pdf
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diff --git a/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/figures/figure_1_spectral_silence_v2.pdf b/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/figures/figure_1_spectral_silence_v2.pdf
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diff --git a/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/figures/figure_3_atom_crossover_v1.pdf b/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/figures/figure_3_atom_crossover_v1.pdf
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diff --git a/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/figures/figure_3_independent_channels_v2.pdf b/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/figures/figure_3_independent_channels_v2.pdf
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diff --git a/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/figures/figure_4_finite_size_v1.pdf b/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/figures/figure_4_finite_size_v1.pdf
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diff --git a/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/figures/figure_4_geometric_hierarchy_v2.pdf b/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/figures/figure_4_geometric_hierarchy_v2.pdf
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diff --git a/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/figures/figure_5_covariance_mechanism_v1.pdf b/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/figures/figure_5_covariance_mechanism_v1.pdf
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diff --git a/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/figures/figure_5_jacobi_atoms_v2.pdf b/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/figures/figure_5_jacobi_atoms_v2.pdf
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diff --git a/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/figures/figure_6_wick_factorization_v3.pdf b/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/figures/figure_6_wick_factorization_v3.pdf
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diff --git a/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/figures/figure_7_topological_holonomy_v3.pdf b/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/figures/figure_7_topological_holonomy_v3.pdf
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diff --git a/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/generated/generated_numbers_v1.tex b/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/generated/generated_numbers_v1.tex
new file mode 100644
index 000000000..7edcf9088
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/generated/generated_numbers_v1.tex
@@ -0,0 +1,30 @@
+\newcommand{\PhysicalMatrices}{20000}
+\newcommand{\PhysicalTestMatrices}{4000}
+\newcommand{\PhysicalRank}{50}
+\newcommand{\PhysicalChannels}{170}
+\newcommand{\TrainingRows}{1024}
+\newcommand{\HaarMatrices}{10000}
+\newcommand{\DeformedMatrices}{10000}
+\newcommand{\SelectedCovFloor}{0.050}
+\newcommand{\DensityHaarLone}{0.2910}
+\newcommand{\DensityCovLone}{0.1237}
+\newcommand{\DensityImprovementPercent}{57.5\%}
+\newcommand{\PhysicalGapRatio}{0.599806}
+\newcommand{\HaarGapRatio}{0.599395}
+\newcommand{\DeformedGapRatio}{0.599200}
+\newcommand{\LargestRank}{800}
+\newcommand{\LargestChannels}{680}
+\newcommand{\LargestAtomMultiplicity}{120}
+\newcommand{\LargestAtomWeightPercent}{30.0\%}
+\newcommand{\LargestInteriorDensityLone}{0.0523}
+\newcommand{\DensityFitExponent}{0.593}
+\newcommand{\BootstrapReplicates}{10000}
+\newcommand{\RootMatricesTotal}{8750}
+\newcommand{\CovarianceAnisotropy}{0.867}
+\newcommand{\PhysicalParticipation}{0.625}
+\newcommand{\NumberVariancePhysEight}{0.696}
+\newcommand{\NumberVarianceHaarEight}{0.570}
+\newcommand{\NumberVarianceCovEight}{0.570}
+\newcommand{\FormFactorPhysHalf}{0.502}
+\newcommand{\FormFactorHaarHalf}{0.495}
+\newcommand{\FormFactorCovHalf}{0.502}
diff --git a/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/generated/generated_numbers_v2.tex b/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/generated/generated_numbers_v2.tex
new file mode 100644
index 000000000..5f3b57ce1
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/generated/generated_numbers_v2.tex
@@ -0,0 +1,22 @@
+\newcommand{\EnergyRawSFF}{50}
+\newcommand{\EnergyConnectedSFF}{0}
+\newcommand{\StructuredFormHalf}{4.476}
+\newcommand{\PhysicalFormHalf}{0.502}
+\newcommand{\JacobiFormHalf}{0.501}
+\newcommand{\GeometricTauOnset}{0.25}
+\newcommand{\GeometricLocalOnset}{0.20}
+\newcommand{\GeometricRampOnset}{0.40}
+\newcommand{\NumberVarianceExtent}{1.0}
+\newcommand{\NumberResidualEight}{0.12582}
+\newcommand{\NumberResidualEightLower}{0.11428}
+\newcommand{\NumberResidualEightUpper}{0.13736}
+\newcommand{\PoissonEndpointRatio}{0.385645}
+\newcommand{\GUEEndpointRatio}{0.598677}
+\newcommand{\StructuredMomenta}{24}
+\newcommand{\StructuredOrbits}{12}
+\newcommand{\GeometricSamplesPerPoint}{4000}
+\newcommand{\SpectralSamplesPerPoint}{4000}
+\newcommand{\BootstrapReplicatesVTwo}{10000}
+\newcommand{\LargestRankVTwo}{800}
+\newcommand{\LargestAtomEachVTwo}{120}
+\newcommand{\LargestConnectedPlateau}{0.7}
diff --git a/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/generated/generated_numbers_v3.tex b/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/generated/generated_numbers_v3.tex
new file mode 100644
index 000000000..b3c34e8c3
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/generated/generated_numbers_v3.tex
@@ -0,0 +1,30 @@
+% Generated from audited v3 artifacts by the release pipeline.
+\newcommand{\MatrixElementBranch}{deformed\_geometric\_eth}
+\newcommand{\MatrixElementBranchText}{The four-channel residual decreases along the genuine many-body sequence and retains a resolved connected component at the largest size.}
+\newcommand{\LargestManyBodyN}{5}
+\newcommand{\LargestManyBodyRank}{36}
+\newcommand{\LargestManyBodyDimension}{4368}
+\newcommand{\LargestNRFour}{0.20906}
+\newcommand{\LargestGaussianRFour}{0.12723}
+\newcommand{\LargestGaussianRFourLow}{0.12657}
+\newcommand{\LargestGaussianRFourHigh}{0.12797}
+\newcommand{\LargestRFourExcess}{0.08183}
+\newcommand{\TopologyBranch}{fixed\_chern\_deformed\_holonomy}
+\newcommand{\TopologyBranchText}{The Chern class and complete spectrum remain fixed while Wilson statistics change significantly and occupy a structured class distinct from the circular-unitary reference.}
+\newcommand{\TopologyPrimaryMesh}{16}
+\newcommand{\TopologyConvergenceMesh}{20}
+\newcommand{\TopologyNThreeChern}{6}
+\newcommand{\TopologyNFourChern}{10}
+\newcommand{\TopologyNThreeGap}{0.051741}
+\newcommand{\TopologyNFourGap}{0.094695}
+\newcommand{\TopologyNThreeGapChangeLow}{0.02777}
+\newcommand{\TopologyNThreeGapChangeHigh}{0.05068}
+\newcommand{\TopologyNFourGapChangeLow}{0.01805}
+\newcommand{\TopologyNFourGapChangeHigh}{0.02835}
+\newcommand{\TopologyNThreeFinalGapRatio}{0.32115}
+\newcommand{\TopologyNFourFinalGapRatio}{0.33175}
+\newcommand{\TopologyNThreeCUERatio}{0.60153}
+\newcommand{\TopologyNFourCUERatio}{0.60079}
+\newcommand{\TopologyMinimumBranchMargin}{1.17980}
+\newcommand{\TopologyMinimumOverlap}{0.83693}
+\newcommand{\TopologyGaugeError}{6.85e-15}
diff --git a/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/generated/generated_tables_v1.tex b/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/generated/generated_tables_v1.tex
new file mode 100644
index 000000000..0c6cc0d80
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/generated/generated_tables_v1.tex
@@ -0,0 +1,13 @@
+\begin{tabular}{rrrrrr}
+\hline\hline
+$D$ & $M$ & samples & atoms/edge & $\Delta\langle r\rangle$ & $L^1_{\rm int}$ \\
+\hline
+16 & 80 & 2000 & 0 & 0.03023 & 0.43375 \\
+50 & 140 & 2000 & 0 & 0.00767 & 0.22916 \\
+112 & 216 & 2000 & 0 & 0.00403 & 0.14094 \\
+210 & 308 & 1000 & 0 & 0.00173 & 0.09624 \\
+352 & 416 & 1000 & 0 & 0.00290 & 0.06866 \\
+546 & 540 & 500 & 6 & 0.00024 & 0.05149 \\
+800 & 680 & 250 & 120 & 0.00423 & 0.05226 \\
+\hline\hline
+\end{tabular}
diff --git a/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/generated/generated_tables_v2.tex b/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/generated/generated_tables_v2.tex
new file mode 100644
index 000000000..9e38a3fb2
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/generated/generated_tables_v2.tex
@@ -0,0 +1,13 @@
+\begin{tabular}{rrrr}
+\hline\hline
+$g$ & $\langle r_F\rangle$ & lower & upper \\
+\hline
+0.02 & 0.577596 & 0.575437 & 0.579755 \\
+0.05 & 0.590540 & 0.589162 & 0.591919 \\
+0.10 & 0.594497 & 0.592683 & 0.596310 \\
+0.20 & 0.598927 & 0.597464 & 0.600390 \\
+0.40 & 0.599034 & 0.597900 & 0.600167 \\
+0.70 & 0.599670 & 0.597824 & 0.601517 \\
+1.00 & 0.600307 & 0.598866 & 0.601749 \\
+\hline\hline
+\end{tabular}
diff --git a/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/generated/generated_tables_v3.tex b/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/generated/generated_tables_v3.tex
new file mode 100644
index 000000000..aad5da441
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/generated/generated_tables_v3.tex
@@ -0,0 +1,10 @@
+% Generated from audited v3 artifacts by the release pipeline.
+\newcommand{\MatrixElementResultRows}{%
+3 & 8 & 16 & 120 & 0.055872 & 0.37093 & 0.21708 & 0.15385 \\
+4 & 10 & 25 & 715 & 0.103502 & 0.24715 & 0.14638 & 0.10078 \\
+5 & 12 & 36 & 4368 & 0.093593 & 0.20906 & 0.12723 & 0.08183 \\
+}
+\newcommand{\TopologyResultRows}{%
+3 & 16 & 6 & 0.051741 & 2.06643 & 0.85325 & 0.32115 & 0.60153 \\
+4 & 25 & 10 & 0.094695 & 1.17980 & 0.83693 & 0.33175 & 0.60079 \\
+}
diff --git a/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/main.pdf b/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/main.pdf
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diff --git a/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/main.tex b/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/main.tex
new file mode 100644
index 000000000..e608d0547
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/main.tex
@@ -0,0 +1,68 @@
+\documentclass[aps,prb,reprint,superscriptaddress,longbibliography,floatfix]{revtex4-2}
+
+\usepackage{amsmath,amssymb,bm}
+\usepackage{booktabs}
+\usepackage{graphicx}
+\usepackage{microtype}
+\usepackage{xcolor}
+\usepackage[colorlinks=true,citecolor=blue!55!black,linkcolor=blue!55!black,urlcolor=blue!55!black]{hyperref}
+\hypersetup{
+  pdftitle={Spectral Silence and Geometric Chaos in an Exactly Degenerate Topological Manifold},
+  pdfauthor={Thomas J. Wang; OKongOYangO},
+  pdfsubject={Exact degeneracy, non-Abelian Berry curvature, geometric chaos, and finite Jacobi form factors}
+}
+
+\graphicspath{{figures/}}
+\input{generated/generated_numbers_v1.tex}
+\input{generated/generated_numbers_v2.tex}
+\input{generated/generated_numbers_v3.tex}
+\input{generated/generated_tables_v3.tex}
+
+\newcommand{\Tr}{\operatorname{Tr}}
+\newcommand{\rank}{\operatorname{rank}}
+\newcommand{\cH}{\mathcal{H}}
+\newcommand{\cS}{\mathcal{S}}
+\newcommand{\dd}{\mathrm{d}}
+
+\begin{document}
+
+\title{Spectral Silence and Geometric Chaos in an\texorpdfstring{\\}{ }
+Exactly Degenerate Topological Manifold}
+
+\author{Thomas J. Wang}
+\affiliation{Tsinghua University, Beijing 100084, China}
+
+\author{OKongOYangO}
+\affiliation{The Pennsylvania State University, University Park, Pennsylvania 16802, USA}
+
+\date{\today}
+
+\begin{abstract}
+Exact degeneracy silences every internal level-spacing diagnostic and elevates quantum geometry into the primary signal. We establish an independently testable hierarchy of projector correlations in a bosonic fractional-quantum-Hall zero-mode manifold. The energy spectral form factor obeys the exact identities \(K_{E,\mathrm{raw}}=D\) and \(K_{E,c}=0\), while the quantum-metric-normalized non-Abelian Berry curvature follows the finite-\(D\) complex-Jacobi ramp over a registered window. Structured-tangent and fixed-projector interventions resolve geometric chaos independently from active rank and intramultiplet spectral statistics; exact boundary atoms at \(D>M\) yield the analytic connected plateau \(k/D\). We then introduce a matrix-element Geometric-ETH test. On the genuine fixed-two-quasihole sequence \(N=3,4,5\), a covariance-whitened, gauge-invariant four-channel residual decreases to \(R_4=\LargestNRFour\) and retains a resolved connected component relative to its matched Gaussian interval, selecting deformed Geometric ETH. On the closed twist torus, a smooth periodic ambient conjugation preserves the complete spectrum, gap, and Chern numbers \(C_1=6,10\) for \(N=3,4\), while Wilson gap ratios change significantly and occupy a structured universality class distinct from circular-unitary transport. Exact degeneracy therefore reveals three complementary geometric layers: finite-Jacobi local correlations, operator-channel memory, and tunable non-Abelian holonomy inside one fixed topological class.
+\end{abstract}
+
+\maketitle
+
+\input{sections/01-introduction.tex}
+\input{sections/02-ensembles.tex}
+\input{sections/03-physical-law.tex}
+\input{sections/04-covariance-eth.tex}
+\input{sections/05-rank-crossover.tex}
+\input{sections/06-thouless-hierarchy.tex}
+\input{sections/08-matrix-elements-topology.tex}
+\input{sections/07-conclusion.tex}
+
+\appendix
+\input{appendices/numerical-methods.tex}
+\input{appendices/matrix-element-topology-v3.tex}
+
+\section*{Code and data availability}
+The public repository \url{https://github.com/JunkaiWang-TheoPhy/Chaos-of-Quantum-Geometry} contains the complete source, tests, seven figures, generated tables, compact numerical artifacts, and the audited article. From \texttt{01\_task\_folder/task\_05/script}, \texttt{bash run\_quick\_verify\_v1.sh} verifies the release contract and focused analytic tests, while \texttt{bash run\_full\_recompute\_v1.sh} executes the complete production pipeline. The machine-readable \texttt{output/release\_manifest\_v1.json} records every Git-resident artifact and every production array with its path, byte size, SHA-256 hash, storage class, and producing command.
+
+\begin{acknowledgments}
+The numerical artifacts, fixed train--validation--test split, matrix-level uncertainty estimates, and figure-generation scripts are retained with the source of this manuscript.
+\end{acknowledgments}
+
+\bibliography{references}
+
+\end{document}
diff --git a/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/references.bib b/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/references.bib
new file mode 100644
index 000000000..903552d16
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/references.bib
@@ -0,0 +1,355 @@
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+}
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+}
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+}
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diff --git a/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/sections/01-introduction.tex b/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/sections/01-introduction.tex
new file mode 100644
index 000000000..abb66527a
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/sections/01-introduction.tex
@@ -0,0 +1,139 @@
+\section{Introduction}
+\label{sec:introduction}
+
+Quantum chaos is conventionally diagnosed in the spectrum of a Hamiltonian.
+After resolving symmetries and unfolding the density of states, chaotic levels
+repel and their long-range correlations approach a Wigner--Dyson random-matrix
+ensemble \cite{bohigas1984,atas2013}.
+The connected spectral form factor packages the same two-level correlations
+into a ramp and plateau.
+The eigenstate thermalization hypothesis (ETH) complements this spectral
+picture by describing matrix elements of observables in the energy basis
+\cite{deutsch1991,srednicki1994,dalessio2016}.
+All three constructions use nonzero energy differences, so exact degeneracy
+opens a complementary regime in which state-space geometry carries the
+resolving information.  For \(D\) states sharing the energy \(E_0\),
+\begin{equation}
+ \begin{aligned}
+ Z_E(t)&=\sum_{a=1}^{D}e^{-itE_a}=D e^{-itE_0},\\
+ K_{E,\mathrm{raw}}(t)&=\frac{|Z_E(t)|^2}{D}=D ,
+ \end{aligned}
+ \label{eq:energy-silence}
+\end{equation}
+and the ensemble-connected form factor is identically zero.  These identities
+exhaust the internal energy statistic while preserving the full projector and
+its response over parameter space.
+
+The alternative studied here is geometric.
+An isolated degenerate eigenspace defines a vector bundle over Hamiltonian
+parameter space.
+Its adiabatic transport is governed by the Wilczek--Zee connection and the
+matrix-valued Berry curvature \cite{kato1950,berry1984,wilczekzee1984};
+the symmetric partner is the quantum metric
+\cite{provostvallee1980,kolodrubetz2017}.
+Adiabatic eigenstate deformations are already known to be sensitive probes of
+integrability breaking \cite{pandey2020}, and the geometry of parameter space
+can distinguish ergodic from integrable random-matrix regimes
+\cite{sharipov2024}.
+Most directly, Chen, Colin-Ellerin, Mamroud, and Papadodimas proposed
+non-Abelian Berry curvature as an intrinsic chaos diagnostic for exactly
+degenerate BPS microstates \cite{chen2026}.
+Their contrast is between structured, often vanishing curvature for smooth
+horizonless sectors and random-matrix-like curvature for supersymmetric black
+hole microstates.
+
+We test that organizing principle in a purely condensed-matter fractional
+topological manifold generated by a local frustration-free parent.
+The manifold is the kernel of a positive semidefinite bosonic
+fractional-quantum-Hall parent Hamiltonian.
+Its degeneracy is exact and algebraic, and its projector is separated from the
+complement by a gap.
+This setting isolates the proposed geometric diagnostic from the special BPS
+mechanism and makes five questions answerable:
+
+\begin{enumerate}
+ \item Does a curvature ramp survive when the energy form factor is exactly
+ silent?
+ \item Does that ramp distinguish random local tangents from structured
+ tangents at the same active rank?
+ \item Can energy chaos and projector-geometric chaos be varied independently?
+ \item Do gauge-invariant response-channel matrix elements approach a
+ covariance-matched Wick law along a genuine many-body sequence?
+ \item Can non-Abelian holonomy change inside a closed bundle while its
+ complete spectrum and Chern class remain fixed?
+\end{enumerate}
+
+Our answers establish five complementary advances across spectrum, local
+geometry, response tensors, topology, and finite-rank structure.
+The metric-normalized curvature is a compression of a fixed signature matrix
+by the row space of projector-to-complement response channels.
+A Haar row space gives an exact finite-dimensional complex Jacobi point
+process, allowing us to derive its connected form factor directly at the
+finite rank used in the calculation.
+The physical random-local-tangent ensemble follows this prediction over the
+registered two-level window.
+A complete momentum-resolved tangent family supplies a same-rank structured
+reference with only a small number of distinct curvature eigenvalues.  The
+adjacent-gap ratio, connected form factor, and number variance place this
+reference in a clearly resolved structured regime.
+
+The central evidence is causal rather than correlational.
+We vary the Hamiltonian restricted to the degenerate fiber,
+\(PHP\), from Poisson to GUE statistics while holding \(P\) and the
+projector-to-complement channels fixed; the energy spectrum changes, whereas
+the Berry curvature remains exactly invariant.
+Separately, we interpolate the tangent channels from Fourier structured to
+random local directions at fixed parent Hamiltonian.
+Local Jacobi repulsion appears at a smaller interpolation strength than the
+full registered form-factor window, while long-range number variance retains
+microscopic memory.
+The resulting order
+\begin{equation}
+ \begin{aligned}
+ \text{local repulsion}
+ &\ \longrightarrow\ \text{two-level ramp}\\
+ &\ \longrightarrow\ \text{long-range rigidity}
+ \end{aligned}
+ \label{eq:headline-hierarchy}
+\end{equation}
+is a measured hierarchy of geometric correlations.
+The form-factor variable is a dimensionless Fourier scale of unfolded
+curvature eigenvalues.  Its connection to real-time dynamics defines a
+separate and promising extension.
+
+Beyond eigenvalue correlations, fixed local operators expose a resolved
+four-channel response cumulant.  Its normalized residual decreases from
+\(N=3\) to \(N=5\), demonstrating progressive Gaussianization together with
+finite-size operator memory relative to the covariance-matched reference.
+On the closed twist torus, a globally periodic ambient conjugation leaves
+every energy and the first Chern class invariant while changing Wilson-loop
+statistics reproducibly.
+The resulting Wilson statistics occupy a structured regime distinct from CUE.
+Together, the response tensor and Wilson sector map how local Jacobi behavior
+coexists with higher and global microscopic structure.
+
+Finally, an independent rank sequence through \(D=\LargestRankVTwo\) resolves
+a finite-dimensional effect unique to signature-compressed ensembles.
+When the active rank exceeds the dimension \(M\) of either signature
+polarization, exact atoms appear at \(\lambda=\pm1\).
+We prove that these deterministic modes reduce the connected plateau from
+one to \(k/D\), where \(k=2M-D\) is the continuous-sector dimension, while the
+continuous complement retains the Jacobi ramp.
+This resolves exact geometric modes and correlated continuous modes within
+one curvature matrix.
+
+The paper is organized as follows.
+Section~\ref{sec:ensembles} derives the projector response, signature
+compression, finite-Jacobi kernel, and atom theorem.
+Section~\ref{sec:physical} introduces the fractional topological manifold and
+the structured same-rank comparison.
+Section~\ref{sec:covariance} performs the independent spectral and geometric
+interventions.
+Section~\ref{sec:rank} gives the finite-rank atom form factors.
+Section~\ref{sec:hierarchy} resolves the correlation hierarchy and its
+statistical meaning.
+Section~\ref{sec:matrix-topology} tests response-channel Wick factorization
+and fixed-Chern Wilson holonomy.
+Appendix~\ref{app:numerics} records the numerical and inference protocols.
+Appendix~\ref{app:matrix-topology} gives the gauge-covariance, Wick,
+Gram-reduction, and bundle-isomorphism derivations.
diff --git a/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/sections/02-ensembles.tex b/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/sections/02-ensembles.tex
new file mode 100644
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@@ -0,0 +1,181 @@
+\section{Projector geometry and finite Jacobi theory}
+\label{sec:ensembles}
+
+\subsection{Gauge-invariant response of a degenerate projector}
+
+Let \(H(\lambda)\) have an isolated \(D\)-dimensional eigenspace at energy
+\(E_0\), with spectral projector \(P\), complement \(Q=1-P\), and reduced
+resolvent
+\begin{equation}
+ R=Q\bigl[Q(H-E_0)Q\bigr]^{-1}Q .
+ \label{eq:reduced-resolvent}
+\end{equation}
+For the tangent \(V_\mu=\partial_\mu H\), define the
+projector-to-complement response channel
+\begin{equation}
+ X_\mu=P V_\mu R .
+ \label{eq:channel}
+\end{equation}
+In bases of the degenerate fiber and its coupled complement, \(X_\mu\) is a
+\(D\times M\) matrix.
+Kato perturbation theory gives, for two real directions \(v,w\),
+\begin{equation}
+ F_{vw}=i\left(X_vX_w^\dagger-X_wX_v^\dagger\right),\qquad
+ \Gamma=X_vX_v^\dagger+X_wX_w^\dagger .
+ \label{eq:curvature-metric}
+\end{equation}
+Here \(F_{vw}\) is Hermitian under our convention, and \(\Gamma\) is the
+positive two-direction quantum metric.
+Both transform by conjugation under a basis change within \(P\), so the
+generalized eigenvalues of \((F_{vw},\Gamma)\) are gauge invariant.
+
+The raw curvature scale depends on tangent normalization and energy
+denominators.
+We remove it by restricting to the \(r=\rank\Gamma\) support and defining
+\begin{equation}
+ \Omega=\Gamma^{-1/2}F_{vw}\Gamma^{-1/2}.
+ \label{eq:normalized-curvature-intro}
+\end{equation}
+This normalization is algebraic and model agnostic.
+It converts the diagnostic into the relative orientation of the two response
+channels.
+With
+\begin{equation}
+ B=\begin{pmatrix}X_v&X_w\end{pmatrix},\qquad
+ J=\begin{pmatrix}0&iI_M\\-iI_M&0\end{pmatrix},
+ \label{eq:BJ}
+\end{equation}
+whitening gives
+\begin{equation}
+ Y=\Gamma^{-1/2}B,\qquad
+ YY^\dagger=I_r,\qquad
+ \Omega=YJY^\dagger .
+ \label{eq:isometry-compression}
+\end{equation}
+Thus \(\Omega\) is a compression of a fixed matrix with \(M\) positive and
+\(M\) negative eigenvalues.
+Its statistics depend only on an \(r\)-plane in
+\(\mathbb C^{2M}\), i.e., a point on a complex Grassmannian.
+This observation makes the random-matrix reference precise: randomness is
+assigned exclusively to the orientation of the whitened response row space.
+
+\subsection{Finite complex-Jacobi point process}
+
+If the row space of \(Y\) is Haar distributed, the continuously distributed
+eigenvalues of Eq.~\eqref{eq:isometry-compression} form a complex Jacobi
+ensemble \cite{zyczkowski2000,collins2005}.
+For \(r\leq M\), all \(k=r\) levels lie in \((-1,1)\) and
+\begin{equation}
+ p(\lambda_1,\ldots,\lambda_k)\propto
+ \prod_{a<b}|\lambda_a-\lambda_b|^2
+ \prod_{a=1}^{k}(1-\lambda_a^2)^{M-r}.
+ \label{eq:jacobi-density}
+\end{equation}
+More generally, let
+\begin{equation}
+ k=\min(r,2M-r),\qquad a=|M-r| .
+ \label{eq:jacobi-parameters}
+\end{equation}
+After the exact boundary levels derived below are removed, the interior joint
+density has the same form as Eq.~\eqref{eq:jacobi-density} with \(r\) replaced
+by \(k\) and exponent \(a\).
+
+Let \(p_n^{(a)}(x)\) be orthonormal on \((-1,1)\) with weight
+\(w_a(x)=(1-x^2)^a\), and define the weighted projection kernel
+\begin{equation}
+ {\cal K}_k(x,y)=\sqrt{w_a(x)w_a(y)}
+ \sum_{n=0}^{k-1}p_n^{(a)}(x)p_n^{(a)}(y).
+ \label{eq:jacobi-kernel}
+\end{equation}
+Its diagonal \(\rho_k(x)={\cal K}_k(x,x)\) integrates to \(k\).
+The finite-rank unfolding is therefore
+\begin{equation}
+ u(x)=\int_{-1}^{x}\rho_k(s)\,\dd s .
+ \label{eq:finite-unfolding}
+\end{equation}
+For the unfolded partition sum
+\(Z_F(\tau)=\sum_{j=1}^{k}e^{-2\pi i\tau u(\lambda_j)}\), we use one
+normalization throughout:
+\begin{equation}
+ \begin{aligned}
+ K_{F,\mathrm{raw}}(\tau)
+ &=\frac{1}{k}\left\langle |Z_F(\tau)|^2\right\rangle,\\
+ K_{F,\mathrm{disc}}(\tau)
+ &=\frac{1}{k}\left|\left\langle Z_F(\tau)\right\rangle\right|^2,\\
+ K_{F,c}(\tau)&=K_{F,\mathrm{raw}}(\tau)
+ -K_{F,\mathrm{disc}}(\tau).
+ \end{aligned}
+ \label{eq:sff-conventions}
+\end{equation}
+The determinantal identity
+\(\rho_2(x,y)=\rho_k(x)\rho_k(y)-|{\cal K}_k(x,y)|^2\) then yields the exact
+finite-\(k\) prediction
+\begin{equation}
+ K_{J,c}^{(k)}(\tau)
+ =1-\frac{1}{k}\int_{-1}^{1}\!\!\dd x\int_{-1}^{1}\!\!\dd y\,
+ e^{-2\pi i\tau[u(x)-u(y)]}|{\cal K}_k(x,y)|^2 .
+ \label{eq:finite-jacobi-sff}
+\end{equation}
+Equation~\eqref{eq:finite-jacobi-sff} generates the finite-\(D\) ramp directly
+and gives
+\(K_{J,c}^{(k)}(0)=0\) from the projector identity and approaches the unit
+plateau when the oscillatory cluster term is washed out.
+We evaluate the double integral by Gauss--Jacobi quadrature; convergence and
+an independent matrix-beta Monte Carlo comparison are given in
+Appendix~\ref{app:numerics}.
+
+The word ``form factor'' in Eq.~\eqref{eq:sff-conventions} denotes a Fourier
+transform of the curvature point process, with \(\tau\) serving as a
+dimensionless geometric Fourier coordinate.  A future dynamical extension
+can connect this coordinate to operator growth and thermalization scales.
+
+\subsection{Boundary-atom theorem and form-factor plateau}
+\label{sec:atom-theorem}
+
+When \(r>M\), the row space \(\cS\subset\mathbb C^{2M}\) must intersect both
+\(M\)-dimensional eigenspaces \(\cH_\pm\) of \(J\):
+\begin{equation}
+ \dim(\cS\cap\cH_\pm)\geq r+M-2M=r-M .
+ \label{eq:intersection-bound}
+\end{equation}
+Every vector in these intersections is an exact eigenvector of the
+compression with eigenvalue \(\pm1\).
+For a generic \(r\)-plane the bound is saturated, giving
+\begin{equation}
+ m_+=m_-=r-M,\qquad k=2M-r.
+ \label{eq:atom-count}
+\end{equation}
+The atoms are deterministic under the Jacobi ensemble, so their connected
+covariance is exactly zero.
+If the full spectrum is normalized by its total rank \(r\), the exact
+connected form factor is consequently
+\begin{equation}
+ K_{J,c}^{\mathrm{full}}(\tau)
+ =\frac{k}{r}K_{J,c}^{(k)}(\tau),\qquad
+ K_{J,c}^{\mathrm{full}}(\infty)=\frac{k}{r}.
+ \label{eq:atom-plateau}
+\end{equation}
+This is an exact finite-dimensional plateau theorem.
+
+For completeness, the raw, non-unfolded form factor retains deterministic
+interference with the atoms.
+Writing
+\begin{equation}
+ \begin{aligned}
+ Z_{\rm full}(s)&=Z_{\rm at}(s)+Z_{\rm int}(s),\\
+ Z_{\rm at}(s)&=m_-e^{2\pi i s}+m_+e^{-2\pi i s},
+ \end{aligned}
+ \label{eq:atom-partition}
+\end{equation}
+gives the exact decomposition
+\begin{equation}
+ K_{\rm raw}^{\rm full}
+ =\frac{|Z_{\rm at}|^2}{r}
+ +\frac{2\,\mathrm{Re}\!\left[
+ Z_{\rm at}^{*}\langle Z_{\rm int}\rangle\right]}{r}
+ +\frac{\langle|Z_{\rm int}|^2\rangle}{r}.
+ \label{eq:atom-raw-decomposition}
+\end{equation}
+Equations~\eqref{eq:atom-plateau} and
+\eqref{eq:atom-raw-decomposition} distinguish deterministic geometry from
+correlated fluctuations and provide two independent numerical closure tests.
diff --git a/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/sections/03-physical-law.tex b/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/sections/03-physical-law.tex
new file mode 100644
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@@ -0,0 +1,157 @@
+\section{Energy-silent fractional topological manifold}
+\label{sec:physical}
+
+\subsection{Exact zero modes and tangent families}
+
+Our physical anchor is a bosonic Kapit--Mueller lattice parent projected to its
+exactly flat lowest band \cite{kapitmueller2010}.
+At particle number \(N=3\) and flux number \(n=10\), the projected contact
+interaction is positive semidefinite and has an isolated zero-mode manifold
+of dimension \(D=\PhysicalRank\).
+The complement reached by local potentials has dimension
+\(M=\PhysicalChannels\) per tangent direction.
+The zero modes are lattice Laughlin quasihole states obeying the cyclic
+\((1,2)\) exclusion rule \cite{laughlin1983,bernevighaldane2008,chenseidel2015}.
+The numerical kernel width is \(5.78\times10^{-16}\), whereas the external
+gap is \(0.106672\).
+
+This is an exact flat band generated by a purely condensed-matter,
+frustration-free parent construction.  Its kernel is algebraic and provides a
+mechanism complementary to supercharge, index, and BPS-shortening mechanisms.
+The open external gap makes \(P\), \(R\), and \(F_{vw}\) well defined, while
+the exact internal degeneracy enforces Eq.~\eqref{eq:energy-silence}.
+
+We compare two local-potential tangent families at this same parent:
+\begin{equation}
+ V[v]=\sum_{\bm x}v_{\bm x}\hat n_{\bm x},\qquad
+ \sum_{\bm x}v_{\bm x}=0.
+ \label{eq:local-potentials}
+\end{equation}
+The physical ensemble contains \(\PhysicalMatrices\) independent random
+tangent pairs, divided before analysis into
+\(12000/4000/4000\) training, validation, and test matrices.
+Every result below uses the untouched \(\PhysicalTestMatrices\)-matrix test
+set.
+
+The structured reference is the complete nonzero Fourier family on the
+\(5\times5\) lattice.
+For momentum \(\bm q\neq0\), take
+\begin{equation}
+ v_{\bm x}^{(\bm q)}\propto\cos(\bm q\cdot\bm x),\qquad
+ w_{\bm x}^{(\bm q)}\propto\sin(\bm q\cdot\bm x),
+ \label{eq:fourier-control}
+\end{equation}
+normalized in the same many-body tangent metric as the random potentials.
+All \(\StructuredMomenta\) nonzero momenta are enumerated, but
+\(\bm q\) and \(-\bm q\) combine into \(\StructuredOrbits\) independent
+orbit-level statistical units.
+Each Fourier pair has the same active rank \(r=50\) as a random pair, yet its
+curvature has at most ten distinct eigenvalues.
+It therefore separates tangent structure from rank, gap, parent Hamiltonian,
+and normalization.
+
+\subsection{Spectral silence and a geometric ramp}
+
+Figure~\ref{fig:spectral-silence} states the main contrast.
+The exact energy form factor follows Eq.~\eqref{eq:energy-silence}: the raw
+curve is \(D=\EnergyRawSFF\), and the connected curve is
+\(\EnergyConnectedSFF\) for every \(t\).
+The curvature spectrum, however, distinguishes structured Fourier tangents
+from random local tangents at the same rank.
+
+\begin{figure*}[t]
+ \includegraphics[width=\textwidth]{figure_1_spectral_silence_v2.pdf}
+ \caption{
+ \textbf{Exact degeneracy silences the energy spectrum, while projector
+ geometry retains correlated fluctuations.}
+ (a) For \(D=50\) exactly degenerate zero modes, the raw energy SFF is the
+ featureless constant \(D\), and the connected SFF vanishes identically.
+ The marks display the coincident energies of the exact manifold.
+ (b) Representative spectra of the metric-normalized curvature
+ \(\Omega\): structured Fourier tangents retain multiplets, whereas random
+ local tangents produce a resolved spectrum comparable to the Haar--Jacobi
+ reference.
+ (c) Connected curvature SFF of the \(\PhysicalTestMatrices\)-matrix physical
+ test ensemble and the exact finite-\(D\) Jacobi prediction from
+ Eq.~\eqref{eq:finite-jacobi-sff}.
+ The Fourier control is plotted against a separate right axis because it is
+ parametrically larger.
+ (d) The physical-minus-Jacobi residual has a simultaneous confidence band
+ compatible with zero over the registered interval
+ \(0.25\leq\tau\leq1.5\), while the inset shows that physical-minus-Haar number
+ variance becomes positive beyond \(L\simeq1\).
+ Here \(t\) in (a) is conjugate to energy, whereas \(\tau\) in (c,d) is only a
+ dimensionless Fourier variable for unfolded curvature eigenvalues.
+ }
+ \label{fig:spectral-silence}
+\end{figure*}
+
+At \(\tau=0.5\), the connected curvature form factors are
+\begin{equation}
+ \begin{aligned}
+ K_{F,c}^{\rm structured}&=\StructuredFormHalf,\\
+ K_{F,c}^{\rm physical}&=\PhysicalFormHalf,\qquad
+ K_{J,c}^{(50)}=\JacobiFormHalf .
+ \end{aligned}
+ \label{eq:form-half}
+\end{equation}
+The physical value is thus close to the parameter-free finite-rank prediction,
+whereas the structured value is almost an order of magnitude larger.
+The agreement is assessed on the whole registered interval with simultaneous
+bands; Eq.~\eqref{eq:form-half} provides one representative value.
+
+\subsection{Three-scale comparison}
+
+A robust geometric-chaos diagnostic combines three resolutions of the same
+point process:
+\begin{equation}
+ P(r)\quad\longleftrightarrow\quad
+ K_{F,c}(\tau)\quad\longleftrightarrow\quad
+ \Sigma^2(L),
+ \label{eq:falsification-triangle}
+\end{equation}
+testing nearest-neighbor repulsion, two-level correlations across Fourier
+scales, and long-range counting fluctuations, respectively.
+Related uses of non-energy spectra emphasize that a ramp probes eigenvalue
+correlations rather than the physical identity of the operator
+\cite{chenludwig2018}.
+
+\begin{figure*}[t]
+ \includegraphics[width=\textwidth]{figure_2_falsification_triangle_v2.pdf}
+ \caption{
+ \textbf{Three-scale comparison for geometric chaos.}
+ (a) Adjacent-gap-ratio distribution of structured Fourier, physical
+ random-local, and independently sampled Haar--Jacobi curvatures.
+ Exact multiplets make the structured distribution singular near zero; the
+ physical and Jacobi bands overlap.
+ (b) Connected curvature SFF.
+ The empirical Haar curve and the analytic determinantal-kernel result are
+ independent references.
+ (c) Number variance after ensemble-CDF unfolding.
+ Random local tangents have Jacobi rigidity at short windows but a resolved
+ excess at long windows, whereas the structured control is nonuniversal
+ throughout.
+ Bands are simultaneous 95\% regions obtained from complete momentum orbits,
+ physical seed blocks, or complete random matrices, with each matrix retained
+ as one statistical unit.
+ }
+ \label{fig:falsification}
+\end{figure*}
+
+Figure~\ref{fig:falsification} resolves two distinct geometric regimes.
+First, the rank-\(50\) Fourier reference occupies the structured branch across
+all three tests.  Second, the physical curvature combines Jacobi local
+statistics with covariance-deformed structure at broader scales.
+Its one-point density has held-out \(L^1\) distance \(\DensityHaarLone\) from
+Haar; a covariance-deformed row-space model reduces this to
+\(\DensityCovLone\), a \(\DensityImprovementPercent\) improvement.
+At long range,
+\begin{equation}
+ \Sigma_{\rm phys}^2(8)-\Sigma_{\rm Haar}^2(8)
+ =\NumberResidualEight
+ \in[\NumberResidualEightLower,\NumberResidualEightUpper].
+ \label{eq:number-residual}
+\end{equation}
+The resulting statement is correlation-scale resolved: Jacobi local
+repulsion and a finite-\(D\) ramp coexist with covariance-deformed one-point
+structure and long-range memory.
diff --git a/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/sections/04-covariance-eth.tex b/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/sections/04-covariance-eth.tex
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@@ -0,0 +1,117 @@
+\section{Independent spectral and geometric interventions}
+\label{sec:covariance}
+
+The preceding comparison could still admit a weak interpretation: perhaps the
+energy and curvature statistics are merely two correlated consequences of a
+single hidden randomness.
+We now intervene on the two blocks of a parameter-dependent Hamiltonian
+separately.
+The decomposition
+\begin{equation}
+ H=PHP+PHQ+QHP+QHQ
+ \label{eq:block-decomposition}
+\end{equation}
+shows why this is possible.
+Internal energy spacings are controlled by \(PHP\), whereas the projector
+response in Eq.~\eqref{eq:channel} is controlled by
+\(P(\partial_\mu H)Q\), the complement resolvent, and their adjoints.
+These are logically distinct data.
+
+\subsection{Changing energy statistics at fixed projector}
+
+For the spectral intervention we use an effective \(D\times D\) fiber
+Hamiltonian
+\begin{equation}
+ h_\alpha=\sqrt{1-\alpha^2}\,h_{\rm P}+\alpha h_{\rm GUE},
+ \qquad 0\leq\alpha\leq1 ,
+ \label{eq:spectral-interpolation}
+\end{equation}
+where \(h_{\rm P}\) has independent exponential spacings and
+\(h_{\rm GUE}\) is an independent complex Gaussian Hermitian matrix.
+Both are centered and matched in Hilbert--Schmidt norm before interpolation.
+We embed \(0.1h_\alpha\) in a fixed target block and place a diagonal
+complement between energies \(2\) and \(3\).
+The external gap stays open throughout, and diagonalization verifies
+\begin{equation}
+ \max_\alpha\|P_\alpha-P_0\|_F=1.15\times10^{-14}.
+ \label{eq:projector-invariance}
+\end{equation}
+The tangent channels and a reference curvature spectrum are held fixed.
+This effective causal control supplies a clean spectral axis; a local
+microscopic realization defines a complementary future program.
+
+Across \(\SpectralSamplesPerPoint\) matrices per value of \(\alpha\), the
+energy adjacent-gap ratio changes from
+\begin{equation}
+ \langle r_E\rangle_{\alpha=0}=\PoissonEndpointRatio,\qquad
+ \langle r_E\rangle_{\alpha=1}=\GUEEndpointRatio ,
+ \label{eq:energy-axis}
+\end{equation}
+while the stored curvature spectrum is unchanged to machine precision.
+Thus conventional spectral chaos evolves at exactly fixed target-projector
+geometry.
+
+\subsection{Changing geometry at fixed exactly degenerate parent}
+
+The complementary intervention leaves the Kapit--Mueller parent, its exact
+zero energy, its projector, and its external gap fixed.
+For each structured Fourier direction \(v_{\bm q}\) and an independent random
+local direction \(\eta_v\), define
+\begin{equation}
+ \begin{aligned}
+ \widetilde v_g&={\cal N}_G\!\left[
+ \sqrt{1-g}\,v_{\bm q}+\sqrt g\,\eta_v\right],\\
+ \widetilde w_g&={\cal N}_G\!\left[
+ \sqrt{1-g}\,w_{\bm q}+\sqrt g\,\eta_w\right],
+ \end{aligned}
+ \label{eq:geometric-interpolation}
+\end{equation}
+where \({\cal N}_G\) mean-centers and normalizes in the physical tangent
+Gram matrix.
+The square-root weights make \(g\) a variance fraction before the final
+normalization.
+We sample \(\GeometricSamplesPerPoint\) independent tangent pairs at each
+positive registered \(g\), maintaining active rank \(50\) throughout.
+
+\begin{figure*}[t]
+ \includegraphics[width=\textwidth]{figure_3_independent_channels_v2.pdf}
+ \caption{
+ \textbf{Energy chaos and projector-geometric chaos are independent
+ channels.}
+ (a) Mean energy adjacent-gap ratio under the effective fixed-projector
+ interpolation in Eq.~\eqref{eq:spectral-interpolation}; it crosses from
+ Poisson to the GUE/Haar interval.
+ (b) The target-projector distance remains at diagonalization roundoff and
+ the supplied curvature spectrum is exactly invariant.
+ (c) At fixed exactly degenerate parent, scrambling only the tangent channels
+ in Eq.~\eqref{eq:geometric-interpolation} changes the curvature gap ratio.
+ Its simultaneous interval first overlaps the Haar--Jacobi interval at
+ \(g=\GeometricLocalOnset\); the first registered nontrivial SFF window occurs
+ at \(g=\GeometricRampOnset\).
+ (d) Logical \(2\times2\) classification.
+ Spectral and geometric chaos can occur separately or together; the original
+ topological flat band occupies the energy-silent/geometrically chaotic
+ quadrant.
+ Bands are 95\% simultaneous intervals over the registered interpolation
+ grids.
+ }
+ \label{fig:independent-channels}
+\end{figure*}
+
+Figure~\ref{fig:independent-channels} gives the operational separation.
+Changing \(PHP\) moves horizontally in panel (d) at fixed
+\(P(\partial H)Q\).  Changing local tangent structure moves vertically at
+fixed exactly degenerate parent.  Consequently, a Jacobi-like curvature
+spectrum directly diagnoses the embedding and response of the degenerate
+subspace.
+It diagnoses how the degenerate subspace is embedded in and responds to its
+surrounding Hilbert space.
+
+The intervention also supplies an ordering test.
+The mean curvature gap-ratio interval first overlaps the Haar reference at
+\(g=\GeometricLocalOnset\), whereas compatibility with the exact finite-\(D\)
+SFF over a registered nonzero \(\tau\) interval first occurs at
+\(g=\GeometricRampOnset\).
+These onsets are confidence-set definitions on a discrete grid.  They
+demonstrate that local repulsion is established before the broader two-level
+ramp under controlled tangent interpolation.
diff --git a/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/sections/05-rank-crossover.tex b/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/sections/05-rank-crossover.tex
new file mode 100644
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@@ -0,0 +1,79 @@
+\section{Exact geometric modes and the Jacobi plateau}
+\label{sec:rank}
+
+The \(D=50\) lattice calculation lies in the atom-free regime \(D<M\).
+To test Eq.~\eqref{eq:atom-plateau}, we use an independent exact
+root-response construction that reaches both sides of the capacity boundary.
+For \(N=3\) particles in \(n\) orbitals, the cyclic Laughlin zero-mode
+dimension and one-tangent descendant capacity are
+\begin{equation}
+ D(n)=\frac{n}{n-3}\binom{n-3}{3},\qquad
+ M(n)=2n(n-3).
+ \label{eq:root-dimensions}
+\end{equation}
+Two independently sampled one-body response maps are assembled in the
+monomial root basis and whitened by a thin QR factorization.
+This directly produces the row isometry in
+Eq.~\eqref{eq:isometry-compression} as an independent construction from the
+physical Kapit--Mueller calculation.
+
+The registered sequence contains \(\RootMatricesTotal\) matrices at
+\[
+ D=16,\ 50,\ 112,\ 210,\ 352,\ 546,\ 800 .
+\]
+It is a finite-rank sequence at fixed particle number \(N=3\), designed to
+resolve the exact capacity transition.
+At \(D=546\), \(M=540\) and the atom theorem requires six levels at each
+boundary.
+At the endpoint \((D,M)=(\LargestRankVTwo,\LargestChannels)\), it requires
+\(\LargestAtomEachVTwo\) levels at each boundary and leaves
+\(k=560\) continuously distributed levels.
+
+\begin{figure*}[t]
+ \includegraphics[width=\textwidth]{figure_5_jacobi_atoms_v2.pdf}
+ \caption{
+ \textbf{Exact boundary atoms reshape the connected plateau while the
+ continuous sector retains the Jacobi ramp.}
+ (a) Full-spectrum connected curvature SFF at the first capacity crossing,
+ \(D=546,M=540\), with six exact levels at each of \(\lambda=\pm1\).
+ (b) Endpoint \(D=800,M=680\), with \(120\) atoms per boundary.
+ The full physical root-response curve follows the full Jacobi prediction,
+ while removing the algebraically identified atoms restores the
+ unit continuous-sector plateau.
+ (c) Across the seven-rank sequence, the exact full connected plateau is
+ \(k/D\); it falls as the deterministic atom weight
+ \(2(D-M)_+/D\) grows.
+ (d) Raw, non-unfolded endpoint SFF separated into atom--atom,
+ atom--continuum, and continuum--continuum terms according to
+ Eq.~\eqref{eq:atom-raw-decomposition}.
+ Their sum closes the full raw form factor to \(1.14\times10^{-13}\).
+ }
+ \label{fig:jacobi-atoms}
+\end{figure*}
+
+The endpoint plateau is therefore fixed analytically:
+\begin{equation}
+ K_{F,c}^{\rm full}(\infty)
+ =\frac{2M-D}{D}
+ =\LargestConnectedPlateau .
+ \label{eq:endpoint-plateau}
+\end{equation}
+The reference curve is obtained in two independent ways: evaluation of the
+determinantal kernel in Eq.~\eqref{eq:finite-jacobi-sff} and matrix-beta
+sampling of the Jacobi ensemble.
+The response spectra are generated independently from both references.
+
+This result refines the meaning of random-matrix-like curvature.
+The full one-point measure at \(D>M\) contains a finite mass fixed at
+\(\pm1\), while the atom-stripped sector displays Jacobi repulsion and its
+finite-rank ramp.
+The exact modes record a dimension-theorem intersection of the accessible row
+space with the two polarizations of \(J\); the ramp probes correlations in the
+remaining orientation.
+Exact geometry and chaotic geometry are therefore compatible within
+orthogonal sectors of the same degenerate manifold.
+
+The algebraic atom count also strengthens the analysis.  Counts are fixed from
+\((D,M)\) before eigenvalues are examined, their numerical positions are
+audited afterward, and both full and continuous-sector normalizations are
+reported.
diff --git a/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/sections/06-thouless-hierarchy.tex b/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/sections/06-thouless-hierarchy.tex
new file mode 100644
index 000000000..9679ebf02
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/sections/06-thouless-hierarchy.tex
@@ -0,0 +1,87 @@
+\section{A hierarchy of geometric correlation scales}
+\label{sec:hierarchy}
+
+The intervention data allow a scale-resolved statement stronger than a
+single endpoint comparison.
+For each \(g\), we subtract the exact finite-\(D\) Jacobi curve and test the
+entire residual process with a simultaneous band.
+For the physical ensemble we repeat the same procedure using eight
+independently seeded blocks.
+Long-range rigidity is tested independently through the number variance
+\begin{equation}
+ \Sigma^2(L)=
+ \left\langle\bigl[N_\xi(x,L)-L\bigr]^2\right\rangle ,
+ \label{eq:number-variance}
+\end{equation}
+where \(N_\xi(x,L)\) counts unfolded curvature levels in a sliding interval of
+length \(L\).
+
+\begin{figure*}[t]
+ \includegraphics[width=\textwidth]{figure_4_geometric_hierarchy_v2.pdf}
+ \caption{
+ \textbf{Controlled hierarchy from structured to random projector geometry.}
+ (a) Residual connected SFF
+ \(K_{F,c}(\tau;g)-K_{J,c}^{(50)}(\tau)\) along the tangent-scrambling
+ interpolation.
+ (b) Root-mean-square residual over the preregistered range
+ \(0.25\leq\tau\leq1.5\).
+ The local adjacent-gap statistic reaches the Haar interval at
+ \(g=\GeometricLocalOnset\), while the first nontrivial registered SFF
+ compatibility window occurs at \(g=\GeometricRampOnset\).
+ (c) Physical random-local-tangent residual with a simultaneous 95\% band;
+ it is compatible with the exact finite-\(D\) curve throughout the registered
+ range.
+ (d) Physical-minus-Haar number variance.
+ Short windows are compatible through \(L=\NumberVarianceExtent\), but the
+ positive long-range residual is resolved thereafter.
+ Onset lines summarize confidence sets on the sampled grids.
+ }
+ \label{fig:geometric-hierarchy}
+\end{figure*}
+
+Three conclusions follow from Fig.~\ref{fig:geometric-hierarchy}.
+First, a small interpolation away from Fourier structure generates local
+level repulsion, while the two-level correlation curve becomes active at a
+larger interpolation strength.
+The registered local and ramp onsets are
+\begin{equation}
+ g_{\rm local}=\GeometricLocalOnset,\qquad
+ g_{\rm ramp}=\GeometricRampOnset .
+ \label{eq:g-onsets}
+\end{equation}
+Second, at the physical random-local endpoint the residual band contains zero
+for every registered \(\tau\in[0.25,1.5]\).
+This is a curve-level finite-\(D\) test; it is more restrictive than matching
+the value or slope at one point.
+
+Third, long-range rigidity defines an additional scale.  The physical number
+variance follows the Haar reference through \(L=\NumberVarianceExtent\), and
+at \(L=8\) Eq.~\eqref{eq:number-residual} resolves a positive simultaneous
+interval.
+The curvature point process therefore loses information in the ordered
+sequence
+\begin{equation}
+ \begin{aligned}
+ \text{local }P(r)
+ &\ \prec\ \text{finite-\(D\) SFF ramp}\\
+ &\ \prec\ \text{long-range }\Sigma^2(L)
+ \end{aligned}
+ \label{eq:geometric-correlation-hierarchy}
+\end{equation}
+where \(A\prec B\) means that \(A\) becomes compatible with the invariant
+reference at a weaker scrambling or shorter correlation scale.
+
+Equation~\eqref{eq:geometric-correlation-hierarchy} defines a geometric
+Thouless hierarchy in the precise sense of confidence-resolved correlation
+lengths in an unfolded curvature spectrum.  Mapping these geometric scales to
+transport, scrambling, and real-time diffusion is a promising dynamical
+extension.
+
+Our geometric-ETH statement is operational and complementary to
+energy-resolved ETH: after removal of a deterministic
+metric envelope, local and intermediate-range correlations of the
+projector-response spectrum approach those of a finite invariant point
+process.
+The held-out one-point covariance improvement and the surviving number
+variance show that higher Grassmannian information remains measurable.  The
+result is covariance-deformed geometric ergodicity.
diff --git a/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/sections/07-conclusion.tex b/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/sections/07-conclusion.tex
new file mode 100644
index 000000000..dfe6569e3
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/sections/07-conclusion.tex
@@ -0,0 +1,75 @@
+\section{Discussion}
+\label{sec:conclusion}
+
+The central result can be stated directly:
+\begin{quote}
+\emph{Exact degeneracy makes the energy spectrum silent, while non-Abelian
+projector geometry reveals a random-matrix correlation ramp, a measurable
+matrix-element cumulant, and deformable global holonomy inside one fixed
+Chern class.}
+\end{quote}
+Each clause has a dedicated test.  Equation~\eqref{eq:energy-silence} proves
+spectral flatness.  The finite-Jacobi kernel supplies the geometric reference
+curve.  The full-rank Fourier family resolves structured and random local
+tangents at equal active rank.  The two blockwise interventions establish
+independent spectral and geometric axes.  The four-channel residual promotes
+the analysis from curvature eigenvalues to invariant response maps.  The
+closed twist torus separates determinant topology from relative Wilson
+transport while preserving every energy.
+
+The resulting picture is sharper than the statement that Berry curvature is
+a random matrix.  The physical one-point density is covariance deformed,
+long-range counting fluctuations retain microscopic information, and exact
+boundary atoms can occupy a macroscopic fraction of the spectrum.  Local
+finite-Jacobi universality, progressive response-channel Gaussianization, and
+structured global holonomy therefore form three ordered geometric scales.
+The analytic atom theorem adds a fourth scale by separating deterministic
+geometric modes from the correlated continuous sector.
+
+The relation to Chen \emph{et al.}~\cite{chen2026} is direct at the level of
+the diagnostic and complementary at the level of mechanism.  Their proposal
+addresses exactly degenerate BPS sectors, supersymmetric black-hole
+microstates, smooth horizonless geometries, and Chern topology over the
+\(\mathcal N=2\) SYK moduli space.  Our frustration-free condensed-matter
+mechanism adds the following capabilities:
+\begin{enumerate}
+ \item a parameter-free finite-\(D\) Jacobi prediction for metric-normalized
+ curvature;
+ \item a same-parent, same-rank structured tangent reference;
+ \item causal separation of \(PHP\) from \(P(\partial H)Q\);
+ \item an exact boundary-atom correction to the connected plateau;
+ \item a gauge-invariant four-channel test on a genuine \(N=3,4,5\) sequence;
+ and
+ \item a closed-surface separation of fixed Chern topology and deformable
+ Wilson holonomy.
+\end{enumerate}
+The common principle is that chaos can be encoded in how a degenerate state
+bundle moves over coupling space even when every state shares one energy.
+
+The current calculation establishes a precise finite-size scope.  The
+fixed-rank sequence quantifies curvature scaling through \(D=800\).  The
+fixed-projector Poisson-to-GUE path is a controlled block intervention.  The
+curvature form factor is treated as a geometric Fourier scale.  The
+many-body response sequence reaches \(N=5\), where the connected four-channel
+component remains resolved.  The Wilson family is an exact isospectral bundle
+construction whose final statistics define a structured class distinct from
+CUE.  These statements provide clean starting points for larger systems,
+local microscopic deformations, and dynamical comparisons.
+
+The next analytic target is the observed decrease of \(R_4\).  An extension
+through \(N=6\), combined with a locality-based derivation, can distinguish an
+emergent Wick law from a deformed fixed tensor.  A second exact-degeneracy
+mechanism can establish cross-model universality.  On the topological side,
+microscopic local deformations that preserve an exact kernel can test the
+fixed-\(C_1\), structured-Wilson branch beyond the controlled ambient orbit.
+A weak lifted-band or driven calculation can then connect the geometric
+hierarchy to real-time dynamics.
+
+For exactly degenerate quantum matter, the practical prescription is clear.
+Compute the isolated projector response, whiten curvature by its quantum
+metric, compare the continuous spectrum with the exact finite-rank Jacobi
+process, test invariant higher response cumulants, integrate determinant
+curvature on a closed surface, retain the relative Wilson spectrum, and map
+the scale at which each reference becomes active.  Under this protocol,
+degeneracy becomes a resource: it isolates a geometric channel of quantum
+chaos with local, operator-level, and topological resolution.
diff --git a/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/sections/08-matrix-elements-topology.tex b/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/sections/08-matrix-elements-topology.tex
new file mode 100644
index 000000000..2d1a7600c
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/overleaf_sync/geometric_eth_large_scale/sections/08-matrix-elements-topology.tex
@@ -0,0 +1,53 @@
+\section{Matrix-element geometry and fixed-Chern holonomy}
+\label{sec:matrix-topology}
+
+The curvature spectrum establishes a geometric correlation hierarchy. We now resolve its matrix-element mechanism and its relation to the topology of the full bundle while preserving the exact zero modes.
+
+\subsection{A gauge-invariant matrix-element test}
+
+Fixed local operators supply an independent test of Gaussian response statistics, because Gaussian tangent coefficients would make \(X[V]\) Gaussian by linearity. We use eight simple mean-zero local density operators in each panel and form the resolvent-dressed maps \(X_\mu=R_QQV_\mu P\). After whitening their measured label covariance, the primary observable is the invariant tensor in Eq.~\eqref{eq:invariant-four-channel-tensor}. Its two covariance-matched Gaussian contractions are derived in Appendix~\ref{app:matrix-topology}; generalized ETH likewise elevates higher matrix-element correlations beyond entrywise statistics \cite{foinikurchan2019,pappalardi2022}.
+
+The finite-size reference is a distribution of \(R_4\) at matched \((D,M,m)\). For every physical panel we generate Gaussian response tensors with the measured target and external covariance spectra, whiten them by the same algorithm, and compare the normalized residual in Eq.~\eqref{eq:wick-residual-appendix}. Complete panels are the resampling units. Independent target- and complement-frame rotations change the raw entries while \(T\), \(T^{\rm Wick}\), and \(R_4\) remain invariant.
+
+\begin{figure*}[t]
+ \includegraphics[width=\textwidth]{figure_6_wick_factorization_v3.pdf}
+ \caption{\textbf{Gauge-invariant four-channel Wick test on a genuine many-body sequence.} (a) Fixed-two-quasihole manifolds \((N,n_\phi,D)=(3,8,16),(4,10,25),(5,12,36)\), including the external gap and full Hilbert-space dimension. (b) Physical local-density and structured Fourier residuals against covariance-matched finite-\((D,M,m)\) Gaussian intervals. (c) The physical excess over the Gaussian median decreases with \(N\) and remains resolved at \(N=5\). (d) Measured target anisotropy and effective external dimension entering the two Wick coefficients. Intervals resample 24 complete operator panels or 2000 complete Gaussian tensors, with every matrix retained as one observation.}
+ \label{fig:wick-factorization}
+\end{figure*}
+
+Figure~\ref{fig:wick-factorization} uses the true sequence \(n_\phi=2N+2\). The Hilbert space reaches \(\LargestManyBodyDimension\) states and the zero-mode rank reaches \(D=\LargestManyBodyRank\). The median physical residual decreases from \(0.37093\) to \(0.24715\) to \(\LargestNRFour\), while the matched Gaussian median decreases from \(0.21708\) to \(0.14638\) to \(\LargestGaussianRFour\). At the largest size the physical excess is \(\LargestRFourExcess\), resolved relative to the Gaussian interval \([\LargestGaussianRFourLow,\LargestGaussianRFourHigh]\).
+
+\MatrixElementBranchText\ This selects the registered branch \texttt{\MatrixElementBranch}: progressive Gaussianization with a resolved connected operator-channel component. The \(N=3,4,5\) sequence supplies the finite-size baseline for an \(N=6\) scaling test.
+
+\subsection{A closed surface at fixed spectrum and Chern class}
+
+For the topology test, the parameter space is the complete twist torus \(T^2_{\theta_x,\theta_y}\). Starting from the physical projected-contact parent, define
+\begin{equation}
+ \begin{aligned}
+ \mathcal U_g(\theta)
+ &=e^{ig\sin\theta_xG_x}e^{ig\sin\theta_yG_y},\\
+ H_g(\theta)
+ &=\mathcal U_g(\theta)H_0(\theta)\mathcal U_g^\dagger(\theta),
+ \end{aligned}
+ \label{eq:main-isospectral-orbit}
+\end{equation}
+where \(G_x,G_y\) are deterministic nearest-neighbor Hermitian one-body generators. The bosonic lift is globally periodic. Hence the complete spectrum and gap are identical for every \(g\), and \(\mathcal U_g\) is a bundle isomorphism that preserves \(C_1\). Nevertheless the connection acquires the projected one-form in Eq.~\eqref{eq:connection-shift}, so non-Abelian Wilson holonomy may change.
+
+Polar-unitary links and plaquette products implement the lattice connection \cite{fukui2005}. We retain determinant topology separately from relative Wilson eigenphases. The circular adjacent-gap ratio is branch free, and the Wilson form factor
+\begin{equation}
+ K_W(k)=\frac{1}{D}\left|\Tr W^k\right|^2
+ \label{eq:wilson-form-factor}
+\end{equation}
+is invariant under a common phase. Both are compared with 10000 independently sampled CUE matrices at the same \(D\). Random local \(U(D)\) frame gauges provide dedicated invariance tests and remain separate from physical scrambling.
+
+\begin{figure*}[t]
+ \includegraphics[width=\textwidth]{figure_7_topological_holonomy_v3.pdf}
+ \caption{\textbf{Fixed Chern topology with deformed non-Abelian Wilson holonomy.} (a) The periodic ambient orbit leaves \(C_1=6,10\) and the external gaps fixed for \(N=3,4\). (b) For \(N=4\), accumulated branch-resolved determinant flux has winding ten at both endpoints, while its local distribution over the transverse twist changes. (c) Seed-cluster intervals of the Wilson circular gap ratio move significantly with \(g\) and occupy a structured range distinct from CUE; a commuting-generator path supplies the reference. (d) The \(N=4\) Wilson SFF at \(g=0\), \(g=1\), and the commuting endpoint compared with the independently sampled CUE mean and simultaneous band. Eight complete noncommuting generator seeds are resampled as clusters.}
+ \label{fig:topological-holonomy}
+\end{figure*}
+
+The accepted \(\TopologyPrimaryMesh\times\TopologyPrimaryMesh\) and \(\TopologyConvergenceMesh\times\TopologyConvergenceMesh\) meshes give \(C_1=\TopologyNThreeChern\) for \(N=3\) and \(C_1=\TopologyNFourChern\) for \(N=4\), with external gaps \(\TopologyNThreeGap\) and \(\TopologyNFourGap\). The minimum accepted determinant-branch margin is \(\TopologyMinimumBranchMargin\), the minimum neighboring-overlap singular value is \(\TopologyMinimumOverlap\), and the maximum random-gauge Wilson-phase error is \(\TopologyGaugeError\). A retained \(12\times12\) preflight identifies a branch alias for one \(N=4,g=1\) seed and motivates the converged \(16/20\) mesh pair.
+
+Under noncommuting generators, the seed-cluster confidence interval for the change in \(\langle r_W\rangle\) is \([\TopologyNThreeGapChangeLow,\TopologyNThreeGapChangeHigh]\) at \(N=3\) and \([\TopologyNFourGapChangeLow,\TopologyNFourGapChangeHigh]\) at \(N=4\). Both intervals are strictly positive. At \(g=1\), the medians \(\TopologyNThreeFinalGapRatio\) and \(\TopologyNFourFinalGapRatio\) occupy a structured range below the CUE medians \(\TopologyNThreeCUERatio\) and \(\TopologyNFourCUERatio\), accompanied by a distinct Wilson SFF.
+
+\TopologyBranchText\ The selected branch is therefore \texttt{\TopologyBranch}: fixed determinant-bundle topology coexists with tunably deformed, structured non-Abelian holonomy. Together with Fig.~\ref{fig:wick-factorization}, it identifies two complementary memories beyond curvature eigenvalue repulsion: a resolved four-channel cumulant and a structured Wilson sector distinct from CUE.
diff --git a/tracks/mps/solutions/Wander-276/verify.sh b/tracks/mps/solutions/Wander-276/verify.sh
new file mode 100755
index 000000000..f8c13f6fa
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/verify.sh
@@ -0,0 +1,6 @@
+#!/usr/bin/env bash
+set -euo pipefail
+
+SOLUTION_DIR="$(cd "$(dirname "${BASH_SOURCE[0]}")" && pwd)"
+cd "${SOLUTION_DIR}/research/01_task_folder/task_05/script"
+PYTHONDONTWRITEBYTECODE=1 bash run_quick_verify_v1.sh

From 6d16d4e7dda9d06f5336ed91d1d9bad44a1b423e Mon Sep 17 00:00:00 2001
From: JunkaiWang-TheoPhy <1181100960@qq.com>
Date: Tue, 4 Aug 2026 09:54:26 +0800
Subject: [PATCH 2/3] feat: deliver sealed N14 response complex

Result: add the independent cubic N=2 SYK response complex, compact N=8--14 artifacts, audited Letter and supplement, and the frozen cohomological_non_gaussian_class verdict for Issue 276.

Boundary: null rejection establishes finite-size memory beyond the registered separable covariance models, not asymptotic Geometric ETH or a complete-covariance non-Gaussianity theorem.

Tested: bash tracks/mps/solutions/Wander-276/verify.sh passes 38 legacy checks, 43 v7 tests, scientific provenance verification, and dual-PDF manuscript auditing.

Co-authored-by: OmX <omx@oh-my-codex.dev>
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diff --git a/tracks/mps/solutions/Wander-276/PR_BODY.md b/tracks/mps/solutions/Wander-276/PR_BODY.md
index 726a39e40..d16d81267 100644
--- a/tracks/mps/solutions/Wander-276/PR_BODY.md
+++ b/tracks/mps/solutions/Wander-276/PR_BODY.md
@@ -1,12 +1,11 @@
 <!-- wander-artwork -->
 ![Wander — Issue #276](https://raw.githubusercontent.com/JunkaiWang-TheoPhy/quantum.harness/664506886413b68cdbc5a362a6075c78fd5d2c46/docs/showcase/ranger-archive/assets/missions-v2/07-quantum-geometry-curved-state-space-v2.png)
 
-> **EN** The world seemed flat only because no one had lifted the tablecloth.
+> **EN** The spectrum is silent; the geometry is not.
 >
-> **中文** 世界之所以显得平坦，只因从未有人掀起那块桌布。
+> **中文** 能谱沉默，几何仍然说话。
 <!-- /wander-artwork -->
 
-<!-- wander-team -->
 ## Team
 
 | Field | Value |
@@ -14,49 +13,55 @@
 | **Team name** | Wander |
 | **Members** | Chenxi Wan, Yedi Shen, Junkai Wang |
 | **Contact email** | WangTheoPhys@outlook.com |
-<!-- /wander-team -->
 
 ## Challenge
 
-Addresses #276: **What is the probe of quantum chaos for a degenerate eigenstate subspace?**
+Addresses #276: **What probes quantum chaos inside an exactly degenerate eigenspace?**
 
-This PR gives an executable answer: the probe is the **non-Abelian quantum geometry of the degenerate projector over coupling space**. Exact degeneracy turns the connected energy spectral form factor into an exact baseline, while Berry curvature, a gauge-invariant four-channel response tensor, and Wilson holonomy resolve the internal complexity of the manifold.
+This PR gives an executable answer: the probe is the **non-Abelian quantum geometry of the protected projector over coupling space**. Exact degeneracy silences internal level statistics, while the response amplitudes (X_a=(1-P)\partial_aP) generate the quantum metric, Berry curvature, gauge-invariant four-channel tensors, and global holonomy.
 
 ## Scientific Advance
 
-| Layer | New capability | Registered result |
-|---|---|---|
-| Exact spectrum | Exact spectral-flatness reference | \(K_{E,c}=0\) identically |
-| Local geometry | Parameter-free finite-\(D\) Jacobi kernel and SFF | Physical curvature tracks the registered Jacobi ramp |
-| Matrix elements | Covariance-whitened four-channel tensor | `deformed_geometric_eth` |
-| Global topology | Isospectral, fixed-Chern Wilson control | `fixed_chern_deformed_holonomy` |
+| Layer | Result |
+|---|---|
+| Exact geometry | (\mathcal Q_{ab}=X_a^\dagger X_b), with metric and Berry curvature as its symmetric and antisymmetric parts |
+| Independent mechanism | Generic cubic (\mathcal N=2) SYK supplies a charge-resolved cohomological BPS manifold independent of the Kapit–Mueller/Laughlin parent |
+| Exact structure | Nilpotency produces orthogonal exact/coexact response branches (X=X_-\oplus X_+), (X_-^\dagger X_+=0) |
+| Sealed test | The complete $N=8,10,12$ pilot and separately sealed, held-out $N=14$ four-channel test reject both registered separable covariance nulls |
+| Controls | Decomposable-supercharge curvature atoms and a one-sided Laughlin Gaussian-null regression |
+
+The new scientific question is sharper than “is the Hamiltonian chaotic?” It asks whether the protected response tensor is controlled by registered two-point covariance data, or whether gauge-invariant four-point memory survives after that matching.
+
+## Outcome-Blind Protocol
 
-## Four Innovations
+The held-out calculation freezes two parameter-free prediction models before opening the outcome sidecars: a collapsed separable covariance null and an exact/coexact Hodge-resolved separable covariance null. Complete disorder realizations—not tangent entries or tensor components—are the uncertainty unit. No scheduler dependency invokes unsealing; seal validation and scoring require a separate explicit action.
 
-1. **Metric-normalized signature compression** maps the many-body projector response to an exact finite-rank complex-Jacobi process.
-2. **Boundary-atom form-factor theory** treats exact \(\lambda=\pm1\) modes algebraically and reaches \(D=800\).
-3. **Matrix-element Geometric ETH** measures a gauge-invariant connected four-channel component on the genuine \(N=3,4,5\) sequence.
-4. **Fixed-Chern holonomy engineering** tunes relative Wilson transport while preserving every energy, the external gap, and \(C_1\).
+**Final held-out verdict:** independent seal validation passed before explicit unsealing, and the frozen branch is `cohomological_non_gaussian_class`.
 
-These capabilities create a condensed-matter bridge from the Berry-curvature chaos program for degenerate BPS microstates to a local frustration-free bosonic Laughlin parent Hamiltonian.
+| $N=14$ sparse sector | Physical median (95% bootstrap) | Collapsed null (97.5% prediction) | Hodge null (97.5% prediction) |
+|---|---:|---:|---:|
+| Adjacent | 0.301529 [0.291527, 0.312061] | [0.111789, 0.111852] | [0.112344, 0.112513] |
+| Central | 0.374993 [0.368980, 0.380473] | [0.111338, 0.111353] | [0.111333, 0.111348] |
 
-## Quantitative Evidence
+Both primary physical intervals are disjoint from both sealed prediction intervals. The prediction JSON was frozen at SHA-256 `fc300dc7e4bdc1be157919e458ac868d3468533cce31108f23c9fba4f7e9f102`; the independently recomputable inference artifact is `177643e07fc6cf210362fc1077070bd1f0ba316b6805042a626de3f96c55a627`.
 
-- 20,000 physical tangent pairs with a frozen `12000/4000/4000` train/validation/test split.
-- At \(\tau=0.5\), physical \(K_{F,c}=0.502\) and finite-Jacobi \(K_{J,c}=0.501\).
-- Four-channel connected excess \(0.15385\to0.10078\to0.08183\) across \(N=3,4,5\).
-- Fixed Chern numbers \(C_1=6,10\) with reproducibly shifted Wilson statistics.
-- Exact rank sequence through \(D=800\), including 120 atoms at each boundary and connected plateau `0.7`.
-- Seven synchronized publication figures and an audited 17-page article.
+## Claim Boundary
+
+- Established: an independent supersymmetric protection mechanism, exact Hodge-resolved response identity, analytic controls, and finite-size $N=8$--$14$ response memory beyond both frozen separable covariance-null families.
+- Not established: asymptotic Geometric ETH, thermalization, real-time chaos, or a thermodynamic-limit theorem.
+- Null rejection, if selected, means memory beyond the frozen separable Hodge/collapsed covariance models; it does not prove non-Gaussianity relative to every possible entrywise covariance model.
 
 ## Deliverables
 
 - [Harness solution overview](https://github.com/JunkaiWang-TheoPhy/quantum.harness/blob/codex/issue-276-quantum-geometry/tracks/mps/solutions/Wander-276/README.md)
-- [Innovation-first research guide](https://github.com/JunkaiWang-TheoPhy/quantum.harness/blob/codex/issue-276-quantum-geometry/tracks/mps/solutions/Wander-276/research/README.md)
-- [Markdown technical report](https://github.com/JunkaiWang-TheoPhy/quantum.harness/blob/codex/issue-276-quantum-geometry/tracks/mps/solutions/Wander-276/research/docs/2026-07-30-task05-technical-report.md)
-- [17-page article](https://github.com/JunkaiWang-TheoPhy/quantum.harness/blob/codex/issue-276-quantum-geometry/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/spectral_silence_and_geometric_chaos_v3.pdf)
-- [Release manifest](https://github.com/JunkaiWang-TheoPhy/quantum.harness/blob/codex/issue-276-quantum-geometry/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/release_manifest_v1.json)
-- [Public research repository](https://github.com/JunkaiWang-TheoPhy/Chaos-of-Quantum-Geometry/tree/codex/task-05-geometric-chaos-baseline)
+- [Research and reproduction guide](https://github.com/JunkaiWang-TheoPhy/quantum.harness/blob/codex/issue-276-quantum-geometry/tracks/mps/solutions/Wander-276/research/README.md)
+- [Letter source](https://github.com/JunkaiWang-TheoPhy/quantum.harness/blob/codex/issue-276-quantum-geometry/tracks/mps/solutions/Wander-276/research/overleaf_sync/cohomological_geometric_eth/main.tex)
+- [Supplement source](https://github.com/JunkaiWang-TheoPhy/quantum.harness/blob/codex/issue-276-quantum-geometry/tracks/mps/solutions/Wander-276/research/overleaf_sync/cohomological_geometric_eth/supplement.tex)
+- [Compiled Letter](https://github.com/JunkaiWang-TheoPhy/quantum.harness/blob/codex/issue-276-quantum-geometry/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/response_complex_memory_v7.pdf)
+- [Compiled Supplemental Material](https://github.com/JunkaiWang-TheoPhy/quantum.harness/blob/codex/issue-276-quantum-geometry/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/response_complex_memory_supplement_v7.pdf)
+- [Machine-generated result report](https://github.com/JunkaiWang-TheoPhy/quantum.harness/blob/codex/issue-276-quantum-geometry/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_geometric_eth_report_v7.md)
+- [Scientific ceiling and literature memo](https://github.com/JunkaiWang-TheoPhy/quantum.harness/blob/codex/issue-276-quantum-geometry/tracks/mps/solutions/Wander-276/research/docs/2026-08-01-scientific-ceiling-strategy.md)
+- [Public research branch](https://github.com/JunkaiWang-TheoPhy/Chaos-of-Quantum-Geometry/tree/codex/task-05-geometric-chaos-baseline)
 
 ## Verification
 
@@ -65,14 +70,6 @@ cd tracks/mps/solutions/Wander-276
 bash verify.sh
 ```
 
-- Release contract: 17/17 checks.
-- Quick path: 38/38 tests.
-- Complete compact suite: 86 passing tests plus six manifest-activated production tests.
-- Article delivery: 25/25 checks across 17 pages and seven figures.
-- Article SHA-256: `a75377f76acd78eb3354e186a57933abdf11abbbe5e9a8abd43482ca8c4e05ad`.
-
-## MPS Track Continuation
-
-The exact-kernel calculation supplies the calibration layer for an MPS extension of Issue #276: reproduce the projector response and four-channel invariant at ED-accessible sizes, then scale the same gauge-invariant observables with a tensor-network representation of the degenerate manifold. The next registered targets are \(N=6\), a second exact-degeneracy mechanism, and a locality-based derivation of the connected channel law.
+The final verifier checks exact identities, controls, the complete pilot and held-out grids, the seal state machine, every compact hash, frozen branch recomputation, figure provenance, byte-exact Letter/Supplement PDFs, and 43 focused v7 tests.
 
-@OkongOyangO, please review the projector-geometry interpretation, the four-channel law, and the fixed-Chern holonomy construction as Wander's ready submission for #276.
+@OkongOyangO, please review the protected-response interpretation, the exact/coexact identity, and the outcome-blind four-channel test as Wander's Issue #276 submission.
diff --git a/tracks/mps/solutions/Wander-276/README.md b/tracks/mps/solutions/Wander-276/README.md
index 61ea74529..49e76b569 100644
--- a/tracks/mps/solutions/Wander-276/README.md
+++ b/tracks/mps/solutions/Wander-276/README.md
@@ -1,10 +1,10 @@
-# Wander — Issue #276: Non-Abelian Quantum Geometry as a Chaos Probe
+# Wander — Issue #276: Chaos in Exactly Degenerate Quantum Manifolds
 
 ![Quantum geometry over an exactly degenerate manifold](https://raw.githubusercontent.com/JunkaiWang-TheoPhy/quantum.harness/664506886413b68cdbc5a362a6075c78fd5d2c46/docs/showcase/ranger-archive/assets/missions-v2/07-quantum-geometry-curved-state-space-v2.png)
 
-> **EN** The world seemed flat only because no one had lifted the tablecloth.
+> **EN** The spectrum is silent; the geometry is not.
 >
-> **中文** 世界之所以显得平坦，只因从未有人掀起那块桌布。
+> **中文** 能谱沉默，几何仍然说话。
 
 ## Team
 
@@ -14,33 +14,62 @@
 | **Members** | Chenxi Wan, Yedi Shen, Junkai Wang |
 | **Contact email** | WangTheoPhys@outlook.com |
 
-## Challenge
+## Challenge and Answer
 
-This submission addresses [QuantumBFS/quantum.harness#276](https://github.com/QuantumBFS/quantum.harness/issues/276): **What is the probe of quantum chaos for a degenerate eigenstate subspace?**
+This submission addresses [QuantumBFS/quantum.harness#276](https://github.com/QuantumBFS/quantum.harness/issues/276): **What probes quantum chaos inside an exactly degenerate eigenspace?**
 
-The executable answer is the **non-Abelian quantum geometry of the degenerate projector over coupling space**. Exact degeneracy makes the connected energy spectral form factor silent, while Berry curvature, the gauge-invariant four-channel response tensor, and Wilson holonomy remain informative.
+The executable answer is the **non-Abelian quantum geometry of the protected projector over coupling space**. If (P(\lambda)) is the degenerate projector and (X_a=(1-P)\partial_aP), then
 
-## Headline Result
+$$\mathcal Q_{ab}=X_a^\dagger X_b,\qquad g_{ab}=\frac{\mathcal Q_{ab}+\mathcal Q_{ba}}{2},\qquad F_{ab}=i(\mathcal Q_{ab}-\mathcal Q_{ba}).$$
 
-The benchmark uses a bosonic Laughlin zero-mode manifold of a Kapit–Mueller parent Hamiltonian. It combines four advances:
+Ordinary level statistics is undefined inside a flat multiplet, but (g), (F), gauge-invariant four-channel contractions, Chern numbers, and Wilson holonomy remain nontrivial.
 
-1. **Metric-normalized signature compression** maps the many-body projector response to an exact finite-rank complex-Jacobi process.
-2. **Boundary-atom form-factor theory** treats exact \(\lambda=\pm1\) modes algebraically and reaches rank \(D=800\).
-3. **Matrix-element Geometric ETH** measures a gauge-invariant connected four-channel component on the genuine \(N=3,4,5\) sequence.
-4. **Fixed-Chern holonomy engineering** tunes relative Wilson transport while preserving the full spectrum, the gap, and the Chern class.
+## Independent Protection Mechanisms
 
-At \(\tau=0.5\), the physical curvature form factor is \(K_{F,c}=0.502\), compared with the finite-Jacobi value \(K_{J,c}=0.501\). The connected four-channel excess decreases as \(0.15385\to0.10078\to0.08183\). The registered result branches are `deformed_geometric_eth` and `fixed_chern_deformed_holonomy`.
+The release no longer rests on one fractional-quantum-Hall example.
+
+| Mechanism | Protected manifold | Exact response structure | Role |
+|---|---|---|---|
+| Kapit–Mueller/Laughlin parent (H=B^\dagger B) | Frustration-free, gapped zero modes | One-sided response (X=-H_\perp^+B^\dagger\delta BP) | Local topological benchmark, Jacobi curvature, fixed-Chern holonomy |
+| Generic cubic (\mathcal N=2) SYK (H=\{Q,Q^\dagger\}) | Charge-resolved harmonic cohomology | Orthogonal exact/coexact response (X=X_-\oplus X_+) | Independent supersymmetric mechanism and sealed covariance test |
+
+Nilpotency gives (X_-^\dagger X_+=0) exactly. The two-sided Hodge decomposition is therefore a physical response-complex structure, not a basis rewrite of the Laughlin calculation.
+
+## Registered Scientific Test
+
+For eight coupling tangents, the code whitens the channel covariance and evaluates the gauge-invariant tensor
+
+$$\mathcal T_{abcd}=\frac1D\operatorname{Tr}(\widehat X_a^\dagger\widehat X_b\widehat X_c^\dagger\widehat X_d).$$
+
+The (N=8,10,12) pilot uses complete disorder realizations as the uncertainty unit. A held-out (N=14) calculation freezes two prediction models before any four-channel outcome is opened:
+
+1. a collapsed separable covariance Gaussian null;
+2. an exact/coexact Hodge-resolved separable covariance Gaussian null.
+
+Safe covariates and predictions are SHA-256 sealed. Unsealing is an explicit, separate command and is never launched by the scheduler dependency chain. The seal was independently checked before opening, and the frozen result is:
+
+| $N=14$ sparse sector | Physical median (95% bootstrap) | Collapsed null (97.5% prediction) | Hodge null (97.5% prediction) |
+|---|---:|---:|---:|
+| Adjacent | 0.301529 [0.291527, 0.312061] | [0.111789, 0.111852] | [0.112344, 0.112513] |
+| Central | 0.374993 [0.368980, 0.380473] | [0.111338, 0.111353] | [0.111333, 0.111348] |
+
+Both nulls miss both primary sectors, selecting `cohomological_non_gaussian_class`.
+
+## Claim Boundary
+
+This submission establishes an **independent model/operator class** for protected quantum-geometric chaos and finite-size $N=8$--$14$ four-channel response memory beyond two preregistered separable covariance nulls. It does **not** claim asymptotic Geometric ETH, conventional energy-resolved ETH, real-time chaos, or a thermodynamic-limit theorem. Null rejection does not by itself prove intrinsic non-Gaussianity after matching every entrywise nonseparable covariance.
 
 ## Deliverables
 
-- [Innovation-first project guide](research/README.md)
-- [Task-level reproduction guide](research/01_task_folder/task_05/README.md)
-- [Markdown technical report](research/docs/2026-07-30-task05-technical-report.md)
-- [17-page article](research/01_task_folder/task_05/script/output/spectral_silence_and_geometric_chaos_v3.pdf)
-- [Machine-readable release manifest](research/01_task_folder/task_05/script/output/release_manifest_v1.json)
-- [Seven publication figures](research/01_task_folder/task_05/script/output/)
-- [Full REVTeX manuscript](research/overleaf_sync/geometric_eth_large_scale/)
-- [Public research repository](https://github.com/JunkaiWang-TheoPhy/Chaos-of-Quantum-Geometry/tree/codex/task-05-geometric-chaos-baseline)
+- [Research and reproduction guide](research/README.md)
+- [Task-level guide](research/01_task_folder/task_05/README.md)
+- [Letter source](research/overleaf_sync/cohomological_geometric_eth/main.tex)
+- [Supplement source](research/overleaf_sync/cohomological_geometric_eth/supplement.tex)
+- [Compiled Letter](research/01_task_folder/task_05/script/output/response_complex_memory_v7.pdf)
+- [Compiled Supplemental Material](research/01_task_folder/task_05/script/output/response_complex_memory_supplement_v7.pdf)
+- [Exact-data result report](research/01_task_folder/task_05/script/output/susy_hodge_geometric_eth_report_v7.md)
+- [Scientific ceiling and literature memo](research/docs/2026-08-01-scientific-ceiling-strategy.md)
+- [Public research branch](https://github.com/JunkaiWang-TheoPhy/Chaos-of-Quantum-Geometry/tree/codex/task-05-geometric-chaos-baseline)
 
 ## Verification
 
@@ -49,18 +78,13 @@ cd tracks/mps/solutions/Wander-276
 bash verify.sh
 ```
 
-Verified release state:
-
-- 17/17 public-release contract checks;
-- 38/38 focused quick-path tests;
-- 86 passing compact-checkout tests plus six production-data tests activated by the manifest-listed arrays;
-- 25/25 article-delivery checks across 17 rendered pages and seven synchronized figures;
-- article SHA-256 `a75377f76acd78eb3354e186a57933abdf11abbbe5e9a8abd43482ca8c4e05ad`.
+The verification path checks the exact Hodge identity, analytic controls, pilot-grid completeness, outcome-blind sealing, artifact hashes, frozen branch selection, figure provenance, and byte-exact Letter/Supplement delivery.
 
-## MPS Growth Path
+## Next Scientific Gate
 
-Issue #276 is registered on the MPS track. This exact-kernel package supplies the finite-size calibration layer for a tensor-network extension: reproduce the projector response and four-channel invariants at the ED-accessible sizes, then scale the same gauge-invariant observables with an MPS representation of the degenerate manifold. The preregistered next targets are \(N=6\), a second exact-degeneracy mechanism, and a locality-based derivation of the connected channel law.
+The finite-size result is designed to expose the next theorem rather than hide it. The two high-ceiling targets are:
 
-## Provenance
+- an asymptotic concentration/scaling law for the covariance-controlled response tensor;
+- a spatially local nilpotent-supercharge model with a stable zero-mode count, open gap, and moving cohomological projector.
 
-The capsule is synchronized from public commit `d0a03ae` of `JunkaiWang-TheoPhy/Chaos-of-Quantum-Geometry`. Compact artifacts are stored in Git; 25 production arrays totaling 447,704,793 bytes are recorded by SHA-256, byte size, and producer command in the release manifest.
+These are journal-ceiling gates, not assumptions built into the current claim.
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/README.md b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/README.md
index 413a6b74a..941fcd9cd 100644
--- a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/README.md
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/README.md
@@ -1,138 +1,74 @@
-# Spectral Silence and Geometric Chaos
+# Task 05 — Protected Response Complex and Geometric ETH
 
-> **One exactly flat energy band. Three geometric correlation scales. A reproducible route to Geometric ETH.**
+This task asks a falsifiable question inside an exactly degenerate manifold: after matching registered two-point response data, does a gauge-invariant four-channel statistic follow a Gaussian Wick law? Across the completed finite-size $N=8$--$14$ sequence, the answer is no for both preregistered separable covariance nulls.
 
-![Spectral flatness and geometric ramp](script/output/figure_1_spectral_silence_v2.png)
+## Physics Object
 
-This task provides a self-contained analytic and numerical baseline for chaos diagnostics inside an exactly degenerate bosonic Laughlin zero-mode manifold. It resolves the spectrum, local non-Abelian curvature, invariant response tensors, and closed-surface holonomy as complementary layers of one quantum-geometric structure.
+For a protected projector (P(\lambda)), define (X_a=(1-P)\partial_aP). Then
 
-## Result at a Glance
+$$\mathcal Q_{ab}=X_a^\dagger X_b,\qquad g_{ab}=\tfrac12(\mathcal Q_{ab}+\mathcal Q_{ba}),\qquad F_{ab}=i(\mathcal Q_{ab}-\mathcal Q_{ba}).$$
 
-| Question | Evidence | Advance |
-|---|---|---|
-| What replaces internal level statistics under exact degeneracy? | \(K_{E,\mathrm{raw}}=D\) and \(K_{E,c}=0\) identically | An exact spectral-flatness reference |
-| Does geometry develop universal correlations? | Physical curvature follows the finite-\(D\) Jacobi ramp over the registered window | Local geometric chaos |
-| How does the full response tensor behave? | Median \(R_4\) evolves \(0.37093\to0.24715\to0.20906\) across \(N=3,4,5\) | `deformed_geometric_eth` |
-| Can topology and relative transport move independently? | \(C_1=6,10\) and the complete spectrum stay fixed while Wilson statistics change significantly | `fixed_chern_deformed_holonomy` |
-| What global structure survives? | Wilson gap-ratio and form-factor data define a structured universality class distinct from CUE | Measurable microscopic memory |
-
-The central article is [*Spectral Silence and Geometric Chaos in an Exactly Degenerate Topological Manifold*](script/output/spectral_silence_and_geometric_chaos_v3.pdf). Its final SHA-256, page count, figures, and source artifacts are recorded by the release manifest and delivery audit.
-
-## Scientific Flow
-
-```mermaid
-flowchart TD
-    A["Kapit–Mueller bosonic Laughlin parent"] --> B["Exact zero-mode projector P"]
-    B --> C["Internal channel PHP"]
-    B --> D["External response P(dH)Q"]
-    C --> E["Controlled Poisson-to-GUE interpolation at fixed P"]
-    D --> F["Metric-normalized Berry curvature"]
-    F --> G["Finite-Jacobi local statistics and ramp"]
-    D --> H["Gauge-invariant four-channel tensor"]
-    H --> I["Resolved connected response cumulant"]
-    B --> J["Closed twist-torus bundle"]
-    J --> K["Fixed C1 with deformable Wilson holonomy"]
-```
-
-## Why the Kapit–Mueller Parent Is Essential
-
-The Kapit–Mueller lattice realizes an exactly flat Chern band whose projected contact interaction supports bosonic Laughlin zero modes. This gives the calculation four rare ingredients simultaneously:
-
-1. an exactly known degenerate kernel;
-2. a finite external excitation gap;
-3. boundary twists that form a closed parameter torus;
-4. local tangent operators whose response maps can be computed and compared at fixed topology.
-
-The parent Hamiltonian is positive semidefinite and frustration free: the target manifold is its exact kernel. This algebraic structure makes spectral flatness exact while allowing the projector to rotate through Hilbert space, which is precisely the regime where quantum geometry becomes the informative observable.
-
-## Algorithmic Innovations
-
-### 1. Metric-normalized signature compression
-
-Projector-to-complement response maps are assembled into a channel matrix and whitened by the quantum metric. The curvature reduces to a compression of a fixed signature matrix by a Stiefel row space. A Haar row space therefore produces an exact finite-dimensional complex-Jacobi point process. This converts a many-body geometric response into a parameter-free random-matrix benchmark at the actual finite rank.
-
-### 2. Exact finite-Jacobi form factor with boundary atoms
-
-The implementation evaluates the determinantal kernel directly by Gauss–Jacobi quadrature. When \(D>M\), exact eigenvalues at \(\lambda=\pm1\) are separated algebraically, yielding the plateau law
-
-$$K_{J,c}^{\mathrm{full}}=\frac{k}{D}K_{J,c}^{(k)},\qquad k=2M-D.$$
-
-This preserves the continuous Jacobi ramp and accounts exactly for deterministic geometric modes.
-
-### 3. Gauge-invariant matrix-element Geometric ETH
+The (\mathcal N=2) SYK supercharge (Q=\sum_{i<j<k}C_{ijk}\psi_i\psi_j\psi_k) obeys (Q^2=0). In a fixed charge sector, its BPS fiber is harmonic cohomology and its parameter response splits exactly as
 
-For response maps \(X_\mu\), the release whitens the channel covariance and evaluates
+$$X=-H_\perp^+(Q\,\delta Q^\dagger+Q^\dagger\delta Q)P=X_-\oplus X_+,qquad X_-^\dagger X_+=0.$$
 
-$$T_{\mu\nu\rho\sigma}=\frac{1}{D}\operatorname{Tr}(\widetilde X_\mu\widetilde X_\nu^\dagger\widetilde X_\rho\widetilde X_\sigma^\dagger).$$
+This exact/coexact decomposition is independent of the one-sided (H=B^\dagger B) Laughlin parent response.
 
-The finite-size reference uses independently generated covariance-matched complex-Gaussian samples. The residual therefore measures a genuine connected operator-channel component while remaining invariant under independent frame rotations in the zero-mode and complementary subspaces.
+## Registered Design
 
-### 4. Fixed-Chern holonomy engineering
-
-A smooth periodic ambient unitary \(\mathcal U_g:T^2\to U(\mathcal H)\) produces an exactly isospectral family \(H_g=\mathcal U_gH_0\mathcal U_g^\dagger\). The bundle isomorphism preserves \(C_1\), while the projected connection acquires a tunable one-form. This creates a controlled laboratory for separating determinant topology from relative non-Abelian transport.
+| Stage | Sizes | Role |
+|---|---|---|
+| Sequential pilot | (N=8,10,12) | Fix observable, covariance signatures, controls, and inference branches |
+| Held out | (N=14) | Freeze predictions from safe covariates, seal them, then explicitly unseal outcomes |
 
-## Reproduction Tiers
+Each size contains central/adjacent charge sectors and sparse/isotropic eight-channel tangent panels. The primary held-out pair is the central/adjacent sparse pair; the isotropic pair is secondary and cannot change the selected branch.
 
-### Tier 0: inspect the frozen evidence
+The frozen branches are: both covariance nulls cover; only the Hodge null covers; both reject with reproducible response memory; the generic response is indistinguishable from the structured control; or feasibility failure. Independent seal validation and explicit opening select `cohomological_non_gaussian_class`.
 
-- [Combined article audit](script/output/geometric_eth_topology_delivery_audit_v3.json)
-- [Matrix-element result](script/output/matrix_element_geometric_eth_v3.json)
-- [Topology result](script/output/topological_holonomy_v3.json)
-- [Release manifest](script/output/release_manifest_v1.json)
-- [Technical report](../../docs/2026-07-30-task05-technical-report.md)
+## Held-Out Result
 
-### Tier 1: quick verification
+| $N=14$ sparse sector | Physical median (95% bootstrap) | Collapsed null (97.5% prediction) | Hodge null (97.5% prediction) |
+|---|---:|---:|---:|
+| Adjacent | 0.301529 [0.291527, 0.312061] | [0.111789, 0.111852] | [0.112344, 0.112513] |
+| Central | 0.374993 [0.368980, 0.380473] | [0.111338, 0.111353] | [0.111333, 0.111348] |
 
-```bash
-cd 01_task_folder/task_05/script
-python -m venv .venv
-source .venv/bin/activate
-python -m pip install -r requirements.txt
-bash run_quick_verify_v1.sh
-```
+The result identifies structured four-point response memory beyond the frozen separable collapsed/Hodge null family. It does not establish intrinsic non-Gaussianity after complete nonseparable entrywise covariance matching.
 
-This read-only path verifies result labels, paper and figure hashes, task isolation, tracked-file size policy, exact Jacobi/form-factor identities, holonomy algebra, Wick contractions, and 38 focused tests.
-
-### Tier 2: rebuild the article
+## Minimal Verification
 
 ```bash
-cd 01_task_folder/task_05/script
-bash run_geometric_eth_topology_article_v3.sh
+cd script
+PYTHONPATH=. pytest -q $(rg --files tests | rg 'v7\.py$')
+python generate_susy_hodge_controls_v7.py
+python verify_susy_hodge_delivery_v7.py
+python verify_susy_hodge_manuscript_v7.py
 ```
 
-The article build uses compact published artifacts and performs a full PDF delivery audit. System tools: `latexmk` and `pdftoppm`.
-
-### Tier 3: full numerical recomputation
+## Build the Delivery
 
 ```bash
-cd 01_task_folder/task_05/script
-bash run_full_recompute_v1.sh
+cd script
+bash run_susy_hodge_delivery_v7.sh
 ```
 
-This production path rebuilds the large-scale, spectral-flatness, matrix-element, topology, figure, and paper layers with resumable checkpoints.
-
-## Artifact Contract
+The script merges the pilot, generates the final result figure and report from frozen artifacts, activates result macros only after the audits pass, compiles the Letter and Supplemental Material, copies the exact PDFs into `script/output/`, and verifies their hashes and render state.
 
-Git contains every source file, test, compact result table, figure, manuscript input, and final verdict required for review. The release manifest records 25 production arrays totaling 447704793 bytes with exact paths, byte sizes, SHA-256 hashes, storage classes, and producing commands. These arrays can be regenerated by Tier 3 and are ready for a future DOI-backed archive.
+## Artifact Map
 
-In a compact checkout, the complete test command reports 86 passing tests and 6 data-dependent tests marked as skipped. Restoring the listed production arrays activates those six tests automatically.
-
-## Figure Guide
-
-| Figure | Scientific role |
+| Artifact | Meaning |
 |---|---|
-| [Figure 1](script/output/figure_1_spectral_silence_v2.png) | Exact spectral flatness beside the geometric ramp |
-| [Figure 2](script/output/figure_2_falsification_triangle_v2.png) | Structured, physical, and finite-Jacobi comparison triangle |
-| [Figure 3](script/output/figure_3_independent_channels_v2.png) | Independently tunable spectral and projector-geometric axes |
-| [Figure 4](script/output/figure_4_geometric_hierarchy_v2.png) | Local-to-ramp-to-long-range correlation hierarchy |
-| [Figure 5](script/output/figure_5_jacobi_atoms_v2.png) | Finite-Jacobi boundary atoms and plateau law |
-| [Figure 6](script/output/figure_6_wick_factorization_v3.png) | Gauge-invariant four-channel residual along \(N=3,4,5\) |
-| [Figure 7](script/output/figure_7_topological_holonomy_v3.png) | Fixed Chern numbers with deformable Wilson holonomy |
-
-## Established Scope and Growth Path
-
-This release establishes exact spectral flatness, finite-rank Jacobi-like local curvature correlations, causal independence of \(PHP\) and \(P(\partial H)Q\), a shrinking connected four-channel component, and changing relative holonomy at fixed complete spectrum and fixed first Chern number.
-
-The next research horizon extends the matrix-element sequence through \(N=6\), derives its scaling from locality, realizes the same invariant law in a second exact-degeneracy mechanism, and connects the geometric hierarchy to real-time dynamics.
-
-The issue-ready handoff is [the Quantum Harness challenge draft](../../docs/2026-07-30-quantum-geometry-harness-challenge-draft.md).
+| `output/susy_hodge_v7_outcomes_pilot_combined.json/.npz` | Complete (N=8,10,12) pilot |
+| `output/susy_hodge_v7_N14_covariates.json` | Outcome-free held-out covariates |
+| `output/susy_hodge_v7_N14_prediction.json/.npz/.sha256` | Frozen numerical predictions and seal |
+| `output/susy_hodge_v7_N14_unsealed.json/.npz` | Explicitly opened outcome payload |
+| `output/susy_hodge_v7_N14_inference.json` | Frozen-branch decision |
+| `output/susy_hodge_v7_controls.json` | Analytic and synthetic controls |
+| `output/figure_susy_hodge_geometric_eth_v7.*` | Main data figure and provenance manifest |
+| `output/response_complex_memory_v7.pdf` | Final Letter |
+| `output/response_complex_memory_supplement_v7.pdf` | Final Supplemental Material |
+| `output/susy_hodge_delivery_audit_v7.json` | Scientific/provenance audit |
+| `output/susy_hodge_manuscript_audit_v7.json` | Paper/PDF audit |
+
+## Interpretation Boundary
+
+The operational label `cohomological_non_gaussian_class`, if selected, means four-point response memory beyond the frozen separable collapsed and Hodge covariance nulls. It does not establish failure of every fully nonseparable Gaussian covariance model. No (N=8\)–(14) result is presented as asymptotic Geometric ETH.
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/analyze_susy_hodge_geometric_eth_v7.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/analyze_susy_hodge_geometric_eth_v7.py
new file mode 100644
index 000000000..df621d327
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/analyze_susy_hodge_geometric_eth_v7.py
@@ -0,0 +1,654 @@
+#!/usr/bin/env python3
+"""Seal and score complete-realization SUSY Hodge predictions v7."""
+
+from __future__ import annotations
+
+import argparse
+import json
+from datetime import datetime, timezone
+from pathlib import Path
+from typing import Any
+
+import numpy as np
+
+from run_susy_hodge_geometric_eth_v7 import (
+    BASE_SEED,
+    CHECKPOINT_ROOT,
+    NULL_REPLICATES,
+    OUTPUT_ROOT,
+    VERSION,
+    _atomic_json,
+    _atomic_npz,
+    _banked_complete_medians,
+    _derived_seed,
+    _validate_file_hash,
+    panel_paths,
+    registered_case_grid,
+    seal_file_hash,
+    sha256,
+    unseal_outcomes,
+    write_safe_covariates,
+)
+from run_susy_hodge_null_bank_v7 import (
+    OUTPUT_ROOT as NULL_BANK_ROOT,
+    null_bank_paths,
+)
+
+
+SCRIPT_ROOT = Path(__file__).resolve().parent
+N14_SAFE_JSON = OUTPUT_ROOT / "susy_hodge_v7_N14_covariates.json"
+N14_PREDICTION_JSON = OUTPUT_ROOT / "susy_hodge_v7_N14_prediction.json"
+N14_PREDICTION_NPZ = OUTPUT_ROOT / "susy_hodge_v7_N14_prediction.npz"
+N14_PREDICTION_SEAL = OUTPUT_ROOT / "susy_hodge_v7_N14_prediction.sha256"
+N14_UNSEALED_JSON = OUTPUT_ROOT / "susy_hodge_v7_N14_unsealed.json"
+N14_UNSEALED_NPZ = OUTPUT_ROOT / "susy_hodge_v7_N14_unsealed.npz"
+N14_INFERENCE_JSON = OUTPUT_ROOT / "susy_hodge_v7_N14_inference.json"
+PILOT_BANK_SAFE_JSON = OUTPUT_ROOT / "susy_hodge_v7_covariates_pilot_banked.json"
+PILOT_BANK_JSON = OUTPUT_ROOT / "susy_hodge_v7_outcomes_pilot_banked.json"
+PILOT_BANK_NPZ = OUTPUT_ROOT / "susy_hodge_v7_outcomes_pilot_banked.npz"
+FORBIDDEN_PREDICTION_TOKENS = ("r4", "four_point", "connected")
+PREDICTION_COVERAGE = 0.975
+PREDICTION_QUANTILES = (0.0125, 0.5, 0.9875)
+PHYSICAL_BOOTSTRAP_REPLICATES = 10_000
+
+
+def _source_hashes() -> dict[str, str]:
+    paths = (
+        Path(__file__).resolve(),
+        SCRIPT_ROOT / "run_susy_hodge_geometric_eth_v7.py",
+        SCRIPT_ROOT / "run_susy_hodge_null_bank_v7.py",
+        SCRIPT_ROOT / "lgeth" / "hodge_wick.py",
+        SCRIPT_ROOT / "lgeth" / "wick_channels.py",
+    )
+    return {str(path.relative_to(SCRIPT_ROOT)): sha256(path) for path in paths}
+
+
+def _array_hash(values: np.ndarray) -> str:
+    contiguous = np.ascontiguousarray(values)
+    import hashlib
+
+    return hashlib.sha256(contiguous.view(np.uint8)).hexdigest()
+
+
+def _group_cases(
+    cases: list[tuple[int, str, int, str]],
+) -> dict[tuple[int, str, str], list[int]]:
+    groups: dict[tuple[int, str, str], list[int]] = {}
+    if not cases:
+        raise ValueError("prediction requires at least one case")
+    for N, sector, realization, panel_kind in sorted(cases):
+        key = (int(N), str(sector), str(panel_kind))
+        groups.setdefault(key, []).append(int(realization))
+    for key, realizations in groups.items():
+        if len(realizations) != len(set(realizations)):
+            raise ValueError(f"duplicate realization in prediction group {key}")
+    return groups
+
+
+def _load_group_banks(
+    N: int,
+    sector: str,
+    panel_kind: str,
+    realizations: list[int],
+    *,
+    null_bank_root: Path,
+) -> tuple[np.ndarray, np.ndarray, list[dict[str, Any]]]:
+    collapsed: list[np.ndarray] = []
+    hodge: list[np.ndarray] = []
+    records: list[dict[str, Any]] = []
+    for realization in realizations:
+        metadata_path, arrays_path = null_bank_paths(
+            null_bank_root,
+            N,
+            sector,
+            realization,
+            panel_kind,
+        )
+        if not metadata_path.is_file() or not arrays_path.is_file():
+            raise FileNotFoundError("missing safe null bank")
+        metadata = json.loads(metadata_path.read_text(encoding="utf-8"))
+        if metadata.get("arrays_sha256") != sha256(arrays_path):
+            raise ValueError("null-bank array hash mismatch")
+        if not metadata.get("passed") or not all(metadata.get("checks", {}).values()):
+            raise ValueError("null bank contains a failed gate")
+        identity = metadata.get("identity", {})
+        expected = (N, sector, realization, panel_kind)
+        observed = tuple(
+            identity.get(key)
+            for key in ("N", "sector", "realization", "panel_kind")
+        )
+        if observed != expected:
+            raise ValueError("null-bank case identity mismatch")
+        with np.load(arrays_path) as arrays:
+            collapsed_values = np.asarray(arrays["collapsed_null"], dtype=float)
+            hodge_values = np.asarray(arrays["hodge_null"], dtype=float)
+        if collapsed_values.ndim != 1 or hodge_values.shape != collapsed_values.shape:
+            raise ValueError("null-bank draw shapes disagree")
+        if not np.all(np.isfinite(collapsed_values)) or not np.all(
+            np.isfinite(hodge_values)
+        ):
+            raise ValueError("null bank contains non-finite draws")
+        collapsed.append(collapsed_values)
+        hodge.append(hodge_values)
+        records.append(
+            {
+                "realization": realization,
+                "metadata_sha256": sha256(metadata_path),
+                "arrays_sha256": sha256(arrays_path),
+            }
+        )
+    return np.asarray(collapsed), np.asarray(hodge), records
+
+
+def aggregate_pilot_from_banks(
+    cases: list[tuple[int, str, int, str]],
+    *,
+    checkpoint_root: Path = CHECKPOINT_ROOT,
+    null_bank_root: Path = NULL_BANK_ROOT,
+    safe_covariates_json: Path = PILOT_BANK_SAFE_JSON,
+    output_json: Path = PILOT_BANK_JSON,
+    output_npz: Path = PILOT_BANK_NPZ,
+    null_replicates: int = NULL_REPLICATES,
+    bootstrap_replicates: int = PHYSICAL_BOOTSTRAP_REPLICATES,
+    seed: int = BASE_SEED,
+) -> dict[str, Any]:
+    """Aggregate completed pilot sidecars using precomputed safe null banks."""
+
+    null_count = int(null_replicates)
+    bootstrap_count = int(bootstrap_replicates)
+    if null_count < 1 or bootstrap_count < 1:
+        raise ValueError("pilot aggregation requires positive replicate counts")
+    groups = _group_cases(cases)
+    write_safe_covariates(
+        cases,
+        root=checkpoint_root,
+        output_json=safe_covariates_json,
+    )
+    output_arrays: dict[str, np.ndarray] = {}
+    summaries: list[dict[str, Any]] = []
+    for (N, sector, panel_kind), realizations in sorted(groups.items()):
+        collapsed_banks, hodge_banks, bank_records = _load_group_banks(
+            N,
+            sector,
+            panel_kind,
+            realizations,
+            null_bank_root=null_bank_root,
+        )
+        physical_values: list[float] = []
+        balances: list[float] = []
+        for realization in realizations:
+            safe_path, arrays_path, outcome_path = panel_paths(
+                checkpoint_root,
+                N,
+                sector,
+                realization,
+                panel_kind,
+            )
+            if not outcome_path.is_file():
+                raise FileNotFoundError("missing sequential-pilot outcome sidecar")
+            safe = json.loads(safe_path.read_text(encoding="utf-8"))
+            outcome = json.loads(outcome_path.read_text(encoding="utf-8"))
+            if (
+                safe.get("arrays_sha256") != sha256(arrays_path)
+                or outcome.get("safe_identity_hash") != safe.get("identity_hash")
+                or outcome.get("safe_arrays_sha256") != safe.get("arrays_sha256")
+            ):
+                raise ValueError("pilot outcome identity mismatch")
+            observed_case = tuple(
+                outcome.get(key)
+                for key in ("N", "sector", "realization", "panel_kind")
+            )
+            if observed_case != (N, sector, realization, panel_kind):
+                raise ValueError("pilot outcome case identity mismatch")
+            physical_values.append(float(outcome["R4"]))
+            balances.append(float(safe["signature"]["hodge_balance"]))
+        physical = np.asarray(physical_values, dtype=float)
+        if not np.all(np.isfinite(physical)):
+            raise ValueError("pilot physical outcome is not finite")
+        physical_bootstrap = _bootstrap_median(
+            physical,
+            bootstrap_count,
+            _derived_seed(seed, N, sector, panel_kind, "pilot_physical_bootstrap"),
+        )
+        collapsed = _banked_complete_medians(
+            collapsed_banks,
+            null_count,
+            _derived_seed(seed, N, sector, panel_kind, "pilot_collapsed"),
+        )
+        hodge = _banked_complete_medians(
+            hodge_banks,
+            null_count,
+            _derived_seed(seed, N, sector, panel_kind, "pilot_hodge"),
+        )
+        prefix = f"N{N}_{sector}_{panel_kind}"
+        output_arrays[f"{prefix}_physical"] = physical
+        output_arrays[f"{prefix}_physical_bootstrap"] = physical_bootstrap
+        output_arrays[f"{prefix}_collapsed_null"] = collapsed
+        output_arrays[f"{prefix}_hodge_null"] = hodge
+        observed_median = float(np.median(physical))
+        collapsed_interval = np.quantile(
+            collapsed, PREDICTION_QUANTILES
+        ).tolist()
+        hodge_interval = np.quantile(hodge, PREDICTION_QUANTILES).tolist()
+        summaries.append(
+            {
+                "N": N,
+                "sector": sector,
+                "panel_kind": panel_kind,
+                "realizations": len(realizations),
+                "observed_median": observed_median,
+                "physical_bootstrap_interval": np.quantile(
+                    physical_bootstrap, [0.025, 0.975]
+                ).tolist(),
+                "collapsed_prediction_interval": collapsed_interval,
+                "hodge_prediction_interval": hodge_interval,
+                "collapsed_covered": collapsed_interval[0]
+                <= observed_median
+                <= collapsed_interval[2],
+                "hodge_covered": hodge_interval[0]
+                <= observed_median
+                <= hodge_interval[2],
+                "median_hodge_balance": float(np.median(balances)),
+                "null_banks": bank_records,
+            }
+        )
+    _atomic_npz(output_npz, **output_arrays)
+    checks = {
+        "complete_requested_grid": sum(
+            item["realizations"] for item in summaries
+        )
+        == len(cases),
+        "finite_outputs": all(
+            np.all(np.isfinite(values)) for values in output_arrays.values()
+        ),
+        "registered_null_replicates": all(
+            values.shape == (null_count,)
+            for key, values in output_arrays.items()
+            if key.endswith("_null")
+        ),
+        "registered_bootstrap_replicates": all(
+            values.shape == (bootstrap_count,)
+            for key, values in output_arrays.items()
+            if key.endswith("_physical_bootstrap")
+        ),
+        "safe_covariates_preexist": Path(safe_covariates_json).is_file(),
+    }
+    payload = {
+        "version": VERSION,
+        "generated_utc": datetime.now(timezone.utc).isoformat(),
+        "uncertainty_unit": "complete_disorder_realization",
+        "null_replicates": null_count,
+        "physical_bootstrap_replicates": bootstrap_count,
+        "prediction_coverage": PREDICTION_COVERAGE,
+        "groups": summaries,
+        "safe_covariates_sha256": sha256(safe_covariates_json),
+        "arrays_sha256": sha256(output_npz),
+        "sources": _source_hashes(),
+        "checks": checks,
+        "passed": all(checks.values()),
+    }
+    if not payload["passed"]:
+        raise RuntimeError(f"banked pilot aggregation failed: {checks}")
+    _atomic_json(output_json, payload)
+    return payload
+
+
+def write_n14_prediction(
+    cases: list[tuple[int, str, int, str]],
+    *,
+    checkpoint_root: Path = CHECKPOINT_ROOT,
+    null_bank_root: Path = NULL_BANK_ROOT,
+    safe_covariates_json: Path = N14_SAFE_JSON,
+    output_json: Path = N14_PREDICTION_JSON,
+    output_npz: Path = N14_PREDICTION_NPZ,
+    seal_path: Path = N14_PREDICTION_SEAL,
+    null_replicates: int = NULL_REPLICATES,
+    seed: int = BASE_SEED,
+) -> dict[str, Any]:
+    """Predict group medians from safe two-point data and seal before unseal."""
+
+    count = int(null_replicates)
+    if count < 1:
+        raise ValueError("prediction requires positive null replicates")
+    groups = _group_cases(cases)
+    sizes = {key[0] for key in groups}
+    if len(sizes) != 1:
+        raise ValueError("a prediction seal must contain exactly one system size")
+    N = next(iter(sizes))
+    required_primary = {(N, "central", "sparse"), (N, "adjacent", "sparse")}
+    if not required_primary.issubset(groups):
+        raise ValueError("prediction is missing the registered sparse primary pair")
+    write_safe_covariates(
+        cases,
+        root=checkpoint_root,
+        output_json=safe_covariates_json,
+    )
+    output_arrays: dict[str, np.ndarray] = {}
+    summaries: list[dict[str, Any]] = []
+    primary_pair: list[dict[str, Any]] = []
+    for (group_N, sector, panel_kind), realizations in sorted(groups.items()):
+        collapsed_banks, hodge_banks, bank_records = _load_group_banks(
+            group_N,
+            sector,
+            panel_kind,
+            realizations,
+            null_bank_root=null_bank_root,
+        )
+        collapsed = _banked_complete_medians(
+            collapsed_banks,
+            count,
+            _derived_seed(seed, group_N, sector, panel_kind, "sealed_collapsed"),
+        )
+        hodge = _banked_complete_medians(
+            hodge_banks,
+            count,
+            _derived_seed(seed, group_N, sector, panel_kind, "sealed_hodge"),
+        )
+        prefix = f"N{group_N}_{sector}_{panel_kind}"
+        output_arrays[f"{prefix}_collapsed"] = collapsed
+        output_arrays[f"{prefix}_hodge"] = hodge
+        record = {
+            "N": group_N,
+            "sector": sector,
+            "panel_kind": panel_kind,
+            "realizations": len(realizations),
+            "realization_ids": realizations,
+            "collapsed_interval": np.quantile(
+                collapsed, PREDICTION_QUANTILES
+            ).tolist(),
+            "hodge_interval": np.quantile(hodge, PREDICTION_QUANTILES).tolist(),
+            "collapsed_array_sha256": _array_hash(collapsed),
+            "hodge_array_sha256": _array_hash(hodge),
+            "null_banks": bank_records,
+        }
+        summaries.append(record)
+        if panel_kind == "sparse" and sector in {"central", "adjacent"}:
+            primary_pair.append(
+                {
+                    key: record[key]
+                    for key in (
+                        "N",
+                        "sector",
+                        "panel_kind",
+                        "realizations",
+                        "collapsed_interval",
+                        "hodge_interval",
+                    )
+                }
+            )
+    _atomic_npz(output_npz, **output_arrays)
+    checks = {
+        "complete_requested_grid": sum(
+            item["realizations"] for item in summaries
+        )
+        == len(cases),
+        "registered_primary_pair": {
+            (item["sector"], item["panel_kind"]) for item in primary_pair
+        }
+        == {("central", "sparse"), ("adjacent", "sparse")},
+        "finite_prediction_arrays": all(
+            np.all(np.isfinite(values)) for values in output_arrays.values()
+        ),
+        "complete_realization_unit": all(
+            item["realizations"] == len(item["realization_ids"])
+            for item in summaries
+        ),
+        "safe_covariates_preexist": Path(safe_covariates_json).is_file(),
+    }
+    payload = {
+        "version": VERSION,
+        "generated_utc": datetime.now(timezone.utc).isoformat(),
+        "system_size": N,
+        "observable": "normalized_response_memory",
+        "uncertainty_unit": "complete_disorder_realization",
+        "prediction_coverage": PREDICTION_COVERAGE,
+        "prediction_quantiles": list(PREDICTION_QUANTILES),
+        "null_replicates": count,
+        "safe_covariates_sha256": sha256(safe_covariates_json),
+        "prediction_arrays_file": Path(output_npz).name,
+        "prediction_arrays_sha256": sha256(output_npz),
+        "sources": _source_hashes(),
+        "groups": summaries,
+        "primary_pair": primary_pair,
+        "checks": checks,
+    }
+    serialized = json.dumps(payload, sort_keys=True).lower()
+    payload["checks"]["no_outcome_leakage"] = not any(
+        token in serialized for token in FORBIDDEN_PREDICTION_TOKENS
+    )
+    payload["passed"] = all(payload["checks"].values())
+    if not payload["passed"]:
+        raise RuntimeError(f"sealed prediction audit failed: {payload['checks']}")
+    _atomic_json(output_json, payload)
+    seal_file_hash(output_json, seal_path)
+    return payload
+
+
+def _bootstrap_median(
+    values: np.ndarray,
+    replicates: int,
+    seed: int,
+) -> np.ndarray:
+    samples = np.asarray(values, dtype=float)
+    count = int(replicates)
+    if samples.ndim != 1 or samples.size < 1 or count < 1:
+        raise ValueError("median bootstrap requires a nonempty realization vector")
+    rng = np.random.default_rng(int(seed))
+    indices = rng.integers(0, samples.size, size=(count, samples.size))
+    return np.median(samples[indices], axis=1)
+
+
+def select_frozen_branch(
+    collapsed_pair_covered: bool,
+    hodge_pair_covered: bool,
+    structured_indistinguishable: bool,
+    numerical_gates_passed: bool,
+) -> str:
+    """Map the registered pair outcome to exactly one frozen result branch."""
+
+    if not numerical_gates_passed:
+        return "feasibility_failure"
+    if collapsed_pair_covered and hodge_pair_covered:
+        return "strong_covariance_universality"
+    if not collapsed_pair_covered and hodge_pair_covered:
+        return "hodge_resolved_geometric_eth"
+    if not collapsed_pair_covered and not hodge_pair_covered:
+        if structured_indistinguishable:
+            return "structured_cohomology"
+        return "cohomological_non_gaussian_class"
+    # A collapsed-only success is not one of the preregistered scientific
+    # branches, so the analysis fails closed instead of inventing a claim.
+    return "feasibility_failure"
+
+
+def _outside_interval(confidence: list[float], interval: list[float]) -> bool:
+    return confidence[1] < interval[0] or confidence[0] > interval[2]
+
+
+def score_unsealed_n14(
+    prediction_json: Path,
+    prediction_seal: Path,
+    unsealed_json: Path,
+    *,
+    output_json: Path = N14_INFERENCE_JSON,
+    bootstrap_replicates: int = PHYSICAL_BOOTSTRAP_REPLICATES,
+    seed: int = BASE_SEED,
+    structured_indistinguishable: bool = False,
+) -> dict[str, Any]:
+    """Score the held-out sparse pair after validating the prediction seal."""
+
+    prediction_hash = _validate_file_hash(prediction_json, prediction_seal)
+    prediction = json.loads(Path(prediction_json).read_text(encoding="utf-8"))
+    if not prediction.get("passed") or not all(prediction.get("checks", {}).values()):
+        raise ValueError("sealed prediction contains a failed gate")
+    unsealed = json.loads(Path(unsealed_json).read_text(encoding="utf-8"))
+    if not unsealed.get("passed"):
+        raise ValueError("unsealed outcome aggregate contains a failed gate")
+    if unsealed.get("prediction_sha256") != prediction_hash:
+        raise ValueError("unsealed aggregate references the wrong prediction")
+    try:
+        prediction_time = datetime.fromisoformat(prediction["generated_utc"])
+        unsealed_time = datetime.fromisoformat(unsealed["unsealed_utc"])
+    except (KeyError, TypeError, ValueError) as error:
+        raise ValueError("prediction/unseal timestamp is invalid") from error
+    if unsealed_time <= prediction_time:
+        raise ValueError("prediction must precede the outcome unseal")
+    records = unsealed.get("records", [])
+    primary = {
+        (int(item["N"]), str(item["sector"]), str(item["panel_kind"])): item
+        for item in prediction["primary_pair"]
+    }
+    results: list[dict[str, Any]] = []
+    for key, predicted in sorted(primary.items()):
+        N, sector, panel_kind = key
+        values = np.asarray(
+            [
+                float(record["R4"])
+                for record in records
+                if (
+                    int(record["N"]),
+                    str(record["sector"]),
+                    str(record["panel_kind"]),
+                )
+                == key
+            ],
+            dtype=float,
+        )
+        if values.size != int(predicted["realizations"]):
+            raise ValueError("unsealed primary realization count mismatch")
+        bootstrap = _bootstrap_median(
+            values,
+            int(bootstrap_replicates),
+            _derived_seed(seed, N, sector, panel_kind, "physical_bootstrap"),
+        )
+        observed = float(np.median(values))
+        confidence = np.quantile(bootstrap, [0.025, 0.975]).tolist()
+        collapsed_interval = [float(value) for value in predicted["collapsed_interval"]]
+        hodge_interval = [float(value) for value in predicted["hodge_interval"]]
+        results.append(
+            {
+                "N": N,
+                "sector": sector,
+                "panel_kind": panel_kind,
+                "realizations": int(values.size),
+                "observed_median": observed,
+                "physical_bootstrap_interval": confidence,
+                "collapsed_prediction_interval": collapsed_interval,
+                "hodge_prediction_interval": hodge_interval,
+                "collapsed_covered": collapsed_interval[0]
+                <= observed
+                <= collapsed_interval[2],
+                "hodge_covered": hodge_interval[0]
+                <= observed
+                <= hodge_interval[2],
+                "robust_outside_both": _outside_interval(
+                    confidence, collapsed_interval
+                )
+                and _outside_interval(confidence, hodge_interval),
+            }
+        )
+    collapsed_pair = all(item["collapsed_covered"] for item in results)
+    hodge_pair = all(item["hodge_covered"] for item in results)
+    robust_non_gaussian = all(item["robust_outside_both"] for item in results)
+    inference_resolved = (
+        collapsed_pair
+        or hodge_pair
+        or bool(structured_indistinguishable)
+        or robust_non_gaussian
+    )
+    numerical_gates = (
+        len(results) == 2
+        and all(np.isfinite(item["observed_median"]) for item in results)
+        and inference_resolved
+    )
+    branch = select_frozen_branch(
+        collapsed_pair,
+        hodge_pair,
+        bool(structured_indistinguishable),
+        numerical_gates,
+    )
+    payload = {
+        "version": VERSION,
+        "unsealed_utc": unsealed.get("unsealed_utc"),
+        "scored_utc": datetime.now(timezone.utc).isoformat(),
+        "prediction_sha256": prediction_hash,
+        "selected_branch": branch,
+        "primary_pair": results,
+        "pair_coverage": {
+            "collapsed": collapsed_pair,
+            "hodge": hodge_pair,
+        },
+        "robust_non_gaussian_excess": robust_non_gaussian,
+        "structured_indistinguishable": bool(structured_indistinguishable),
+        "physical_bootstrap_replicates": int(bootstrap_replicates),
+        "checks": {
+            "valid_prediction_seal": True,
+            "prediction_precedes_unseal": unsealed_time > prediction_time,
+            "complete_primary_pair": len(results) == 2,
+            "complete_realization_uncertainty": all(
+                item["realizations"] > 0 for item in results
+            ),
+            "registered_branch_resolved": inference_resolved,
+        },
+    }
+    payload["passed"] = all(payload["checks"].values())
+    _atomic_json(output_json, payload)
+    return payload
+
+
+def _parser() -> argparse.ArgumentParser:
+    parser = argparse.ArgumentParser(description=__doc__)
+    subparsers = parser.add_subparsers(dest="command", required=True)
+    predict = subparsers.add_parser("predict")
+    predict.add_argument("--null-replicates", type=int, default=NULL_REPLICATES)
+    unseal = subparsers.add_parser("unseal")
+    unseal.add_argument(
+        "--bootstrap-replicates",
+        type=int,
+        default=PHYSICAL_BOOTSTRAP_REPLICATES,
+    )
+    pilot = subparsers.add_parser("pilot")
+    pilot.add_argument("--sizes", type=int, nargs="+", required=True)
+    pilot.add_argument("--null-replicates", type=int, default=NULL_REPLICATES)
+    pilot.add_argument(
+        "--bootstrap-replicates",
+        type=int,
+        default=PHYSICAL_BOOTSTRAP_REPLICATES,
+    )
+    return parser
+
+
+def main() -> None:
+    args = _parser().parse_args()
+    if args.command == "pilot":
+        payload = aggregate_pilot_from_banks(
+            registered_case_grid(tuple(args.sizes)),
+            null_replicates=args.null_replicates,
+            bootstrap_replicates=args.bootstrap_replicates,
+        )
+    elif args.command == "predict":
+        cases = registered_case_grid((14,))
+        payload = write_n14_prediction(
+            cases,
+            null_replicates=args.null_replicates,
+        )
+    else:
+        cases = registered_case_grid((14,))
+        unseal_outcomes(
+            cases,
+            prediction_json=N14_PREDICTION_JSON,
+            prediction_seal=N14_PREDICTION_SEAL,
+            output_json=N14_UNSEALED_JSON,
+            output_npz=N14_UNSEALED_NPZ,
+        )
+        payload = score_unsealed_n14(
+            N14_PREDICTION_JSON,
+            N14_PREDICTION_SEAL,
+            N14_UNSEALED_JSON,
+            bootstrap_replicates=args.bootstrap_replicates,
+        )
+    print(json.dumps(payload, indent=2, sort_keys=True))
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/generate_susy_hodge_controls_v7.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/generate_susy_hodge_controls_v7.py
new file mode 100644
index 000000000..c860656be
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/generate_susy_hodge_controls_v7.py
@@ -0,0 +1,205 @@
+#!/usr/bin/env python3
+"""Generate analytic decomposable and one-sided control audit v7."""
+
+from __future__ import annotations
+
+import hashlib
+import json
+from pathlib import Path
+from typing import Any
+
+import numpy as np
+
+from lgeth.hodge_response import (
+    HodgeSignature,
+    decomposable_curvature,
+    hodge_response,
+)
+from lgeth.hodge_wick import hodge_gaussian_r4_reference
+from lgeth.susy_cohomology import (
+    analytic_decomposable_curvature_multiplicities,
+    decomposable_bps_rank,
+    decomposable_couplings,
+    decomposable_tangent,
+    solve_bps_frame,
+)
+from lgeth.wick_channels import gaussian_r4_reference
+
+
+SCRIPT_ROOT = Path(__file__).resolve().parent
+OUTPUT_JSON = SCRIPT_ROOT / "output" / "susy_hodge_v7_controls.json"
+VERSION = "v7"
+
+
+def sha256(path: Path) -> str:
+    digest = hashlib.sha256()
+    with Path(path).open("rb") as handle:
+        for block in iter(lambda: handle.read(1 << 20), b""):
+            digest.update(block)
+    return digest.hexdigest()
+
+
+def _atomic_json(path: Path, payload: dict[str, Any]) -> None:
+    path = Path(path)
+    path.parent.mkdir(parents=True, exist_ok=True)
+    temporary = path.with_suffix(path.suffix + ".tmp")
+    temporary.write_text(
+        json.dumps(payload, indent=2, sort_keys=True),
+        encoding="utf-8",
+    )
+    temporary.replace(path)
+
+
+def _source_hashes() -> dict[str, str]:
+    paths = (
+        Path(__file__).resolve(),
+        SCRIPT_ROOT / "lgeth" / "susy_cohomology.py",
+        SCRIPT_ROOT / "lgeth" / "hodge_response.py",
+        SCRIPT_ROOT / "lgeth" / "hodge_wick.py",
+        SCRIPT_ROOT / "lgeth" / "wick_channels.py",
+    )
+    return {str(path.relative_to(SCRIPT_ROOT)): sha256(path) for path in paths}
+
+
+def _atomic_summary(
+    matrix: np.ndarray,
+    alpha: float,
+) -> tuple[dict[str, int], float, list[float]]:
+    eigenvalues = np.linalg.eigvalsh(0.5 * (matrix + matrix.conj().T))
+    target = 1.0 / float(alpha) ** 2
+    tolerance = 2e-11
+    counts = {
+        "negative": int(np.count_nonzero(np.isclose(eigenvalues, -target, atol=tolerance))),
+        "zero": int(np.count_nonzero(np.isclose(eigenvalues, 0.0, atol=tolerance))),
+        "positive": int(np.count_nonzero(np.isclose(eigenvalues, target, atol=tolerance))),
+    }
+    atoms = np.asarray([-target, 0.0, target])
+    error = float(np.max(np.min(np.abs(eigenvalues[:, None] - atoms[None, :]), axis=1)))
+    return counts, error, eigenvalues.tolist()
+
+
+def _one_sided_signature() -> HodgeSignature:
+    target = np.asarray([0.42, 0.27, 0.18, 0.09, 0.04])
+    external = np.asarray([0.51, 0.31, 0.18])
+    zero_target = np.zeros_like(target)
+    return HodgeSignature(
+        channel_count=8,
+        target_rank=5,
+        minus_weight=1.0,
+        plus_weight=0.0,
+        hodge_balance=0.0,
+        minus_channel_covariance=np.eye(8),
+        plus_channel_covariance=np.zeros((8, 8)),
+        minus_target_eigenvalues=target,
+        plus_target_eigenvalues=zero_target,
+        minus_external_eigenvalues=external,
+        plus_external_eigenvalues=np.empty(0),
+        minus_target_effective_rank=3.5,
+        plus_target_effective_rank=0.0,
+        minus_external_effective_rank=2.5,
+        plus_external_effective_rank=0.0,
+        minus_target_entropy=0.8,
+        plus_target_entropy=0.0,
+        minus_external_entropy=0.8,
+        plus_external_entropy=0.0,
+        orthogonality_relative_error=0.0,
+    )
+
+
+def generate_controls(output_json: Path = OUTPUT_JSON) -> dict[str, Any]:
+    """Write exact curvature atoms and immutable one-sided null regression."""
+
+    alpha = 1.7
+    couplings6 = decomposable_couplings(6, alpha)
+    frame6 = solve_bps_frame(6, 3, couplings6, dense_cutoff=64)
+    tangents6 = np.stack(
+        [
+            decomposable_tangent(6, "12", 3),
+            decomposable_tangent(6, "13", 4),
+        ]
+    )
+    response6 = hodge_response(frame6, couplings6, tangents6)
+    diagonal_counts, diagonal_error, diagonal_eigenvalues = _atomic_summary(
+        decomposable_curvature(response6, 0), alpha
+    )
+    off_counts, off_error, off_eigenvalues = _atomic_summary(
+        decomposable_curvature(response6, 0, 1), alpha
+    )
+    expected_diagonal = analytic_decomposable_curvature_multiplicities(
+        6, 3, "diagonal"
+    )
+    expected_off = analytic_decomposable_curvature_multiplicities(
+        6, 3, "off_diagonal"
+    )
+
+    couplings8 = decomposable_couplings(8, alpha)
+    rank8 = decomposable_bps_rank(8, 4)
+    frame8 = solve_bps_frame(
+        8,
+        4,
+        couplings8,
+        dense_cutoff=128,
+        expected_rank_override=rank8,
+    )
+
+    signature = _one_sided_signature()
+    hodge_reference = hodge_gaussian_r4_reference(signature, 8, 32, 211)
+    immutable_reference = gaussian_r4_reference(
+        signature.minus_target_eigenvalues,
+        signature.minus_external_eigenvalues,
+        8,
+        32,
+        211,
+    )
+    one_sided_difference = float(
+        np.max(np.abs(hodge_reference - immutable_reference))
+    )
+    checks = {
+        "N6_diagonal_multiplicities": diagonal_counts == expected_diagonal,
+        "N6_off_diagonal_multiplicities": off_counts == expected_off,
+        "N6_curvature_atoms": max(diagonal_error, off_error) < 2e-11,
+        "N8_decomposable_rank": frame8.projector_frame.shape[1] == rank8 == 60,
+        "N8_open_gap": frame8.gap > 1e-10,
+        "one_sided_exact_regression": one_sided_difference == 0.0,
+    }
+    payload = {
+        "version": VERSION,
+        "sources": _source_hashes(),
+        "decomposable_N6": {
+            "alpha": alpha,
+            "bps_rank": int(frame6.projector_frame.shape[1]),
+            "gap": float(frame6.gap),
+            "diagonal_multiplicities": diagonal_counts,
+            "off_diagonal_multiplicities": off_counts,
+            "diagonal_max_atom_error": diagonal_error,
+            "off_diagonal_max_atom_error": off_error,
+            "diagonal_eigenvalues": diagonal_eigenvalues,
+            "off_diagonal_eigenvalues": off_eigenvalues,
+        },
+        "decomposable_N8": {
+            "bps_rank": int(frame8.projector_frame.shape[1]),
+            "expected_rank": rank8,
+            "gap": float(frame8.gap),
+            "kernel_residual": float(frame8.kernel_residual),
+        },
+        "one_sided_regression": {
+            "samples": 32,
+            "seed": 211,
+            "max_absolute_difference": one_sided_difference,
+        },
+        "checks": checks,
+        "passed": all(checks.values()),
+    }
+    if not payload["passed"]:
+        raise RuntimeError(f"SUSY/Hodge control audit failed: {checks}")
+    _atomic_json(output_json, payload)
+    return payload
+
+
+def main() -> None:
+    payload = generate_controls()
+    print(json.dumps(payload, indent=2, sort_keys=True))
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/lgeth/hodge_response.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/lgeth/hodge_response.py
new file mode 100644
index 000000000..f66c3ff34
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/lgeth/hodge_response.py
@@ -0,0 +1,446 @@
+"""Exact/coexact BPS-projector responses for cubic N=2 SYK complexes."""
+
+from __future__ import annotations
+
+from dataclasses import dataclass
+
+import numpy as np
+
+from .susy_cohomology import BPSFrame, cubic_supercharge, cubic_triples
+from .wick_channels import (
+    WickResult,
+    channel_covariance,
+    four_channel_tensor,
+    target_covariance,
+    whiten_channel_labels,
+)
+
+
+@dataclass(frozen=True)
+class HodgeResponse:
+    """Resolved complement-to-BPS response for a tangent panel."""
+
+    minus: np.ndarray
+    plus: np.ndarray
+    total: np.ndarray
+    direct: np.ndarray
+    branch_sum_relative_error: float
+    direct_relative_error: float
+    orthogonality_relative_error: float
+    target_leakage: float
+    checks: dict[str, bool]
+
+
+@dataclass(frozen=True)
+class HodgeSignature:
+    """Gauge-invariant safe two-point data for a resolved response panel."""
+
+    channel_count: int
+    target_rank: int
+    minus_weight: float
+    plus_weight: float
+    hodge_balance: float
+    minus_channel_covariance: np.ndarray
+    plus_channel_covariance: np.ndarray
+    minus_target_eigenvalues: np.ndarray
+    plus_target_eigenvalues: np.ndarray
+    minus_external_eigenvalues: np.ndarray
+    plus_external_eigenvalues: np.ndarray
+    minus_target_effective_rank: float
+    plus_target_effective_rank: float
+    minus_external_effective_rank: float
+    plus_external_effective_rank: float
+    minus_target_entropy: float
+    plus_target_entropy: float
+    minus_external_entropy: float
+    plus_external_entropy: float
+    orthogonality_relative_error: float
+
+
+def _relative_error(first: np.ndarray, second: np.ndarray) -> float:
+    denominator = max(float(np.linalg.norm(second)), np.finfo(float).tiny)
+    return float(np.linalg.norm(first - second) / denominator)
+
+
+def _pseudoinverse_apply(frame: BPSFrame, rhs: np.ndarray) -> np.ndarray:
+    complement = np.asarray(frame.complement_frame, dtype=complex)
+    energies = np.asarray(frame.positive_energies, dtype=float)
+    if complement.shape[1] != energies.size or np.any(energies <= 0.0):
+        raise ValueError("BPS complement frame and energies are inconsistent")
+    coordinates = complement.conj().T @ np.asarray(rhs, dtype=complex)
+    return complement @ (coordinates / energies[:, None])
+
+
+def projector_derivative_from_response(
+    projector_frame: np.ndarray,
+    response: np.ndarray,
+) -> np.ndarray:
+    """Reconstruct dP from X = (1-P)dP P."""
+
+    frame = np.asarray(projector_frame, dtype=complex)
+    values = np.asarray(response, dtype=complex)
+    if values.shape != frame.shape:
+        raise ValueError("projector frame and response shape disagree")
+    derivative = values @ frame.conj().T + frame @ values.conj().T
+    return 0.5 * (derivative + derivative.conj().T)
+
+
+def project_moduli_tangents(
+    couplings: np.ndarray,
+    candidates: np.ndarray,
+    *,
+    relative_tolerance: float = 1e-12,
+) -> np.ndarray:
+    """Remove the complex radial/phase line and orthonormalize row tangents."""
+
+    coefficients = np.asarray(couplings, dtype=complex)
+    values = np.asarray(candidates, dtype=complex)
+    if coefficients.ndim != 1 or values.ndim != 2:
+        raise ValueError("couplings and tangent candidates have wrong dimensions")
+    if values.shape[1] != coefficients.size or values.shape[0] < 1:
+        raise ValueError("tangent candidates have the wrong shape")
+    norm_squared = float(np.vdot(coefficients, coefficients).real)
+    if norm_squared <= 0.0:
+        raise ValueError("coupling vector has zero norm")
+    overlaps = values @ coefficients.conj()
+    projected = values - np.outer(overlaps / norm_squared, coefficients)
+    q, r = np.linalg.qr(projected.T, mode="reduced")
+    diagonal = np.diag(r)
+    scale = max(float(np.linalg.norm(projected, ord=2)), np.finfo(float).tiny)
+    if diagonal.size != values.shape[0] or np.any(
+        np.abs(diagonal) <= float(relative_tolerance) * scale
+    ):
+        raise ValueError("projected tangent candidates do not have full rank")
+    phases = diagonal / np.abs(diagonal)
+    q = q * phases[None, :]
+    tangents = np.asarray(q.T, dtype=complex)
+    if not np.allclose(
+        tangents @ tangents.conj().T,
+        np.eye(values.shape[0]),
+        atol=5e-13,
+        rtol=5e-13,
+    ):
+        raise RuntimeError("moduli tangent orthonormalization failed")
+    if float(np.max(np.abs(tangents @ coefficients.conj()))) > 5e-13:
+        raise RuntimeError("moduli tangent retains radial or phase leakage")
+    return tangents
+
+
+def coupling_panels(
+    couplings: np.ndarray,
+    panel_size: int,
+    seed: int,
+) -> dict[str, np.ndarray]:
+    """Return deterministic sparse and isotropic coupling-space panels."""
+
+    coefficients = np.asarray(couplings, dtype=complex)
+    size = int(panel_size)
+    if coefficients.ndim != 1 or not 1 <= size < coefficients.size - 1:
+        raise ValueError("invalid coupling panel dimensions")
+    sparse_seed, isotropic_seed = np.random.SeedSequence(int(seed)).spawn(2)
+    sparse_rng = np.random.default_rng(sparse_seed)
+    isotropic_rng = np.random.default_rng(isotropic_seed)
+    coordinates = sparse_rng.permutation(coefficients.size)[:size]
+    sparse_candidates = np.eye(coefficients.size, dtype=complex)[coordinates]
+    isotropic_candidates = isotropic_rng.normal(
+        size=(size, coefficients.size)
+    ) + 1j * isotropic_rng.normal(size=(size, coefficients.size))
+    return {
+        "sparse": project_moduli_tangents(coefficients, sparse_candidates),
+        "isotropic": project_moduli_tangents(
+            coefficients,
+            isotropic_candidates,
+        ),
+    }
+
+
+def _positive_spectrum(values: np.ndarray, rtol: float = 1e-12) -> np.ndarray:
+    spectrum = np.maximum(np.asarray(values, dtype=float), 0.0)
+    if spectrum.size == 0:
+        return spectrum
+    largest = float(np.max(spectrum))
+    if largest <= 0.0:
+        return np.empty(0, dtype=float)
+    return spectrum[spectrum > float(rtol) * largest]
+
+
+def _effective_rank(values: np.ndarray) -> float:
+    spectrum = _positive_spectrum(values)
+    if spectrum.size == 0:
+        return 0.0
+    return float(np.sum(spectrum) ** 2 / np.sum(spectrum**2))
+
+
+def _spectral_entropy(values: np.ndarray) -> float:
+    spectrum = _positive_spectrum(values)
+    if spectrum.size <= 1:
+        return 0.0
+    probabilities = spectrum / np.sum(spectrum)
+    return float(
+        -np.sum(probabilities * np.log(probabilities)) / np.log(spectrum.size)
+    )
+
+
+def _branch_spectra(values: np.ndarray) -> tuple[np.ndarray, np.ndarray]:
+    branch = np.asarray(values, dtype=complex)
+    target_rank = branch.shape[-1]
+    if float(np.linalg.norm(branch)) <= np.finfo(float).tiny:
+        return np.zeros(target_rank, dtype=float), np.empty(0, dtype=float)
+    target = np.linalg.eigvalsh(target_covariance(branch))
+    target = np.maximum(np.asarray(target, dtype=float), 0.0)
+    external = external_covariance_eigenvalues_scalable(branch)
+    return target, external
+
+
+def external_covariance_eigenvalues_scalable(
+    channels: np.ndarray,
+    rtol: float = 1e-12,
+) -> np.ndarray:
+    """Return the external spectrum from the smaller exact Gram side.
+
+    The nonzero spectra of ``S S^dagger`` and ``S^dagger S`` agree.  Choosing
+    the smaller side changes neither the observable nor the null covariance,
+    while avoiding the prohibitive ``(mD)^2`` allocation at central N=14.
+    """
+
+    values = np.asarray(channels, dtype=complex)
+    if values.ndim != 3:
+        raise ValueError("channels must have shape (label, ambient, rank)")
+    labels, ambient, rank = values.shape
+    stacked = values.transpose(1, 0, 2).reshape(ambient, labels * rank)
+    if ambient <= labels * rank:
+        covariance = stacked @ stacked.conj().T / labels
+    else:
+        covariance = stacked.conj().T @ stacked / labels
+    covariance = 0.5 * (covariance + covariance.conj().T)
+    eigenvalues = np.linalg.eigvalsh(covariance)
+    largest = max(float(eigenvalues[-1]), 0.0)
+    if largest <= 0.0:
+        raise ValueError("external covariance has no positive support")
+    return np.asarray(
+        eigenvalues[eigenvalues > float(rtol) * largest],
+        dtype=float,
+    )
+
+
+def scalable_covariance_matched_wick(
+    channels: np.ndarray,
+    rtol: float = 1e-10,
+) -> WickResult:
+    """Evaluate the frozen four-channel statistic with scalable covariance."""
+
+    whitened = whiten_channel_labels(channels, rtol=rtol)
+    values = whitened.channels
+    rank = values.shape[-1]
+    left = target_covariance(values)
+    left_eigenvalues = np.linalg.eigvalsh(left)
+    right_eigenvalues = external_covariance_eigenvalues_scalable(values)
+    left_trace = float(np.sum(left_eigenvalues))
+    right_trace = float(np.sum(right_eigenvalues))
+    A_left = (
+        rank
+        * float(np.sum(left_eigenvalues**2))
+        / (left_trace * left_trace)
+    )
+    B_right = (
+        rank
+        * float(np.sum(right_eigenvalues**2))
+        / (right_trace * right_trace)
+    )
+    tensor = four_channel_tensor(values)
+    identity = np.eye(values.shape[0])
+    wick = (
+        A_left * np.einsum("mn,rs->mnrs", identity, identity)
+        + B_right * np.einsum("ms,rn->mnrs", identity, identity)
+    )
+    connected = tensor - wick
+    denominator = float(np.linalg.norm(wick))
+    if denominator <= 0.0:
+        raise RuntimeError("Wick tensor has zero norm")
+    return WickResult(
+        tensor=tensor,
+        wick_tensor=wick,
+        connected=connected,
+        R4=float(np.linalg.norm(connected) / denominator),
+        A_left=A_left,
+        B_right=B_right,
+        left_eigenvalues=left_eigenvalues,
+        right_eigenvalues=right_eigenvalues,
+        channel_covariance_eigenvalues=whitened.covariance_eigenvalues,
+    )
+
+
+def hodge_signature(response: HodgeResponse) -> HodgeSignature:
+    """Reduce a resolved response to safe gauge-invariant two-point data."""
+
+    minus = np.asarray(response.minus, dtype=complex)
+    plus = np.asarray(response.plus, dtype=complex)
+    if minus.shape != plus.shape or minus.ndim != 3:
+        raise ValueError("Hodge branches must share (label, ambient, rank) shape")
+    minus_weight = float(np.sum(np.abs(minus) ** 2))
+    plus_weight = float(np.sum(np.abs(plus) ** 2))
+    total_weight = minus_weight + plus_weight
+    if total_weight <= 0.0:
+        raise ValueError("Hodge response has zero total weight")
+    balance = float(4.0 * minus_weight * plus_weight / total_weight**2)
+    minus_target, minus_external = _branch_spectra(minus)
+    plus_target, plus_external = _branch_spectra(plus)
+    minus_channel = (
+        channel_covariance(minus)
+        if minus_weight > np.finfo(float).tiny
+        else np.zeros((minus.shape[0], minus.shape[0]), dtype=complex)
+    )
+    plus_channel = (
+        channel_covariance(plus)
+        if plus_weight > np.finfo(float).tiny
+        else np.zeros((plus.shape[0], plus.shape[0]), dtype=complex)
+    )
+    cross_scale = max(
+        float(np.linalg.norm(minus) * np.linalg.norm(plus)),
+        np.finfo(float).tiny,
+    )
+    cross = np.einsum(
+        "mai,maj->mij",
+        minus.conj(),
+        plus,
+        optimize=True,
+    )
+    orthogonality = float(np.linalg.norm(cross) / cross_scale)
+    return HodgeSignature(
+        channel_count=int(minus.shape[0]),
+        target_rank=int(minus.shape[-1]),
+        minus_weight=minus_weight,
+        plus_weight=plus_weight,
+        hodge_balance=balance,
+        minus_channel_covariance=minus_channel,
+        plus_channel_covariance=plus_channel,
+        minus_target_eigenvalues=minus_target,
+        plus_target_eigenvalues=plus_target,
+        minus_external_eigenvalues=minus_external,
+        plus_external_eigenvalues=plus_external,
+        minus_target_effective_rank=_effective_rank(minus_target),
+        plus_target_effective_rank=_effective_rank(plus_target),
+        minus_external_effective_rank=_effective_rank(minus_external),
+        plus_external_effective_rank=_effective_rank(plus_external),
+        minus_target_entropy=_spectral_entropy(minus_target),
+        plus_target_entropy=_spectral_entropy(plus_target),
+        minus_external_entropy=_spectral_entropy(minus_external),
+        plus_external_entropy=_spectral_entropy(plus_external),
+        orthogonality_relative_error=orthogonality,
+    )
+
+
+def decomposable_curvature(
+    response: HodgeResponse,
+    first: int,
+    second: int | None = None,
+) -> np.ndarray:
+    """Return the Hermitian Appendix-D curvature matrix from Hodge branches."""
+
+    minus = np.asarray(response.minus, dtype=complex)
+    plus = np.asarray(response.plus, dtype=complex)
+    left = int(first)
+    if not 0 <= left < minus.shape[0]:
+        raise IndexError("first curvature channel is out of range")
+    if second is None:
+        curvature = (
+            minus[left].conj().T @ minus[left]
+            - plus[left].conj().T @ plus[left]
+        )
+    else:
+        right = int(second)
+        if not 0 <= right < minus.shape[0] or right == left:
+            raise IndexError("second curvature channel is invalid")
+        ordered = (
+            minus[left].conj().T @ minus[right]
+            - plus[right].conj().T @ plus[left]
+        )
+        curvature = ordered + ordered.conj().T
+    return 0.5 * (curvature + curvature.conj().T)
+
+
+def hodge_response(
+    frame: BPSFrame,
+    couplings: np.ndarray,
+    tangents: np.ndarray,
+    *,
+    tolerance: float = 5e-10,
+) -> HodgeResponse:
+    """Compute exact, coexact, summed, and direct resolvent responses."""
+
+    coefficients = np.asarray(couplings, dtype=complex)
+    directions = np.asarray(tangents, dtype=complex)
+    coordinates = len(cubic_triples(frame.N))
+    if coefficients.shape != (coordinates,):
+        raise ValueError("cubic coupling vector has the wrong shape")
+    if directions.ndim != 2 or directions.shape[1] != coordinates:
+        raise ValueError("tangent panel has the wrong shape")
+    if directions.shape[0] < 1:
+        raise ValueError("tangent panel is empty")
+    projector = np.asarray(frame.projector_frame, dtype=complex)
+    minus_values: list[np.ndarray] = []
+    plus_values: list[np.ndarray] = []
+    direct_values: list[np.ndarray] = []
+    for tangent in directions:
+        dq_in = cubic_supercharge(frame.N, frame.charge - 3, tangent)
+        dq_out = cubic_supercharge(frame.N, frame.charge, tangent)
+        rhs_minus = frame.q_in @ (dq_in.getH() @ projector)
+        rhs_plus = frame.q_out.getH() @ (dq_out @ projector)
+        d_hamiltonian = (
+            dq_in @ frame.q_in.getH()
+            + frame.q_in @ dq_in.getH()
+            + dq_out.getH() @ frame.q_out
+            + frame.q_out.getH() @ dq_out
+        ).tocsr()
+        rhs_direct = d_hamiltonian @ projector
+        minus_values.append(-_pseudoinverse_apply(frame, rhs_minus))
+        plus_values.append(-_pseudoinverse_apply(frame, rhs_plus))
+        direct_values.append(-_pseudoinverse_apply(frame, rhs_direct))
+    minus = np.asarray(minus_values, dtype=complex)
+    plus = np.asarray(plus_values, dtype=complex)
+    direct = np.asarray(direct_values, dtype=complex)
+    total = minus + plus
+    branch_sum_error = _relative_error(total, minus + plus)
+    direct_error = _relative_error(total, direct)
+    orthogonality_errors: list[float] = []
+    for left, right in zip(minus, plus, strict=True):
+        scale = max(
+            float(np.linalg.norm(left) * np.linalg.norm(right)),
+            np.finfo(float).tiny,
+        )
+        orthogonality_errors.append(
+            float(np.linalg.norm(left.conj().T @ right) / scale)
+        )
+    orthogonality_error = max(orthogonality_errors)
+    total_norm = max(float(np.linalg.norm(total)), np.finfo(float).tiny)
+    leakage = float(
+        np.linalg.norm(
+            np.einsum(
+                "ir,mij->mrj",
+                projector.conj(),
+                total,
+                optimize=True,
+            )
+        )
+        / total_norm
+    )
+    checks = {
+        "finite_response": bool(
+            np.all(np.isfinite(total.real)) and np.all(np.isfinite(total.imag))
+        ),
+        "branch_sum": branch_sum_error < float(tolerance),
+        "direct_resolvent": direct_error < float(tolerance),
+        "hodge_orthogonality": orthogonality_error < float(tolerance),
+        "target_leakage": leakage < float(tolerance),
+    }
+    return HodgeResponse(
+        minus=minus,
+        plus=plus,
+        total=total,
+        direct=direct,
+        branch_sum_relative_error=branch_sum_error,
+        direct_relative_error=direct_error,
+        orthogonality_relative_error=orthogonality_error,
+        target_leakage=leakage,
+        checks=checks,
+    )
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/lgeth/hodge_wick.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/lgeth/hodge_wick.py
new file mode 100644
index 000000000..29fa21134
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/lgeth/hodge_wick.py
@@ -0,0 +1,202 @@
+"""Covariance-matched Gaussian nulls for exact/coexact response branches."""
+
+from __future__ import annotations
+
+from collections.abc import Sequence
+
+import numpy as np
+
+from .hodge_response import HodgeSignature
+from .wick_channels import (
+    _fast_covariance_matched_r4,
+    gaussian_r4_reference,
+    sample_matched_gaussian_channels,
+)
+
+
+def _positive(values: np.ndarray, rtol: float = 1e-12) -> np.ndarray:
+    spectrum = np.maximum(np.asarray(values, dtype=float), 0.0)
+    if spectrum.ndim != 1 or spectrum.size == 0:
+        return np.empty(0, dtype=float)
+    largest = float(np.max(spectrum))
+    if largest <= 0.0:
+        return np.empty(0, dtype=float)
+    return spectrum[spectrum > float(rtol) * largest]
+
+
+def _haar_unitary(size: int, rng: np.random.Generator) -> np.ndarray:
+    gaussian = rng.normal(size=(size, size)) + 1j * rng.normal(
+        size=(size, size)
+    )
+    q, r = np.linalg.qr(gaussian)
+    diagonal = np.diag(r)
+    phases = np.ones(size, dtype=complex)
+    nonzero = np.abs(diagonal) > np.finfo(float).tiny
+    phases[nonzero] = diagonal[nonzero] / np.abs(diagonal[nonzero])
+    return np.asarray(q * phases[None, :], dtype=complex)
+
+
+def _sample_branch(
+    target_eigenvalues: np.ndarray,
+    external_eigenvalues: np.ndarray,
+    channel_covariance: np.ndarray,
+    channel_count: int,
+    weight_fraction: float,
+    rng: np.random.Generator,
+) -> np.ndarray:
+    target_full = np.maximum(np.asarray(target_eigenvalues, dtype=float), 0.0)
+    external = _positive(external_eigenvalues)
+    if target_full.ndim != 1 or target_full.size == 0 or external.size == 0:
+        raise ValueError("nonzero Hodge branch has empty covariance support")
+    if float(np.sum(target_full)) <= 0.0:
+        raise ValueError("nonzero Hodge branch has zero target covariance")
+    target_full = target_full / np.sum(target_full)
+    external = external / np.sum(external)
+    gaussian = (
+        rng.normal(size=(channel_count, external.size, target_full.size))
+        + 1j
+        * rng.normal(size=(channel_count, external.size, target_full.size))
+    ) / np.sqrt(2.0)
+    local = (
+        np.sqrt(external)[None, :, None]
+        * gaussian
+        * np.sqrt(target_full)[None, None, :]
+    )
+    target_rotation = _haar_unitary(target_full.size, rng)
+    rotated = np.einsum(
+        "mai,ij->maj",
+        local,
+        target_rotation,
+        optimize=True,
+    )
+    label_covariance = np.asarray(channel_covariance, dtype=complex)
+    if label_covariance.shape != (channel_count, channel_count):
+        raise ValueError("Hodge branch channel covariance has the wrong shape")
+    label_covariance = 0.5 * (label_covariance + label_covariance.conj().T)
+    eigenvalues, eigenvectors = np.linalg.eigh(label_covariance)
+    eigenvalues = np.maximum(eigenvalues, 0.0)
+    trace = float(np.sum(eigenvalues))
+    if trace <= 0.0:
+        raise ValueError("nonzero Hodge branch has zero channel covariance")
+    label_root = (
+        eigenvectors * np.sqrt(eigenvalues * channel_count / trace)[None, :]
+    ) @ eigenvectors.conj().T
+    correlated = np.einsum(
+        "mn,nai->mai",
+        label_root,
+        rotated,
+        optimize=True,
+    )
+    return np.sqrt(float(weight_fraction)) * correlated
+
+
+def sample_hodge_gaussian_channels(
+    signature: HodgeSignature,
+    channel_count: int,
+    rng: np.random.Generator,
+) -> np.ndarray:
+    """Draw one response tensor from the safe two-branch Hodge signature."""
+
+    labels = int(channel_count)
+    if labels < 1 or labels != int(signature.channel_count):
+        raise ValueError("channel count disagrees with the Hodge signature")
+    weights = np.asarray(
+        [signature.minus_weight, signature.plus_weight],
+        dtype=float,
+    )
+    if np.any(weights < 0.0) or float(np.sum(weights)) <= 0.0:
+        raise ValueError("Hodge branch weights must be nonnegative and nonzero")
+    active = np.flatnonzero(weights > np.finfo(float).tiny * np.sum(weights))
+    if active.size == 1:
+        if int(active[0]) == 0:
+            target = _positive(signature.minus_target_eigenvalues)
+            external = _positive(signature.minus_external_eigenvalues)
+        else:
+            target = _positive(signature.plus_target_eigenvalues)
+            external = _positive(signature.plus_external_eigenvalues)
+        return sample_matched_gaussian_channels(
+            target,
+            external,
+            labels,
+            rng,
+        )
+    fractions = weights / np.sum(weights)
+    minus = _sample_branch(
+        signature.minus_target_eigenvalues,
+        signature.minus_external_eigenvalues,
+        signature.minus_channel_covariance,
+        labels,
+        float(fractions[0]),
+        rng,
+    )
+    plus = _sample_branch(
+        signature.plus_target_eigenvalues,
+        signature.plus_external_eigenvalues,
+        signature.plus_channel_covariance,
+        labels,
+        float(fractions[1]),
+        rng,
+    )
+    if minus.shape[0] != plus.shape[0] or minus.shape[2] != plus.shape[2]:
+        raise RuntimeError("Hodge branch samples do not share channel and target axes")
+    return np.concatenate([minus, plus], axis=1)
+
+
+def hodge_gaussian_r4_reference(
+    signature: HodgeSignature,
+    channel_count: int,
+    samples: int,
+    seed: int,
+) -> np.ndarray:
+    """Return deterministic finite-size R4 samples for one Hodge signature."""
+
+    count = int(samples)
+    labels = int(channel_count)
+    if count < 1:
+        raise ValueError("Hodge Gaussian reference requires at least one sample")
+    weights = np.asarray(
+        [signature.minus_weight, signature.plus_weight],
+        dtype=float,
+    )
+    active = np.flatnonzero(weights > np.finfo(float).tiny * np.sum(weights))
+    if active.size == 1:
+        if int(active[0]) == 0:
+            target = _positive(signature.minus_target_eigenvalues)
+            external = _positive(signature.minus_external_eigenvalues)
+        else:
+            target = _positive(signature.plus_target_eigenvalues)
+            external = _positive(signature.plus_external_eigenvalues)
+        return gaussian_r4_reference(target, external, labels, count, int(seed))
+    rng = np.random.default_rng(int(seed))
+    result = np.empty(count, dtype=float)
+    for sample in range(count):
+        channels = sample_hodge_gaussian_channels(signature, labels, rng)
+        result[sample] = _fast_covariance_matched_r4(channels)
+    return result
+
+
+def complete_realization_null(
+    signatures: Sequence[HodgeSignature],
+    samples: int,
+    seed: int,
+) -> np.ndarray:
+    """Draw medians using one complete Gaussian tensor per realization."""
+
+    records = tuple(signatures)
+    count = int(samples)
+    if not records or count < 1:
+        raise ValueError("complete-realization null requires records and samples")
+    labels = int(records[0].channel_count)
+    if any(int(record.channel_count) != labels for record in records):
+        raise ValueError("Hodge signatures have inconsistent channel counts")
+    rng = np.random.default_rng(int(seed))
+    result = np.empty(count, dtype=float)
+    for sample in range(count):
+        values = [
+            _fast_covariance_matched_r4(
+                sample_hodge_gaussian_channels(record, labels, rng)
+            )
+            for record in records
+        ]
+        result[sample] = float(np.median(values))
+    return result
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/lgeth/susy_cohomology.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/lgeth/susy_cohomology.py
new file mode 100644
index 000000000..5f351d090
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/lgeth/susy_cohomology.py
@@ -0,0 +1,308 @@
+"""Charge-resolved cubic N=2 SYK cochain complexes and BPS frames."""
+
+from __future__ import annotations
+
+from dataclasses import dataclass
+from functools import lru_cache
+from itertools import combinations
+from math import comb
+
+import numpy as np
+import scipy.sparse as sp
+
+
+@dataclass(frozen=True)
+class BPSFrame:
+    """Spectral Hodge frame for one fixed fermion-number sector."""
+
+    N: int
+    charge: int
+    basis: tuple[int, ...]
+    projector_frame: np.ndarray
+    complement_frame: np.ndarray
+    positive_energies: np.ndarray
+    gap: float
+    kernel_residual: float
+    orthogonality_error: float
+    expected_rank: int
+    q_in: sp.csr_matrix
+    q_out: sp.csr_matrix
+    hamiltonian: sp.csr_matrix
+
+
+@lru_cache(maxsize=None)
+def charge_basis(N: int, charge: int) -> tuple[int, ...]:
+    """Return sorted occupation bit strings in a fixed charge sector."""
+
+    modes = int(N)
+    particles = int(charge)
+    if modes < 1:
+        raise ValueError("N must be positive")
+    if particles < 0 or particles > modes:
+        return ()
+    return tuple(
+        state
+        for state in range(1 << modes)
+        if state.bit_count() == particles
+    )
+
+
+@lru_cache(maxsize=None)
+def cubic_triples(N: int) -> tuple[tuple[int, int, int], ...]:
+    """Return the lexicographically ordered cubic coupling coordinates."""
+
+    modes = int(N)
+    if modes < 3:
+        raise ValueError("a cubic supercharge requires N >= 3")
+    return tuple(combinations(range(modes), 3))
+
+
+def normalized_complex_couplings(N: int, seed: int) -> np.ndarray:
+    """Draw a deterministic unit-norm isotropic complex three-form."""
+
+    rng = np.random.default_rng(int(seed))
+    values = rng.normal(size=comb(int(N), 3)) + 1j * rng.normal(
+        size=comb(int(N), 3)
+    )
+    norm = float(np.linalg.norm(values))
+    if norm <= 0.0:
+        raise RuntimeError("complex coupling draw has zero norm")
+    return np.asarray(values / norm, dtype=complex)
+
+
+def _create(state: int, mode: int) -> tuple[int, int] | None:
+    """Apply one fermion creation operator in the occupation basis."""
+
+    bit = 1 << int(mode)
+    if int(state) & bit:
+        return None
+    parity = (int(state) & (bit - 1)).bit_count() % 2
+    return int(state) | bit, (-1 if parity else 1)
+
+
+def _apply_cubic_creation(
+    state: int,
+    triple: tuple[int, int, int],
+) -> tuple[int, int] | None:
+    """Apply psi_i psi_j psi_k, respecting right-to-left operator order."""
+
+    current = int(state)
+    sign = 1
+    for mode in reversed(triple):
+        result = _create(current, mode)
+        if result is None:
+            return None
+        current, factor = result
+        sign *= factor
+    return current, sign
+
+
+def cubic_supercharge(
+    N: int,
+    charge: int,
+    couplings: np.ndarray,
+) -> sp.csr_matrix:
+    """Return Q_r: H_r -> H_{r+3} for a cubic complex supercharge."""
+
+    modes = int(N)
+    source_charge = int(charge)
+    triples = cubic_triples(modes)
+    coefficients = np.asarray(couplings, dtype=complex)
+    if coefficients.shape != (len(triples),):
+        raise ValueError("cubic coupling vector has the wrong shape")
+    source = charge_basis(modes, source_charge)
+    target = charge_basis(modes, source_charge + 3)
+    target_lookup = {state: index for index, state in enumerate(target)}
+    rows: list[int] = []
+    columns: list[int] = []
+    data: list[complex] = []
+    for column, state in enumerate(source):
+        for coordinate, triple in enumerate(triples):
+            applied = _apply_cubic_creation(state, triple)
+            if applied is None:
+                continue
+            target_state, sign = applied
+            row = target_lookup.get(target_state)
+            if row is None:
+                raise RuntimeError("cubic creation left the target charge sector")
+            amplitude = coefficients[coordinate] * sign
+            if amplitude != 0.0:
+                rows.append(row)
+                columns.append(column)
+                data.append(amplitude)
+    return sp.coo_matrix(
+        (np.asarray(data, dtype=complex), (rows, columns)),
+        shape=(len(target), len(source)),
+        dtype=complex,
+    ).tocsr()
+
+
+def charge_hamiltonian(
+    N: int,
+    charge: int,
+    couplings: np.ndarray,
+) -> sp.csr_matrix:
+    """Return H_r = Q Q^dagger + Q^dagger Q in one charge sector."""
+
+    q_in = cubic_supercharge(N, int(charge) - 3, couplings)
+    q_out = cubic_supercharge(N, int(charge), couplings)
+    return (q_in @ q_in.getH() + q_out.getH() @ q_out).tocsr()
+
+
+def expected_generic_bps_rank(N: int, charge: int) -> int:
+    """Return the registered generic BPS rank for even-N central sectors."""
+
+    modes = int(N)
+    particles = int(charge)
+    if modes % 2:
+        raise ValueError("the registered rank contract requires even N")
+    middle = modes // 2
+    if particles == middle:
+        return 2 * 3 ** (middle - 1)
+    if abs(particles - middle) == 1:
+        return 3 ** (middle - 1)
+    return 0
+
+
+def decomposable_couplings(N: int, alpha: float = 1.0) -> np.ndarray:
+    """Return C_3 = alpha e_1 wedge e_2 wedge e_3."""
+
+    scale = float(alpha)
+    if scale <= 0.0:
+        raise ValueError("decomposable coupling scale must be positive")
+    triples = cubic_triples(int(N))
+    values = np.zeros(len(triples), dtype=complex)
+    values[triples.index((0, 1, 2))] = scale
+    return values
+
+
+def decomposable_tangent(N: int, family: str, site: int) -> np.ndarray:
+    """Return one canonical tangent preserving the decomposable three-form locus."""
+
+    pairs = {"12": (0, 1), "13": (0, 2), "23": (1, 2)}
+    label = str(family)
+    if label not in pairs:
+        raise ValueError("decomposable tangent family must be 12, 13, or 23")
+    external = int(site)
+    if external < 3 or external >= int(N):
+        raise ValueError("decomposable tangent site must lie outside modes 1,2,3")
+    triple = tuple(sorted((*pairs[label], external)))
+    triples = cubic_triples(int(N))
+    values = np.zeros(len(triples), dtype=complex)
+    values[triples.index(triple)] = 1.0
+    return values
+
+
+def _safe_combination(n: int, k: int) -> int:
+    return 0 if int(k) < 0 or int(k) > int(n) else comb(int(n), int(k))
+
+
+def decomposable_bps_rank(N: int, charge: int) -> int:
+    """Return 3 binom(N-2, r-1) for the decomposable model."""
+
+    return 3 * _safe_combination(int(N) - 2, int(charge) - 1)
+
+
+def analytic_decomposable_curvature_multiplicities(
+    N: int,
+    charge: int,
+    kind: str,
+) -> dict[str, int]:
+    """Return Appendix-D multiplicities for diagonal/off-diagonal tangents."""
+
+    modes = int(N)
+    particles = int(charge)
+    label = str(kind)
+    if label == "diagonal":
+        positive = _safe_combination(modes - 4, particles - 3)
+        negative = _safe_combination(modes - 4, particles - 1)
+    elif label == "off_diagonal":
+        positive = _safe_combination(modes - 4, particles - 2)
+        negative = positive
+    else:
+        raise ValueError("curvature kind must be diagonal or off_diagonal")
+    rank = decomposable_bps_rank(modes, particles)
+    zero = rank - positive - negative
+    if zero < 0:
+        raise RuntimeError("analytic curvature multiplicities exceed BPS rank")
+    return {"negative": negative, "zero": zero, "positive": positive}
+
+
+def solve_bps_frame(
+    N: int,
+    charge: int,
+    couplings: np.ndarray,
+    *,
+    dense_cutoff: int = 4096,
+    relative_tolerance: float = 1e-10,
+    expected_rank_override: int | None = None,
+) -> BPSFrame:
+    """Diagonalize one registered sector and certify its harmonic fiber."""
+
+    basis = charge_basis(int(N), int(charge))
+    if not basis:
+        raise ValueError("registered charge sector is empty")
+    if len(basis) > int(dense_cutoff):
+        raise ValueError("charge sector exceeds the current dense cutoff")
+    expected = (
+        expected_generic_bps_rank(N, charge)
+        if expected_rank_override is None
+        else int(expected_rank_override)
+    )
+    if expected <= 0 or expected >= len(basis):
+        raise ValueError("charge sector is outside the registered BPS sequence")
+    q_in = cubic_supercharge(N, int(charge) - 3, couplings)
+    q_out = cubic_supercharge(N, int(charge), couplings)
+    hamiltonian = (q_in @ q_in.getH() + q_out.getH() @ q_out).tocsr()
+    dense = hamiltonian.toarray()
+    dense = 0.5 * (dense + dense.conj().T)
+    eigenvalues, eigenvectors = np.linalg.eigh(dense)
+    scale = max(1.0, float(np.max(np.abs(eigenvalues))))
+    tolerance = float(relative_tolerance) * scale
+    if float(np.max(np.abs(eigenvalues[:expected]))) > tolerance:
+        raise RuntimeError("generic BPS eigenvalues exceed the registered tolerance")
+    if float(eigenvalues[expected]) <= tolerance:
+        raise RuntimeError("generic BPS nullity exceeds the registered rank")
+    projector_frame = np.asarray(eigenvectors[:, :expected], dtype=complex)
+    complement_frame = np.asarray(eigenvectors[:, expected:], dtype=complex)
+    positive_energies = np.asarray(eigenvalues[expected:], dtype=float)
+    kernel_residual = float(
+        np.linalg.norm(hamiltonian @ projector_frame, ord="fro")
+    )
+    orthogonality_error = max(
+        float(
+            np.linalg.norm(
+                projector_frame.conj().T @ projector_frame
+                - np.eye(expected),
+                ord="fro",
+            )
+        ),
+        float(
+            np.linalg.norm(
+                complement_frame.conj().T @ complement_frame
+                - np.eye(complement_frame.shape[1]),
+                ord="fro",
+            )
+        ),
+        float(
+            np.linalg.norm(
+                projector_frame.conj().T @ complement_frame,
+                ord="fro",
+            )
+        ),
+    )
+    return BPSFrame(
+        N=int(N),
+        charge=int(charge),
+        basis=basis,
+        projector_frame=projector_frame,
+        complement_frame=complement_frame,
+        positive_energies=positive_energies,
+        gap=float(positive_energies[0]),
+        kernel_residual=kernel_residual,
+        orthogonality_error=orthogonality_error,
+        expected_rank=expected,
+        q_in=q_in,
+        q_out=q_out,
+        hamiltonian=hamiltonian,
+    )
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/make_susy_hodge_figure_v7.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/make_susy_hodge_figure_v7.py
new file mode 100644
index 000000000..b12ce8f76
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/make_susy_hodge_figure_v7.py
@@ -0,0 +1,552 @@
+#!/usr/bin/env python3
+"""Generate the Hodge-resolved SUSY response inference figure and report."""
+
+from __future__ import annotations
+
+import hashlib
+import json
+from pathlib import Path
+from typing import Any
+
+import matplotlib
+
+matplotlib.use("Agg")
+import matplotlib.pyplot as plt
+import numpy as np
+from matplotlib.lines import Line2D
+from matplotlib.patches import FancyBboxPatch
+
+from merge_susy_hodge_pilot_v7 import OUTPUT_JSON as PILOT_JSON
+
+
+SCRIPT_ROOT = Path(__file__).resolve().parent
+OUTPUT_ROOT = SCRIPT_ROOT / "output"
+INFERENCE_JSON = OUTPUT_ROOT / "susy_hodge_v7_N14_inference.json"
+FIGURE_PDF = OUTPUT_ROOT / "figure_susy_hodge_geometric_eth_v7.pdf"
+FIGURE_PNG = OUTPUT_ROOT / "figure_susy_hodge_geometric_eth_v7.png"
+MANIFEST_JSON = OUTPUT_ROOT / "figure_susy_hodge_geometric_eth_v7.json"
+REPORT_MD = OUTPUT_ROOT / "susy_hodge_geometric_eth_report_v7.md"
+ALLOWED_BRANCHES = {
+    "strong_covariance_universality",
+    "hodge_resolved_geometric_eth",
+    "cohomological_non_gaussian_class",
+    "structured_cohomology",
+    "feasibility_failure",
+}
+
+
+def sha256(path: Path) -> str:
+    digest = hashlib.sha256()
+    with Path(path).open("rb") as handle:
+        for block in iter(lambda: handle.read(1 << 20), b""):
+            digest.update(block)
+    return digest.hexdigest()
+
+
+def _atomic_json(path: Path, payload: dict[str, Any]) -> None:
+    path = Path(path)
+    path.parent.mkdir(parents=True, exist_ok=True)
+    temporary = path.with_suffix(path.suffix + ".tmp")
+    temporary.write_text(
+        json.dumps(payload, indent=2, sort_keys=True),
+        encoding="utf-8",
+    )
+    temporary.replace(path)
+
+
+def _atomic_text(path: Path, value: str) -> None:
+    path = Path(path)
+    path.parent.mkdir(parents=True, exist_ok=True)
+    temporary = path.with_suffix(path.suffix + ".tmp")
+    temporary.write_text(value, encoding="utf-8")
+    temporary.replace(path)
+
+
+def _load(path: Path) -> dict[str, Any]:
+    payload = json.loads(Path(path).read_text(encoding="utf-8"))
+    if payload.get("version") != "v7":
+        raise ValueError(f"figure source has the wrong version: {path}")
+    if not payload.get("passed") or not all(payload.get("checks", {}).values()):
+        raise ValueError(f"figure source failed its checks: {path}")
+    return payload
+
+
+def _style() -> None:
+    plt.rcParams.update(
+        {
+            "font.family": "serif",
+            "font.serif": ["STIXGeneral", "DejaVu Serif"],
+            "mathtext.fontset": "stix",
+            "font.size": 8.3,
+            "axes.titlesize": 9.1,
+            "axes.labelsize": 8.5,
+            "xtick.labelsize": 7.4,
+            "ytick.labelsize": 7.4,
+            "legend.fontsize": 6.8,
+            "axes.linewidth": 0.75,
+            "xtick.major.width": 0.65,
+            "ytick.major.width": 0.65,
+            "pdf.fonttype": 42,
+            "ps.fonttype": 42,
+        }
+    )
+
+
+def _panel_label(axis: Any, label: str) -> None:
+    axis.text(
+        -0.12,
+        1.08,
+        label,
+        transform=axis.transAxes,
+        fontsize=9.3,
+        fontweight="bold",
+        va="top",
+    )
+
+
+def _interval_error(interval: list[float]) -> tuple[float, np.ndarray]:
+    values = np.asarray(interval, dtype=float)
+    if values.shape == (2,):
+        center = float(np.mean(values))
+        return center, np.asarray([[center - values[0]], [values[1] - center]])
+    if values.shape == (3,):
+        center = float(values[1])
+        return center, np.asarray([[center - values[0]], [values[2] - center]])
+    raise ValueError("interval must contain two or three values")
+
+
+def _draw_interval(
+    axis: Any,
+    x: float,
+    interval: list[float],
+    *,
+    color: str,
+    marker: str,
+    zorder: int,
+) -> None:
+    center, errors = _interval_error(interval)
+    axis.errorbar(
+        [x],
+        [center],
+        yerr=errors,
+        fmt=marker,
+        color=color,
+        ms=4.0,
+        lw=1.15,
+        capsize=2.0,
+        zorder=zorder,
+    )
+
+
+def _branch_statement(branch: str) -> str:
+    statements = {
+        "strong_covariance_universality": (
+            "Both covariance-only nulls cover the held-out sparse pair; the "
+            "current data support strong finite-size covariance universality."
+        ),
+        "hodge_resolved_geometric_eth": (
+            "Only the branch-resolved null covers the held-out pair; the Hodge "
+            "decomposition supplies predictive information beyond collapsed covariance."
+        ),
+        "cohomological_non_gaussian_class": (
+            "Neither covariance-only null covers the held-out pair, and the "
+            "complete-realization uncertainty remains separated; a reproducible "
+            "cohomological four-point memory survives the registered separable "
+            "Hodge-covariance matching."
+        ),
+        "structured_cohomology": (
+            "The generic response is not separated from the decomposable control "
+            "under the frozen diagnostics."
+        ),
+        "feasibility_failure": (
+            "At least one numerical, sealing, or preregistered inference gate failed; "
+            "no scientific universality branch is claimed."
+        ),
+    }
+    return statements[branch]
+
+
+def _write_report(
+    path: Path,
+    pilot: dict[str, Any],
+    inference: dict[str, Any],
+    pilot_hash: str,
+    inference_hash: str,
+) -> None:
+    branch = str(inference["selected_branch"])
+    primary_lines = []
+    for item in sorted(inference["primary_pair"], key=lambda value: value["sector"]):
+        primary_lines.append(
+            "- {sector}: observed median {observed:.8f}, physical bootstrap "
+            "[{physical_low:.8f}, {physical_high:.8f}], collapsed prediction "
+            "[{collapsed_low:.8f}, {collapsed_high:.8f}], Hodge prediction "
+            "[{hodge_low:.8f}, {hodge_high:.8f}].".format(
+                sector=item["sector"],
+                observed=float(item["observed_median"]),
+                physical_low=float(item["physical_bootstrap_interval"][0]),
+                physical_high=float(item["physical_bootstrap_interval"][1]),
+                collapsed_low=float(item["collapsed_prediction_interval"][0]),
+                collapsed_high=float(item["collapsed_prediction_interval"][-1]),
+                hodge_low=float(item["hodge_prediction_interval"][0]),
+                hodge_high=float(item["hodge_prediction_interval"][-1]),
+            )
+        )
+    report = f"""# Hodge-resolved Geometric ETH result report
+
+## Verdict
+
+Selected frozen branch: `{branch}`.
+
+{_branch_statement(branch)}
+
+## Established
+
+- The charge-resolved cubic $\\mathcal N=2$ SYK BPS response splits into numerically orthogonal exact and coexact branches and agrees with the direct resolvent response under the registered tests.
+- The pilot contains {len(pilot['groups'])} complete size/sector/panel groups and uses complete disorder realizations as its uncertainty unit.
+- The held-out central/adjacent sparse pair was scored only after validating prediction SHA-256 `{inference['prediction_sha256']}`.
+
+{chr(10).join(primary_lines)}
+
+## Not established
+
+- This is not conventional energy-resolved ETH, a real-time chaos result, or a thermodynamic-limit theorem.
+- Generic $\\mathcal N=2$ SYK is an independent supersymmetric protection mechanism, but it is not a spatially local model; locality universality requires a later nilpotent lattice-supercharge benchmark.
+- Berry-curvature chaos in this model is prior art. The contribution tested here is the pre-outcome response-complex/two-point prediction of a gauge-invariant four-channel statistic.
+- The Gaussian nulls match the registered collapsed or branch-resolved marginal covariance data, not the complete entrywise covariance operator. Rejection therefore establishes failure of the frozen separable Hodge-Gaussian response law; by itself it does not distinguish intrinsic non-Gaussianity from unmodeled nonseparable two-point structure.
+
+## Relation to prior work
+
+- [Fu, Gaiotto, Maldacena, and Sachdev, *Supersymmetric SYK models*](https://arxiv.org/abs/1610.08917).
+- [Chen, Colin-Ellerin, Mamroud, and Papadodimas, *Chaos of Berry curvature for BPS microstates*](https://arxiv.org/abs/2604.23287).
+- [Chen, Lin, and Shenker, *BPS Chaos*](https://arxiv.org/abs/2407.19387).
+- [Huijse and Schoutens, *Supersymmetry, lattice fermions, independence complexes and cohomology theory*](https://arxiv.org/abs/0903.0784).
+
+## Provenance
+
+- Pilot JSON SHA-256: `{pilot_hash}`.
+- Held-out inference JSON SHA-256: `{inference_hash}`.
+- Uncertainty unit: `{pilot['uncertainty_unit']}`.
+"""
+    _atomic_text(path, report)
+
+
+def make_figure(
+    *,
+    pilot_json: Path = PILOT_JSON,
+    inference_json: Path = INFERENCE_JSON,
+    output_pdf: Path = FIGURE_PDF,
+    output_png: Path = FIGURE_PNG,
+    manifest_json: Path = MANIFEST_JSON,
+    report_md: Path = REPORT_MD,
+) -> dict[str, Any]:
+    """Generate the final four-panel evidence figure and Markdown report."""
+
+    pilot = _load(pilot_json)
+    inference = _load(inference_json)
+    branch = str(inference.get("selected_branch"))
+    if branch not in ALLOWED_BRANCHES:
+        raise ValueError("held-out inference has an unknown branch")
+    groups = pilot.get("groups", [])
+    expected_grid = {
+        (N, sector, panel)
+        for N in (8, 10, 12)
+        for sector in ("central", "adjacent")
+        for panel in ("sparse", "isotropic")
+    }
+    observed_grid = {
+        (int(item["N"]), str(item["sector"]), str(item["panel_kind"]))
+        for item in groups
+    }
+    if observed_grid != expected_grid:
+        raise ValueError("pilot figure grid is incomplete")
+    primary = inference.get("primary_pair", [])
+    if {
+        (int(item["N"]), str(item["sector"]), str(item["panel_kind"]))
+        for item in primary
+    } != {(14, "central", "sparse"), (14, "adjacent", "sparse")}:
+        raise ValueError("held-out primary pair is incomplete")
+    group_map = {
+        (int(item["N"]), str(item["sector"]), str(item["panel_kind"])): item
+        for item in groups
+    }
+
+    _style()
+    colors = {
+        "physical": "#1A1A1A",
+        "collapsed": "#0072B2",
+        "hodge": "#7A4EAB",
+        "central": "#D55E00",
+        "adjacent": "#009E73",
+    }
+    figure, axes = plt.subplots(2, 2, figsize=(7.0, 5.25), constrained_layout=True)
+
+    axis = axes[0, 0]
+    _panel_label(axis, "(a)")
+    axis.set_axis_off()
+    boxes = [
+        (0.02, 0.58, 0.25, 0.25, "Laughlin parent\n" r"$B^\dagger B$", "#E8F2FA"),
+        (0.39, 0.58, 0.23, 0.25, "protected fiber\n" r"$P(\lambda)$", "#F2F2F2"),
+        (0.72, 0.70, 0.24, 0.18, "$X_-$ exact", "#FBE8DD"),
+        (0.72, 0.44, 0.24, 0.18, "$X_+$ coexact", "#E3F3EC"),
+    ]
+    for x, y, width, height, label, color in boxes:
+        patch = FancyBboxPatch(
+            (x, y),
+            width,
+            height,
+            boxstyle="round,pad=0.015",
+            linewidth=0.8,
+            edgecolor="#5C626A",
+            facecolor=color,
+            transform=axis.transAxes,
+        )
+        axis.add_patch(patch)
+        axis.text(
+            x + width / 2,
+            y + height / 2,
+            label,
+            ha="center",
+            va="center",
+            transform=axis.transAxes,
+        )
+    axis.annotate(
+        "",
+        xy=(0.39, 0.705),
+        xytext=(0.27, 0.705),
+        xycoords=axis.transAxes,
+        textcoords=axis.transAxes,
+        arrowprops={"arrowstyle": "->", "lw": 1.0, "color": "#5C626A"},
+    )
+    axis.text(
+        0.33,
+        0.86,
+        "one-sided",
+        ha="center",
+        va="bottom",
+        transform=axis.transAxes,
+        fontsize=7.2,
+        color="#4F5660",
+    )
+    for y in (0.79, 0.53):
+        axis.annotate(
+            "",
+            xy=(0.72, y),
+            xytext=(0.62, 0.705),
+            xycoords=axis.transAxes,
+            textcoords=axis.transAxes,
+            arrowprops={"arrowstyle": "->", "lw": 1.0, "color": "#5C626A"},
+        )
+    axis.text(
+        0.50,
+        0.24,
+        r"$Q^2=0:\quad X=X_-\oplus X_+,\qquad X_-^\dagger X_+=0$",
+        ha="center",
+        transform=axis.transAxes,
+        fontsize=8.8,
+    )
+    axis.text(
+        0.50,
+        0.08,
+        "safe two-point Hodge data  $\\longrightarrow$  sealed four-channel test",
+        ha="center",
+        transform=axis.transAxes,
+        fontsize=7.4,
+        color="#4F5660",
+    )
+    axis.set_title("Protection mechanism becomes a response complex", pad=5)
+
+    axis = axes[0, 1]
+    _panel_label(axis, "(b)")
+    for sector in ("central", "adjacent"):
+        for panel, linestyle, marker in (
+            ("sparse", "-", "o"),
+            ("isotropic", "--", "s"),
+        ):
+            values = [
+                group_map[(N, sector, panel)]["median_hodge_balance"]
+                for N in (8, 10, 12)
+            ]
+            axis.plot(
+                (8, 10, 12),
+                values,
+                color=colors[sector],
+                ls=linestyle,
+                marker=marker,
+                lw=1.25,
+                ms=3.8,
+            )
+    axis.set_xticks((8, 10, 12))
+    axis.set_ylim(-0.03, 1.05)
+    axis.set_xlabel("number of complex fermions $N$")
+    axis.set_ylabel("median Hodge balance $\\eta_H$")
+    axis.set_title("Two-point geometry resolves charge structure", pad=5)
+    handles = [
+        Line2D([0], [0], color=colors["central"], lw=1.3, label="central"),
+        Line2D([0], [0], color=colors["adjacent"], lw=1.3, label="adjacent"),
+        Line2D([0], [0], color="#555", ls="-", marker="o", lw=1.1, label="sparse"),
+        Line2D([0], [0], color="#555", ls="--", marker="s", lw=1.1, label="isotropic"),
+    ]
+    axis.legend(handles=handles, frameon=False, ncol=2, loc="center right")
+
+    axis = axes[1, 0]
+    _panel_label(axis, "(c)")
+    pilot_primary = [
+        group_map[(N, sector, "sparse")]
+        for N in (8, 10, 12)
+        for sector in ("central", "adjacent")
+    ]
+    x_values = np.arange(len(pilot_primary), dtype=float)
+    for x, item in zip(x_values, pilot_primary, strict=True):
+        _draw_interval(
+            axis,
+            x - 0.17,
+            item["physical_bootstrap_interval"],
+            color=colors["physical"],
+            marker="o",
+            zorder=4,
+        )
+        _draw_interval(
+            axis,
+            x,
+            item["collapsed_prediction_interval"],
+            color=colors["collapsed"],
+            marker="s",
+            zorder=3,
+        )
+        _draw_interval(
+            axis,
+            x + 0.17,
+            item["hodge_prediction_interval"],
+            color=colors["hodge"],
+            marker="^",
+            zorder=3,
+        )
+    axis.set_xticks(
+        x_values,
+        [
+            f"{item['N']}\n{'C' if item['sector'] == 'central' else 'A'}"
+            for item in pilot_primary
+        ],
+    )
+    axis.set_ylabel("normalized four-channel memory")
+    axis.set_xlabel("pilot sparse panels: size / sector")
+    axis.set_ylim(bottom=0.0)
+    axis.set_title("Pilot: safe covariance does not fix four points", pad=5)
+    axis.legend(
+        handles=[
+            Line2D([0], [0], color=colors["physical"], marker="o", lw=1.1, label="physical 95% bootstrap"),
+            Line2D([0], [0], color=colors["collapsed"], marker="s", lw=1.1, label="collapsed 97.5%"),
+            Line2D([0], [0], color=colors["hodge"], marker="^", lw=1.1, label="Hodge 97.5%"),
+        ],
+        frameon=False,
+        loc="upper right",
+    )
+
+    axis = axes[1, 1]
+    _panel_label(axis, "(d)")
+    ordered_primary = sorted(primary, key=lambda item: item["sector"], reverse=True)
+    for x, item in enumerate(ordered_primary):
+        _draw_interval(
+            axis,
+            x - 0.17,
+            item["physical_bootstrap_interval"],
+            color=colors["physical"],
+            marker="o",
+            zorder=4,
+        )
+        _draw_interval(
+            axis,
+            x,
+            item["collapsed_prediction_interval"],
+            color=colors["collapsed"],
+            marker="s",
+            zorder=3,
+        )
+        _draw_interval(
+            axis,
+            x + 0.17,
+            item["hodge_prediction_interval"],
+            color=colors["hodge"],
+            marker="^",
+            zorder=3,
+        )
+    axis.set_xticks(
+        np.arange(2),
+        [str(item["sector"]) for item in ordered_primary],
+    )
+    axis.set_xlim(-0.55, 1.55)
+    axis.set_ylim(bottom=0.0)
+    axis.set_ylabel("normalized four-channel memory")
+    axis.set_title("Held-out $N=14$: prediction sealed before opening", pad=5)
+    axis.text(
+        0.50,
+        0.97,
+        branch.replace("_", " "),
+        transform=axis.transAxes,
+        ha="center",
+        va="top",
+        fontsize=7.6,
+        fontweight="bold",
+        color="#8B1A1A" if branch != "strong_covariance_universality" else "#1B6E3C",
+    )
+
+    output_pdf = Path(output_pdf)
+    output_png = Path(output_png)
+    output_pdf.parent.mkdir(parents=True, exist_ok=True)
+    output_png.parent.mkdir(parents=True, exist_ok=True)
+    figure.savefig(output_pdf, bbox_inches="tight")
+    figure.savefig(output_png, dpi=300, bbox_inches="tight")
+    plt.close(figure)
+
+    pilot_hash = sha256(pilot_json)
+    inference_hash = sha256(inference_json)
+    _write_report(
+        report_md,
+        pilot,
+        inference,
+        pilot_hash,
+        inference_hash,
+    )
+    checks = {
+        "complete_pilot_grid": observed_grid == expected_grid,
+        "complete_heldout_pair": len(primary) == 2,
+        "known_selected_branch": branch in ALLOWED_BRANCHES,
+        "figure_outputs_exist": output_pdf.is_file() and output_png.is_file(),
+        "source_backed_report_exists": Path(report_md).is_file(),
+    }
+    manifest = {
+        "version": "v7",
+        "selected_branch": branch,
+        "pilot_group_count": len(groups),
+        "inputs": {
+            Path(pilot_json).name: pilot_hash,
+            Path(inference_json).name: inference_hash,
+        },
+        "outputs": {
+            Path(output_pdf).name: sha256(output_pdf),
+            Path(output_png).name: sha256(output_png),
+            Path(report_md).name: sha256(report_md),
+        },
+        "plotted_values": {
+            "pilot_groups": groups,
+            "heldout_primary_pair": primary,
+        },
+        "caption": (
+            "Hodge-resolved response-complex test across generic cubic "
+            "supersymmetric cohomology: safe two-point charge structure, "
+            "complete-realization pilot inference, and sealed held-out verdict."
+        ),
+        "checks": checks,
+        "passed": all(checks.values()),
+    }
+    _atomic_json(manifest_json, manifest)
+    return manifest
+
+
+def main() -> None:
+    manifest = make_figure()
+    print(json.dumps(manifest, indent=2, sort_keys=True))
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/make_susy_hodge_manuscript_assets_v7.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/make_susy_hodge_manuscript_assets_v7.py
new file mode 100644
index 000000000..87916cb0a
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/make_susy_hodge_manuscript_assets_v7.py
@@ -0,0 +1,286 @@
+#!/usr/bin/env python3
+"""Build result-conditioned manuscript assets from audited v7 artifacts."""
+
+from __future__ import annotations
+
+import argparse
+import json
+import shutil
+from datetime import datetime, timezone
+from pathlib import Path
+from typing import Any
+
+from merge_susy_hodge_pilot_v7 import OUTPUT_JSON as PILOT_JSON
+from make_susy_hodge_figure_v7 import (
+    FIGURE_PDF,
+    MANIFEST_JSON as FIGURE_MANIFEST_JSON,
+)
+from run_susy_hodge_geometric_eth_v7 import _atomic_json, sha256
+from analyze_susy_hodge_geometric_eth_v7 import N14_INFERENCE_JSON
+
+
+SCRIPT_ROOT = Path(__file__).resolve().parent
+REPO_ROOT = SCRIPT_ROOT.parents[2]
+OUTPUT_ROOT = SCRIPT_ROOT / "output"
+MANUSCRIPT_ROOT = REPO_ROOT / "overleaf_sync" / "cohomological_geometric_eth"
+RESULTS_TEX = MANUSCRIPT_ROOT / "generated" / "results_v7.tex"
+FIGURE_TARGET = MANUSCRIPT_ROOT / "figures" / FIGURE_PDF.name
+MANIFEST_JSON = OUTPUT_ROOT / "susy_hodge_manuscript_assets_v7.json"
+PUBLISHABLE_BRANCHES = {
+    "strong_covariance_universality",
+    "hodge_resolved_geometric_eth",
+    "cohomological_non_gaussian_class",
+    "structured_cohomology",
+}
+
+
+def _load_passed(path: Path) -> dict[str, Any]:
+    payload = json.loads(Path(path).read_text(encoding="utf-8"))
+    if (
+        payload.get("version") != "v7"
+        or not payload.get("passed")
+        or not all(payload.get("checks", {}).values())
+    ):
+        raise ValueError(f"manuscript source failed its audit: {path}")
+    return payload
+
+
+def _atomic_text(path: Path, value: str) -> None:
+    target = Path(path)
+    target.parent.mkdir(parents=True, exist_ok=True)
+    temporary = target.with_suffix(target.suffix + ".tmp")
+    temporary.write_text(value, encoding="utf-8")
+    temporary.replace(target)
+
+
+def _atomic_copy(source: Path, target: Path) -> None:
+    destination = Path(target)
+    destination.parent.mkdir(parents=True, exist_ok=True)
+    temporary = destination.with_suffix(destination.suffix + ".tmp")
+    shutil.copyfile(source, temporary)
+    temporary.replace(destination)
+
+
+def _macro(name: str, value: str) -> str:
+    return rf"\newcommand{{\{name}}}{{{value}}}"
+
+
+def _expected_pilot_grid(groups: list[dict[str, Any]]) -> bool:
+    observed = {
+        (int(item["N"]), str(item["sector"]), str(item["panel_kind"]))
+        for item in groups
+    }
+    expected = {
+        (size, sector, panel)
+        for size in (8, 10, 12)
+        for sector in ("central", "adjacent")
+        for panel in ("sparse", "isotropic")
+    }
+    return observed == expected
+
+
+def _expected_primary_pair(records: list[dict[str, Any]]) -> bool:
+    return {
+        (int(item["N"]), str(item["sector"]), str(item["panel_kind"]))
+        for item in records
+    } == {(14, "central", "sparse"), (14, "adjacent", "sparse")}
+
+
+def _branch_abstract(branch: str, rejected_groups: int) -> str:
+    opening = (
+        "Exactly degenerate quantum manifolds have no internal level statistics, "
+        "but their projectors move over coupling space. We formulate this motion as "
+        "a response complex and compare one-sided frustration-free constraints with "
+        "the orthogonal exact/coexact response of charge-resolved cubic "
+        r"$\mathcal N=2$ Sachdev--Ye--Kitaev cohomology. "
+        f"In the sequential $N=8,10,12$ pilot, {rejected_groups} of 12 "
+        "size/sector/panel groups reject both registered separable covariance nulls. "
+    )
+    endings = {
+        "strong_covariance_universality": (
+            "A prediction sealed before the held-out $N=14$ opening covers the "
+            "central/adjacent sparse pair under both nulls, supporting a finite-size "
+            "covariance-universal response law."
+        ),
+        "hodge_resolved_geometric_eth": (
+            "A prediction sealed before the held-out $N=14$ opening covers the "
+            "central/adjacent sparse pair only after resolving the Hodge branches, "
+            "establishing predictive mechanism dependence beyond collapsed covariance."
+        ),
+        "cohomological_non_gaussian_class": (
+            "A prediction sealed before the held-out $N=14$ opening is rejected by "
+            "both nulls for the central/adjacent sparse pair, establishing structured "
+            "four-point memory beyond the frozen separable Hodge-covariance law, "
+            "without claiming complete entrywise covariance matching."
+        ),
+        "structured_cohomology": (
+            "The held-out $N=14$ response remains statistically indistinguishable "
+            "from the registered decomposable cohomological control, selecting a "
+            "structured rather than covariance-universal response class."
+        ),
+    }
+    return opening + endings[branch]
+
+
+def _interval_macro(interval: list[float]) -> str:
+    return rf"$[{float(interval[0]):.6f},\,{float(interval[-1]):.6f}]$"
+
+
+def build_manuscript_assets(
+    *,
+    pilot_json: Path = PILOT_JSON,
+    inference_json: Path = N14_INFERENCE_JSON,
+    figure_manifest_json: Path = FIGURE_MANIFEST_JSON,
+    figure_pdf: Path = FIGURE_PDF,
+    results_tex: Path = RESULTS_TEX,
+    figure_target: Path = FIGURE_TARGET,
+    manifest_json: Path = MANIFEST_JSON,
+) -> dict[str, Any]:
+    """Enable result prose only after all compact sources and hashes pass."""
+
+    pilot = _load_passed(pilot_json)
+    inference = _load_passed(inference_json)
+    figure_manifest = _load_passed(figure_manifest_json)
+    groups = list(pilot.get("groups", []))
+    primary = list(inference.get("primary_pair", []))
+    branch = str(inference.get("selected_branch"))
+    if not _expected_pilot_grid(groups):
+        raise ValueError("manuscript pilot grid is incomplete")
+    if not _expected_primary_pair(primary):
+        raise ValueError("manuscript held-out primary pair is incomplete")
+    if branch not in PUBLISHABLE_BRANCHES:
+        raise ValueError("held-out branch is not publishable")
+    if (
+        figure_manifest.get("inputs", {}).get(Path(pilot_json).name)
+        != sha256(pilot_json)
+        or figure_manifest.get("inputs", {}).get(Path(inference_json).name)
+        != sha256(inference_json)
+        or figure_manifest.get("outputs", {}).get(Path(figure_pdf).name)
+        != sha256(figure_pdf)
+        or figure_manifest.get("selected_branch") != branch
+    ):
+        raise ValueError("figure manifest does not match manuscript sources")
+
+    rejected_groups = sum(
+        not bool(item.get("collapsed_covered"))
+        and not bool(item.get("hodge_covered"))
+        for item in groups
+    )
+    primary_by_sector = {str(item["sector"]): item for item in primary}
+    adjacent = primary_by_sector["adjacent"]
+    central = primary_by_sector["central"]
+    pilot_sentence = (
+        f"Across the complete $N=8,10,12$ pilot, {rejected_groups} of 12 "
+        "groups reject both registered separable covariance nulls under "
+        "complete-realization resampling."
+    )
+    result_sentence = (
+        "The held-out adjacent and central medians are "
+        f"{float(adjacent['observed_median']):.6f} and "
+        f"{float(central['observed_median']):.6f}; their complete-realization "
+        "confidence intervals do not overlap either sealed covariance prediction."
+    )
+    prediction_sha = str(inference.get("prediction_sha256", ""))
+    if len(prediction_sha) != 64:
+        raise ValueError("inference does not contain a full prediction hash")
+    lines = [
+        "% Generated from audited v7 inference; do not edit.",
+        r"\newif\ifheldoutcomplete",
+        r"\heldoutcompletetrue",
+        _macro("HeldoutAbstract", _branch_abstract(branch, rejected_groups)),
+        _macro("HeldoutBranch", branch.replace("_", r"\_")),
+        _macro("HeldoutResultSentence", result_sentence),
+        _macro("PilotResultSentence", pilot_sentence),
+        _macro("HeldoutSeal", prediction_sha[:12]),
+        _macro(
+            "HeldoutAdjacentObserved",
+            f"{float(adjacent['observed_median']):.6f}",
+        ),
+        _macro(
+            "HeldoutAdjacentPhysical",
+            _interval_macro(adjacent["physical_bootstrap_interval"]),
+        ),
+        _macro(
+            "HeldoutAdjacentCollapsed",
+            _interval_macro(adjacent["collapsed_prediction_interval"]),
+        ),
+        _macro(
+            "HeldoutAdjacentHodge",
+            _interval_macro(adjacent["hodge_prediction_interval"]),
+        ),
+        _macro(
+            "HeldoutCentralObserved",
+            f"{float(central['observed_median']):.6f}",
+        ),
+        _macro(
+            "HeldoutCentralPhysical",
+            _interval_macro(central["physical_bootstrap_interval"]),
+        ),
+        _macro(
+            "HeldoutCentralCollapsed",
+            _interval_macro(central["collapsed_prediction_interval"]),
+        ),
+        _macro(
+            "HeldoutCentralHodge",
+            _interval_macro(central["hodge_prediction_interval"]),
+        ),
+    ]
+    _atomic_text(results_tex, "\n".join(lines) + "\n")
+    _atomic_copy(figure_pdf, figure_target)
+    checks = {
+        "complete_pilot_grid": _expected_pilot_grid(groups),
+        "complete_primary_pair": _expected_primary_pair(primary),
+        "publishable_registered_branch": branch in PUBLISHABLE_BRANCHES,
+        "figure_manifest_matches_sources": True,
+        "result_macro_enabled": r"\heldoutcompletetrue"
+        in Path(results_tex).read_text(encoding="utf-8"),
+        "figure_copy_exact": sha256(figure_target) == sha256(figure_pdf),
+    }
+    manifest = {
+        "version": "v7",
+        "generated_utc": datetime.now(timezone.utc).isoformat(),
+        "selected_branch": branch,
+        "prediction_sha256": prediction_sha,
+        "inputs": {
+            Path(pilot_json).name: sha256(pilot_json),
+            Path(inference_json).name: sha256(inference_json),
+            Path(figure_manifest_json).name: sha256(figure_manifest_json),
+            Path(figure_pdf).name: sha256(figure_pdf),
+        },
+        "outputs": {
+            str(Path(results_tex).name): sha256(results_tex),
+            str(Path(figure_target).name): sha256(figure_target),
+        },
+        "checks": checks,
+        "passed": all(checks.values()),
+    }
+    if not manifest["passed"]:
+        raise RuntimeError(f"manuscript asset build failed: {checks}")
+    _atomic_json(manifest_json, manifest)
+    return manifest
+
+
+def _parser() -> argparse.ArgumentParser:
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument("--pilot-json", type=Path, default=PILOT_JSON)
+    parser.add_argument("--inference-json", type=Path, default=N14_INFERENCE_JSON)
+    parser.add_argument(
+        "--figure-manifest-json", type=Path, default=FIGURE_MANIFEST_JSON
+    )
+    parser.add_argument("--figure-pdf", type=Path, default=FIGURE_PDF)
+    return parser
+
+
+def main() -> None:
+    args = _parser().parse_args()
+    payload = build_manuscript_assets(
+        pilot_json=args.pilot_json,
+        inference_json=args.inference_json,
+        figure_manifest_json=args.figure_manifest_json,
+        figure_pdf=args.figure_pdf,
+    )
+    print(json.dumps(payload, indent=2, sort_keys=True))
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/merge_susy_hodge_pilot_v7.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/merge_susy_hodge_pilot_v7.py
new file mode 100644
index 000000000..36999ead6
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/merge_susy_hodge_pilot_v7.py
@@ -0,0 +1,195 @@
+#!/usr/bin/env python3
+"""Merge independently opened v7 pilot sizes into one audited artifact."""
+
+from __future__ import annotations
+
+import argparse
+import json
+from datetime import datetime, timezone
+from pathlib import Path
+from typing import Any, Sequence
+
+import numpy as np
+
+from run_susy_hodge_geometric_eth_v7 import _atomic_json, _atomic_npz, sha256
+
+
+SCRIPT_ROOT = Path(__file__).resolve().parent
+OUTPUT_ROOT = SCRIPT_ROOT / "output"
+DEFAULT_JSONS = (
+    OUTPUT_ROOT / "susy_hodge_v7_outcomes_pilot_banked.json",
+    OUTPUT_ROOT / "susy_hodge_v7_outcomes_pilot_N10_banked.json",
+    OUTPUT_ROOT / "susy_hodge_v7_outcomes_pilot_N12_banked.json",
+)
+DEFAULT_NPZS = (
+    OUTPUT_ROOT / "susy_hodge_v7_outcomes_pilot_banked.npz",
+    OUTPUT_ROOT / "susy_hodge_v7_outcomes_pilot_N10_banked.npz",
+    OUTPUT_ROOT / "susy_hodge_v7_outcomes_pilot_N12_banked.npz",
+)
+OUTPUT_JSON = OUTPUT_ROOT / "susy_hodge_v7_outcomes_pilot_combined.json"
+OUTPUT_NPZ = OUTPUT_ROOT / "susy_hodge_v7_outcomes_pilot_combined.npz"
+
+
+def _load_passed(path: Path) -> dict[str, Any]:
+    payload = json.loads(Path(path).read_text(encoding="utf-8"))
+    if (
+        payload.get("version") != "v7"
+        or not payload.get("passed")
+        or not all(payload.get("checks", {}).values())
+    ):
+        raise ValueError(f"pilot source failed its audit: {path}")
+    return payload
+
+
+def merge_pilot_artifacts(
+    json_paths: Sequence[Path],
+    npz_paths: Sequence[Path],
+    *,
+    output_json: Path = OUTPUT_JSON,
+    output_npz: Path = OUTPUT_NPZ,
+    expected_sizes: Sequence[int] = (8, 10, 12),
+) -> dict[str, Any]:
+    """Merge compact per-size artifacts without reopening raw outcome sidecars."""
+
+    json_sources = tuple(Path(path) for path in json_paths)
+    npz_sources = tuple(Path(path) for path in npz_paths)
+    sizes = tuple(int(size) for size in expected_sizes)
+    if not json_sources or len(json_sources) != len(npz_sources):
+        raise ValueError("pilot merge requires paired JSON and NPZ sources")
+    if len(sizes) != len(set(sizes)):
+        raise ValueError("expected pilot sizes must be unique")
+
+    payloads = [_load_passed(path) for path in json_sources]
+    uncertainty_units = {item.get("uncertainty_unit") for item in payloads}
+    null_counts = {int(item.get("null_replicates", -1)) for item in payloads}
+    bootstrap_counts = {
+        int(item.get("physical_bootstrap_replicates", -1)) for item in payloads
+    }
+    coverages = {float(item.get("prediction_coverage", -1.0)) for item in payloads}
+    if (
+        len(uncertainty_units) != 1
+        or len(null_counts) != 1
+        or len(bootstrap_counts) != 1
+        or len(coverages) != 1
+    ):
+        raise ValueError("pilot source protocols disagree")
+
+    groups: list[dict[str, Any]] = []
+    arrays: dict[str, np.ndarray] = {}
+    source_records: list[dict[str, Any]] = []
+    for json_path, npz_path, payload in zip(
+        json_sources, npz_sources, payloads, strict=True
+    ):
+        if payload.get("arrays_sha256") != sha256(npz_path):
+            raise ValueError(f"pilot NPZ hash mismatch: {npz_path}")
+        with np.load(npz_path, allow_pickle=False) as source_arrays:
+            for key in source_arrays.files:
+                if key in arrays:
+                    raise ValueError(f"duplicate pilot array key: {key}")
+                arrays[key] = np.asarray(source_arrays[key]).copy()
+        groups.extend(list(payload.get("groups", [])))
+        source_records.append(
+            {
+                "json_file": json_path.name,
+                "json_sha256": sha256(json_path),
+                "npz_file": npz_path.name,
+                "npz_sha256": sha256(npz_path),
+                "safe_covariates_sha256": payload.get("safe_covariates_sha256"),
+            }
+        )
+
+    identities = [
+        (int(item["N"]), str(item["sector"]), str(item["panel_kind"]))
+        for item in groups
+    ]
+    if len(identities) != len(set(identities)):
+        raise ValueError("pilot merge contains duplicate size/sector/panel groups")
+    expected_grid = {
+        (size, sector, panel)
+        for size in sizes
+        for sector in ("central", "adjacent")
+        for panel in ("sparse", "isotropic")
+    }
+    observed_grid = set(identities)
+    expected_array_keys = {
+        f"N{size}_{sector}_{panel}_{suffix}"
+        for size, sector, panel in expected_grid
+        for suffix in (
+            "physical",
+            "physical_bootstrap",
+            "collapsed_null",
+            "hodge_null",
+        )
+    }
+    if observed_grid != expected_grid:
+        raise ValueError("pilot merge does not match the registered size grid")
+    if set(arrays) != expected_array_keys:
+        raise ValueError("pilot merge arrays do not match the registered groups")
+
+    _atomic_npz(output_npz, **arrays)
+    checks = {
+        "all_sources_passed": all(
+            payload.get("passed") and all(payload.get("checks", {}).values())
+            for payload in payloads
+        ),
+        "complete_registered_grid": observed_grid == expected_grid,
+        "unique_group_identities": len(identities) == len(set(identities)),
+        "complete_array_grid": set(arrays) == expected_array_keys,
+        "finite_arrays": all(np.all(np.isfinite(value)) for value in arrays.values()),
+        "common_complete_realization_protocol": uncertainty_units
+        == {"complete_disorder_realization"},
+        "positive_registered_counts": next(iter(null_counts)) > 0
+        and next(iter(bootstrap_counts)) > 0,
+    }
+    result = {
+        "version": "v7",
+        "generated_utc": datetime.now(timezone.utc).isoformat(),
+        "uncertainty_unit": next(iter(uncertainty_units)),
+        "null_replicates": next(iter(null_counts)),
+        "physical_bootstrap_replicates": next(iter(bootstrap_counts)),
+        "prediction_coverage": next(iter(coverages)),
+        "registered_sizes": list(sizes),
+        "groups": sorted(
+            groups,
+            key=lambda item: (
+                int(item["N"]),
+                str(item["sector"]),
+                str(item["panel_kind"]),
+            ),
+        ),
+        "source_pilot_artifacts": source_records,
+        "arrays_sha256": sha256(output_npz),
+        "sources": {Path(__file__).name: sha256(Path(__file__))},
+        "checks": checks,
+        "passed": all(checks.values()),
+    }
+    if not result["passed"]:
+        raise RuntimeError(f"pilot merge failed: {checks}")
+    _atomic_json(output_json, result)
+    return result
+
+
+def _parser() -> argparse.ArgumentParser:
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument("--jsons", type=Path, nargs="+", default=list(DEFAULT_JSONS))
+    parser.add_argument("--npzs", type=Path, nargs="+", default=list(DEFAULT_NPZS))
+    parser.add_argument("--output-json", type=Path, default=OUTPUT_JSON)
+    parser.add_argument("--output-npz", type=Path, default=OUTPUT_NPZ)
+    parser.add_argument("--sizes", type=int, nargs="+", default=[8, 10, 12])
+    return parser
+
+
+def main() -> None:
+    args = _parser().parse_args()
+    payload = merge_pilot_artifacts(
+        args.jsons,
+        args.npzs,
+        output_json=args.output_json,
+        output_npz=args.output_npz,
+        expected_sizes=args.sizes,
+    )
+    print(json.dumps(payload, indent=2, sort_keys=True))
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/figure_susy_hodge_geometric_eth_v7.json b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/figure_susy_hodge_geometric_eth_v7.json
new file mode 100644
index 000000000..7cf88f031
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/figure_susy_hodge_geometric_eth_v7.json
@@ -0,0 +1,3269 @@
+{
+  "caption": "Hodge-resolved response-complex test across generic cubic supersymmetric cohomology: safe two-point charge structure, complete-realization pilot inference, and sealed held-out verdict.",
+  "checks": {
+    "complete_heldout_pair": true,
+    "complete_pilot_grid": true,
+    "figure_outputs_exist": true,
+    "known_selected_branch": true,
+    "source_backed_report_exists": true
+  },
+  "inputs": {
+    "susy_hodge_v7_N14_inference.json": "177643e07fc6cf210362fc1077070bd1f0ba316b6805042a626de3f96c55a627",
+    "susy_hodge_v7_outcomes_pilot_combined.json": "152084fc502e38074ed0d8163f8582c01b9e5de46c12a53d2ced4994d1a74617"
+  },
+  "outputs": {
+    "figure_susy_hodge_geometric_eth_v7.pdf": "f081c5f162778e5e45a48adba1ea08c37e8521c725725922a0ec3a35bda74a54",
+    "figure_susy_hodge_geometric_eth_v7.png": "252c337189afb6f0adea8142573e2e459a41e7226932e5954711ff0c7f5eb341",
+    "susy_hodge_geometric_eth_report_v7.md": "a085aedfbb2ce48ff26804d8be02334dac8447ff3d899056285db2eab8930cdf"
+  },
+  "passed": true,
+  "pilot_group_count": 12,
+  "plotted_values": {
+    "heldout_primary_pair": [
+      {
+        "N": 14,
+        "collapsed_covered": false,
+        "collapsed_prediction_interval": [
+          0.11178894327406741,
+          0.11182073355743845,
+          0.11185243656607288
+        ],
+        "hodge_covered": false,
+        "hodge_prediction_interval": [
+          0.11234396147287215,
+          0.11242666326099385,
+          0.11251284962232763
+        ],
+        "observed_median": 0.3015287195325017,
+        "panel_kind": "sparse",
+        "physical_bootstrap_interval": [
+          0.2915274750468075,
+          0.3120611443736316
+        ],
+        "realizations": 24,
+        "robust_outside_both": true,
+        "sector": "adjacent"
+      },
+      {
+        "N": 14,
+        "collapsed_covered": false,
+        "collapsed_prediction_interval": [
+          0.1113377289462959,
+          0.11134480106449174,
+          0.11135301768590472
+        ],
+        "hodge_covered": false,
+        "hodge_prediction_interval": [
+          0.11133252105193724,
+          0.11133957071189352,
+          0.11134819894894332
+        ],
+        "observed_median": 0.3749925716126603,
+        "panel_kind": "sparse",
+        "physical_bootstrap_interval": [
+          0.3689804933327322,
+          0.38047305142967947
+        ],
+        "realizations": 24,
+        "robust_outside_both": true,
+        "sector": "central"
+      }
+    ],
+    "pilot_groups": [
+      {
+        "N": 8,
+        "collapsed_covered": false,
+        "collapsed_prediction_interval": [
+          0.28774443822769635,
+          0.2923719696932815,
+          0.29747553580253777
+        ],
+        "hodge_covered": false,
+        "hodge_prediction_interval": [
+          0.3059263591384163,
+          0.312032433068657,
+          0.31831694112765746
+        ],
+        "median_hodge_balance": 0.07040982426906839,
+        "null_banks": [
+          {
+            "arrays_sha256": "7e4e820c450f1e3921d889e56fd5dd8f1cc0b85efebb0e01082f72896eadd975",
+            "metadata_sha256": "3dfd016bb6cffc1bb3cea44405bd5280344c764350ac059703b2cd7af9449afc",
+            "realization": 0
+          },
+          {
+            "arrays_sha256": "5f2b5ee2045d7e634ea2eb75be49f59d044c694db0d31dd96b554075d16baf64",
+            "metadata_sha256": "426b5d1187b3c2609ffc029b233659fa5d7f51dbceb53049b1411582ce42a2c7",
+            "realization": 1
+          },
+          {
+            "arrays_sha256": "e821d455d25eeb8440515614400268c3f0091781c64cc042d2447b8056df6259",
+            "metadata_sha256": "b2ecdc748cb7bafdf6ae3709e2a4a32fc1db34ed18e5074f5a9d103d7131f2b0",
+            "realization": 2
+          },
+          {
+            "arrays_sha256": "a7a8d2092c29178d35912a48018e334d1d8e025a24288af6ba3a3e2ce65eaec2",
+            "metadata_sha256": "3206a8d888f29b824c67418a84a5c7b7dd7c2d2318c431a9eb358fbe52609375",
+            "realization": 3
+          },
+          {
+            "arrays_sha256": "8eebc9f3ff729229002bbff88eb1599faae9681fd7aec883a3c73e0559a2a826",
+            "metadata_sha256": "728581e912fe0ee4cbdf3066fdd0dc6160bdbb82dbf258e515e0d11e28d73fd8",
+            "realization": 4
+          },
+          {
+            "arrays_sha256": "c613197503272fc266f8aea0f6746f3a16c0e9c4845ba71c91f5e4d9df165997",
+            "metadata_sha256": "16357f2902cfb4cacaa672f9bec6c8882756684d39de8ec27ee3f0739abdd840",
+            "realization": 5
+          },
+          {
+            "arrays_sha256": "584c834366b823aee9effb07a037b555f39fe7efc3a24bda79004f52557d8c4b",
+            "metadata_sha256": "8f3bacf052da6950912eb5ebc5776e397806bdcb25928e68e8774c94d1465592",
+            "realization": 6
+          },
+          {
+            "arrays_sha256": "71a95506502428f05bdbd1fed08f5bace55dac555c8975f99f53ea65f0bd2e87",
+            "metadata_sha256": "9e05a0d39b40afca583d4950bd7fc0df1cbdc15b38406ad50e28fb2846b21a3b",
+            "realization": 7
+          },
+          {
+            "arrays_sha256": "85c77b070a9c54276bc752de236c1c658f3f999cd1b92f0ecc53f0a8649ea71b",
+            "metadata_sha256": "3dce74e5717170ecad93c4de0e68a4454cb19be3df4706c8ea024a4241faaba6",
+            "realization": 8
+          },
+          {
+            "arrays_sha256": "a9b039b58718984c9643c6984dd524ebc9bbedcaa82140b530ae5f698f755b36",
+            "metadata_sha256": "0e4f603d7eee9972673ae54f75878e0534dfe5defac2f785ff60de1648baa301",
+            "realization": 9
+          },
+          {
+            "arrays_sha256": "90e82fda00d060444958a4b38f7fa5b2728e91e7b4fffbc69aca75f50ad852fc",
+            "metadata_sha256": "574932aeb9b422627ba393a783a7fb8924128448d0d1ac51302e1900c60df1ba",
+            "realization": 10
+          },
+          {
+            "arrays_sha256": "95b821b9a32ae48211a34b3b8819e6c0758a041f7a6cbb471148d0fabebdaa2b",
+            "metadata_sha256": "217223c8912f1bbe708dadb2e0a12ba9fa5e6b36e3a6bd583d4f864bf0c41637",
+            "realization": 11
+          },
+          {
+            "arrays_sha256": "f182e61e5d9880bdfe13b1e7b148ddebf13bf12e00e018798fe85fda84f00490",
+            "metadata_sha256": "2c9453e6cbeb420dc8a6cf80a7bcb33221f23a7594610310369a79a30c358e1a",
+            "realization": 12
+          },
+          {
+            "arrays_sha256": "d9634ea5aa3830b539c122ffc2024ceb09ec73398d23f785baae66b001b66fcb",
+            "metadata_sha256": "ba0d05489fc8d01eed51fc4c1eecd10ac981e9df32b9080cd80cc4578ac2edff",
+            "realization": 13
+          },
+          {
+            "arrays_sha256": "85e233efd41b6223f3988f25135d922407ad1f0c288f2bef39b718f1d529e35f",
+            "metadata_sha256": "5b1ce1bd4f1e6fbab140cec48b0b62bc2f914b10b4ccd43efdef40181eb4b469",
+            "realization": 14
+          },
+          {
+            "arrays_sha256": "e4289b64b3dce047b9fd985f6adcdc0a3e3252f7ff3b8281da3d939092b94900",
+            "metadata_sha256": "cac306e55cc899f1bf75bc99ccf1c649e342b09c325229724acae01529109365",
+            "realization": 15
+          },
+          {
+            "arrays_sha256": "a63b9e21218662bebf0c4d088c4b2c839e6bfd28fe3bbc0261f6d01fd5006249",
+            "metadata_sha256": "744076addebecf804a815872fc7e81114ad6a9d71ca6f28a81c111e8d3788ef7",
+            "realization": 16
+          },
+          {
+            "arrays_sha256": "b66785aa3497256bb2cea0b6a986c3bca2fa26266184862c65f90112421a555c",
+            "metadata_sha256": "5bf89be8cd9fd3f57a2618cc003767bb31981e2f968b6ca07e529643b6ec5b36",
+            "realization": 17
+          },
+          {
+            "arrays_sha256": "11e79fc31c5cc3e182f8ef0f562a2c87ccf634d12a1db3076bac07470d44dcb1",
+            "metadata_sha256": "9e739c2f1ed1871341c81027a95e84a55be69b335b8a7b140a0419cfcf409c7d",
+            "realization": 18
+          },
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+}
\ No newline at end of file
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/figure_susy_hodge_geometric_eth_v7.pdf b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/figure_susy_hodge_geometric_eth_v7.pdf
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diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/response_complex_memory_supplement_v7.pdf b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/response_complex_memory_supplement_v7.pdf
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diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/response_complex_memory_v7.pdf b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/response_complex_memory_v7.pdf
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diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_delivery_audit_v7.json b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_delivery_audit_v7.json
new file mode 100644
index 000000000..deb784bba
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_delivery_audit_v7.json
@@ -0,0 +1,51 @@
+{
+  "artifact_hashes": {
+    "controls_json": "854e782121ad9bfbe6dfb6fc2e4d24fa4e1deab0f61812c96618cfa1c6851861",
+    "figure_manifest": "c7e1e142242c2481cb8346af72b8ff8d2b6ef40a4f4c04943890f504eb70949d",
+    "figure_pdf": "f081c5f162778e5e45a48adba1ea08c37e8521c725725922a0ec3a35bda74a54",
+    "figure_png": "252c337189afb6f0adea8142573e2e459a41e7226932e5954711ff0c7f5eb341",
+    "inference_json": "177643e07fc6cf210362fc1077070bd1f0ba316b6805042a626de3f96c55a627",
+    "pilot_json": "152084fc502e38074ed0d8163f8582c01b9e5de46c12a53d2ced4994d1a74617",
+    "pilot_npz": "d1061c85fda0fb91b2974fe7389f577b6b657173b1f906e41868674b12d0cc6b",
+    "prediction_json": "fc300dc7e4bdc1be157919e458ac868d3468533cce31108f23c9fba4f7e9f102",
+    "prediction_npz": "f8b2dde1c8563c39caa2b800b7c4e2595c8f1c3365a3d851b06e252279dbd903",
+    "prediction_seal": "8e9bbd6e248cc8034ce3f118db518257b4face2fbb028f2fd133ff3c04b9cd44",
+    "report_md": "a085aedfbb2ce48ff26804d8be02334dac8447ff3d899056285db2eab8930cdf",
+    "safe_json": "dbf51fe8d19864fb499ae9a83b2683fbecf3aed1209ae9fbb787ede0c212a7bb",
+    "unsealed_json": "372229acd39d7b8a30d5ca5bc1460fd62b81a589b5c68f707d8bccade6e70faf"
+  },
+  "checks": {
+    "all_required_files_exist": true,
+    "analytic_controls_passed": true,
+    "complete_inference_primary_pair": true,
+    "complete_pilot_grid": true,
+    "complete_prediction_primary_pair": true,
+    "curvature_atom_control": true,
+    "figure_and_report_hashes": true,
+    "figure_branch_matches_inference": true,
+    "figure_manifest_passed": true,
+    "inference_passed": true,
+    "inference_references_prediction": true,
+    "one_sided_control": true,
+    "pilot_array_hash": true,
+    "pilot_passed": true,
+    "prediction_array_hash": true,
+    "prediction_has_no_outcome_leakage": true,
+    "prediction_passed": true,
+    "prediction_precedes_unseal": true,
+    "prediction_safe_covariate_hash": true,
+    "report_has_claim_boundary_and_sources": true,
+    "safe_covariates_have_no_outcome_leakage": true,
+    "safe_covariates_passed": true,
+    "selected_branch_recomputed": true,
+    "unsealed_passed": true,
+    "unsealed_references_prediction": true,
+    "valid_prediction_seal": true
+  },
+  "generated_utc": "2026-08-04T01:54:03.863688+00:00",
+  "passed": true,
+  "prediction_sha256": "fc300dc7e4bdc1be157919e458ac868d3468533cce31108f23c9fba4f7e9f102",
+  "recomputed_branch": "cohomological_non_gaussian_class",
+  "selected_branch": "cohomological_non_gaussian_class",
+  "version": "v7"
+}
\ No newline at end of file
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_geometric_eth_report_v7.md b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_geometric_eth_report_v7.md
new file mode 100644
index 000000000..f2a49c668
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_geometric_eth_report_v7.md
@@ -0,0 +1,36 @@
+# Hodge-resolved Geometric ETH result report
+
+## Verdict
+
+Selected frozen branch: `cohomological_non_gaussian_class`.
+
+Neither covariance-only null covers the held-out pair, and the complete-realization uncertainty remains separated; a reproducible cohomological four-point memory survives the registered separable Hodge-covariance matching.
+
+## Established
+
+- The charge-resolved cubic $\mathcal N=2$ SYK BPS response splits into numerically orthogonal exact and coexact branches and agrees with the direct resolvent response under the registered tests.
+- The pilot contains 12 complete size/sector/panel groups and uses complete disorder realizations as its uncertainty unit.
+- The held-out central/adjacent sparse pair was scored only after validating prediction SHA-256 `fc300dc7e4bdc1be157919e458ac868d3468533cce31108f23c9fba4f7e9f102`.
+
+- adjacent: observed median 0.30152872, physical bootstrap [0.29152748, 0.31206114], collapsed prediction [0.11178894, 0.11185244], Hodge prediction [0.11234396, 0.11251285].
+- central: observed median 0.37499257, physical bootstrap [0.36898049, 0.38047305], collapsed prediction [0.11133773, 0.11135302], Hodge prediction [0.11133252, 0.11134820].
+
+## Not established
+
+- This is not conventional energy-resolved ETH, a real-time chaos result, or a thermodynamic-limit theorem.
+- Generic $\mathcal N=2$ SYK is an independent supersymmetric protection mechanism, but it is not a spatially local model; locality universality requires a later nilpotent lattice-supercharge benchmark.
+- Berry-curvature chaos in this model is prior art. The contribution tested here is the pre-outcome response-complex/two-point prediction of a gauge-invariant four-channel statistic.
+- The Gaussian nulls match the registered collapsed or branch-resolved marginal covariance data, not the complete entrywise covariance operator. Rejection therefore establishes failure of the frozen separable Hodge-Gaussian response law; by itself it does not distinguish intrinsic non-Gaussianity from unmodeled nonseparable two-point structure.
+
+## Relation to prior work
+
+- [Fu, Gaiotto, Maldacena, and Sachdev, *Supersymmetric SYK models*](https://arxiv.org/abs/1610.08917).
+- [Chen, Colin-Ellerin, Mamroud, and Papadodimas, *Chaos of Berry curvature for BPS microstates*](https://arxiv.org/abs/2604.23287).
+- [Chen, Lin, and Shenker, *BPS Chaos*](https://arxiv.org/abs/2407.19387).
+- [Huijse and Schoutens, *Supersymmetry, lattice fermions, independence complexes and cohomology theory*](https://arxiv.org/abs/0903.0784).
+
+## Provenance
+
+- Pilot JSON SHA-256: `152084fc502e38074ed0d8163f8582c01b9e5de46c12a53d2ced4994d1a74617`.
+- Held-out inference JSON SHA-256: `177643e07fc6cf210362fc1077070bd1f0ba316b6805042a626de3f96c55a627`.
+- Uncertainty unit: `complete_disorder_realization`.
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_manuscript_assets_v7.json b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_manuscript_assets_v7.json
new file mode 100644
index 000000000..380ff98ba
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_manuscript_assets_v7.json
@@ -0,0 +1,25 @@
+{
+  "checks": {
+    "complete_pilot_grid": true,
+    "complete_primary_pair": true,
+    "figure_copy_exact": true,
+    "figure_manifest_matches_sources": true,
+    "publishable_registered_branch": true,
+    "result_macro_enabled": true
+  },
+  "generated_utc": "2026-08-04T01:30:55.991534+00:00",
+  "inputs": {
+    "figure_susy_hodge_geometric_eth_v7.json": "c7e1e142242c2481cb8346af72b8ff8d2b6ef40a4f4c04943890f504eb70949d",
+    "figure_susy_hodge_geometric_eth_v7.pdf": "f081c5f162778e5e45a48adba1ea08c37e8521c725725922a0ec3a35bda74a54",
+    "susy_hodge_v7_N14_inference.json": "177643e07fc6cf210362fc1077070bd1f0ba316b6805042a626de3f96c55a627",
+    "susy_hodge_v7_outcomes_pilot_combined.json": "152084fc502e38074ed0d8163f8582c01b9e5de46c12a53d2ced4994d1a74617"
+  },
+  "outputs": {
+    "figure_susy_hodge_geometric_eth_v7.pdf": "f081c5f162778e5e45a48adba1ea08c37e8521c725725922a0ec3a35bda74a54",
+    "results_v7.tex": "a1257d1744f1085ee518a36ca9ed2574dec608cb7f71c766a082745f3acc858d"
+  },
+  "passed": true,
+  "prediction_sha256": "fc300dc7e4bdc1be157919e458ac868d3468533cce31108f23c9fba4f7e9f102",
+  "selected_branch": "cohomological_non_gaussian_class",
+  "version": "v7"
+}
\ No newline at end of file
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_manuscript_audit_v7.json b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_manuscript_audit_v7.json
new file mode 100644
index 000000000..792a9b34e
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_manuscript_audit_v7.json
@@ -0,0 +1,35 @@
+{
+  "artifact_hashes": {
+    "figure_susy_hodge_geometric_eth_v7.pdf": "f081c5f162778e5e45a48adba1ea08c37e8521c725725922a0ec3a35bda74a54",
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+    "main.pdf": "9fe357a5bfce5e6efd60a3c8bf0a1b73a4eac4ee15f9bb8844f51d2f7e1252ee",
+    "main.tex": "a03ad4b46ae9431b509c025909dfc9a307e4709de3c2047980f346179a612ab5",
+    "response_complex_memory_supplement_v7.pdf": "e43a5a2f62494bb7595f790de5643d6244d782402478f36fdcc7c511176b79c5",
+    "response_complex_memory_v7.pdf": "9fe357a5bfce5e6efd60a3c8bf0a1b73a4eac4ee15f9bb8844f51d2f7e1252ee",
+    "results_v7.tex": "a1257d1744f1085ee518a36ca9ed2574dec608cb7f71c766a082745f3acc858d",
+    "supplement.log": "4a3bd359b9d5ed024bed900b9b1291fd789489aeff9a4d06d94cea4bc18ec4f8",
+    "supplement.pdf": "e43a5a2f62494bb7595f790de5643d6244d782402478f36fdcc7c511176b79c5",
+    "supplement.tex": "91a5edd3e299ca97348ffee8c25ac0049e3e169c42adbc59a5cb76e734d63a38",
+    "susy_hodge_manuscript_assets_v7.json": "ccf63b88ce4fe8a71bd87c3a4c97ee8b55645dad3a808a693f2daa044b8e3092"
+  },
+  "checks": {
+    "archived_pdf_exact": true,
+    "archived_supplement_exact": true,
+    "asset_manifest_passed": true,
+    "clean_latex_log": true,
+    "clean_supplement_log": true,
+    "compiled_pdf_structure": true,
+    "compiled_supplement_structure": true,
+    "figure_source_hash": true,
+    "heldout_result_enabled": true,
+    "main_uses_generated_results": true,
+    "result_source_hash": true,
+    "selected_branch_in_source": true,
+    "supplement_uses_generated_results": true
+  },
+  "generated_utc": "2026-08-04T01:54:04.257681+00:00",
+  "passed": true,
+  "prediction_sha256": "fc300dc7e4bdc1be157919e458ac868d3468533cce31108f23c9fba4f7e9f102",
+  "selected_branch": "cohomological_non_gaussian_class",
+  "version": "v7"
+}
\ No newline at end of file
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_v7_N14_covariates.json b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_v7_N14_covariates.json
new file mode 100644
index 000000000..e39c5f8b0
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_v7_N14_covariates.json
@@ -0,0 +1,6155 @@
+{
+  "checks": {
+    "all_safe_checks": true,
+    "complete_requested_grid": true,
+    "no_outcome_leakage": true
+  },
+  "passed": true,
+  "records": [
+    {
+      "arrays_sha256": "ccc702aa83f8021eb3aa2f67dc3949798abcb5a44efacf3dae527c696861fa90",
+      "checks": {
+        "branch_sum": true,
+        "direct_resolvent": true,
+        "finite_hodge_signature": true,
+        "finite_response": true,
+        "full_channel_support": true,
+        "hodge_orthogonality": true,
+        "no_outcome_leakage": true,
+        "safe_arrays_exclude_response_matrices": true,
+        "target_leakage": true
+      },
+      "generated_utc": "2026-08-01T16:42:00.253660+00:00",
+      "identity": {
+        "N": 14,
+        "charge": 7,
+        "kernel_identity_hash": "80bcec06366a7329d97cee0e4b8e13093e1157315a6c26b1671f7a252e72e2fe",
+        "panel_kind": "sparse",
+        "panel_seed": 1763853356421777176,
+        "realization": 0,
+        "sector": "central",
+        "sources": {
+          "lgeth/hodge_response.py": "dad431f6a3873b2cb5542c07efd9b9c29f96f0375947f81947998783f362469e",
+          "lgeth/hodge_wick.py": "f80fc96fa1408c0df2e15d4f804bac17feef9c59e9fbc511dd5052ef591e04c7",
+          "lgeth/susy_cohomology.py": "4b8c6d62f45a7de1a696fcba7228a575cf1745ab82968732ef3d6238bbf9672a",
+          "lgeth/wick_channels.py": "e1faedf5c98f660756e077445a88d05013bc6810f5b0f69aa8fc0dc6fe13469b",
+          "run_susy_hodge_geometric_eth_v7.py": "781b1e40594405697bdff010bb2a433496fd2cd1c6400acd288103a86a6abe0a"
+        },
+        "version": "v7"
+      },
+      "identity_hash": "44f17703002e5d8496af042ae29f3602f4c4998705aa400167d7ef572d12e12f",
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+        "complement_rank": 1974,
+        "gap": 0.05948871912595825,
+        "kernel_residual": 1.9751282882134734e-14
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+      "passed": true,
+      "signature": {
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+        "hodge_balance": 0.9999999999999998,
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+        "minus_weight": 5219.474068767745,
+        "orthogonality_relative_error": 1.0791710079627175e-16,
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+        "plus_target_effective_rank": 747.7840119457766,
+        "plus_target_entropy": 0.9353314755810784,
+        "plus_weight": 5219.474068767739,
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+      },
+      "spectrum_lengths": {
+        "minus_channel_covariance": 64,
+        "minus_external_eigenvalues": 913,
+        "minus_target_eigenvalues": 1458,
+        "plus_channel_covariance": 64,
+        "plus_external_eigenvalues": 913,
+        "plus_target_eigenvalues": 1458
+      }
+    },
+    {
+      "arrays_sha256": "19a0e93f9bb71ac87be3e6be0fffbeaf3f76ccfee8081d0dd7d0dd71710883ee",
+      "checks": {
+        "branch_sum": true,
+        "direct_resolvent": true,
+        "finite_hodge_signature": true,
+        "finite_response": true,
+        "full_channel_support": true,
+        "hodge_orthogonality": true,
+        "no_outcome_leakage": true,
+        "safe_arrays_exclude_response_matrices": true,
+        "target_leakage": true
+      },
+      "generated_utc": "2026-08-01T17:05:25.242541+00:00",
+      "identity": {
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+        "charge": 7,
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+        "panel_kind": "isotropic",
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+        "realization": 0,
+        "sector": "central",
+        "sources": {
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\ No newline at end of file
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_v7_N14_inference.json b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_v7_N14_inference.json
new file mode 100644
index 000000000..fa41f1a4e
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_v7_N14_inference.json
@@ -0,0 +1,72 @@
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+}
\ No newline at end of file
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_v7_N14_prediction.json b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_v7_N14_prediction.json
new file mode 100644
index 000000000..916cff993
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_v7_N14_prediction.json
@@ -0,0 +1,733 @@
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\ No newline at end of file
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_v7_N14_prediction.npz b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_v7_N14_prediction.npz
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diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_v7_N14_prediction.sha256 b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_v7_N14_prediction.sha256
new file mode 100644
index 000000000..0ee04cf7c
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_v7_N14_prediction.sha256
@@ -0,0 +1 @@
+fc300dc7e4bdc1be157919e458ac868d3468533cce31108f23c9fba4f7e9f102  susy_hodge_v7_N14_prediction.json
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_v7_N14_unsealed.json b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_v7_N14_unsealed.json
new file mode 100644
index 000000000..5010436c2
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_v7_N14_unsealed.json
@@ -0,0 +1,973 @@
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\ No newline at end of file
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_v7_covariates_pilot.json b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_v7_covariates_pilot.json
new file mode 100644
index 000000000..ace3e87f8
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_v7_covariates_pilot.json
@@ -0,0 +1,16395 @@
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\ No newline at end of file
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_v7_covariates_pilot_N10_banked.json b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_v7_covariates_pilot_N10_banked.json
new file mode 100644
index 000000000..c8fa8e392
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_v7_covariates_pilot_N10_banked.json
@@ -0,0 +1,12299 @@
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\ No newline at end of file
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_v7_covariates_pilot_N12_banked.json b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_v7_covariates_pilot_N12_banked.json
new file mode 100644
index 000000000..1d35d6d6e
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_v7_covariates_pilot_N12_banked.json
@@ -0,0 +1,8203 @@
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\ No newline at end of file
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_v7_covariates_pilot_banked.json b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_v7_covariates_pilot_banked.json
new file mode 100644
index 000000000..ace3e87f8
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_v7_covariates_pilot_banked.json
@@ -0,0 +1,16395 @@
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+        "finite_response": true,
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+    }
+  ],
+  "version": "v7"
+}
\ No newline at end of file
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_v7_outcomes_pilot.json b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_v7_outcomes_pilot.json
new file mode 100644
index 000000000..99865b2ba
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_v7_outcomes_pilot.json
@@ -0,0 +1,106 @@
+{
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+  "checks": {
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+}
\ No newline at end of file
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_v7_outcomes_pilot.npz b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_v7_outcomes_pilot.npz
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diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_v7_outcomes_pilot_N10_banked.json b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_v7_outcomes_pilot_N10_banked.json
new file mode 100644
index 000000000..029efa358
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_v7_outcomes_pilot_N10_banked.json
@@ -0,0 +1,1091 @@
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+      ],
+      "observed_median": 0.36508816908827135,
+      "panel_kind": "sparse",
+      "physical_bootstrap_interval": [
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+      ],
+      "realizations": 48,
+      "sector": "central"
+    }
+  ],
+  "null_replicates": 2000,
+  "passed": true,
+  "physical_bootstrap_replicates": 10000,
+  "prediction_coverage": 0.975,
+  "safe_covariates_sha256": "6f021619e935297bc11fc251e07f8f1bcdf8bbee572d629669e173917ab53e87",
+  "sources": {
+    "analyze_susy_hodge_geometric_eth_v7.py": "ddaf04888905bdaca031c1e4a6119fa1cfbf4b126fd115ba775ae6c0a6a9338b",
+    "lgeth/hodge_wick.py": "f80fc96fa1408c0df2e15d4f804bac17feef9c59e9fbc511dd5052ef591e04c7",
+    "lgeth/wick_channels.py": "e1faedf5c98f660756e077445a88d05013bc6810f5b0f69aa8fc0dc6fe13469b",
+    "run_susy_hodge_geometric_eth_v7.py": "5e19899855b917a8b455510ce76ab47ac15396395668ad0538b7137caaec9cbe",
+    "run_susy_hodge_null_bank_v7.py": "ce16015e03e721852c73be952f24990b02e45cf787545881b96f42c1271dbc98"
+  },
+  "uncertainty_unit": "complete_disorder_realization",
+  "version": "v7"
+}
\ No newline at end of file
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_v7_outcomes_pilot_N10_banked.npz b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_v7_outcomes_pilot_N10_banked.npz
new file mode 100644
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diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_v7_outcomes_pilot_N12_banked.json b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_v7_outcomes_pilot_N12_banked.json
new file mode 100644
index 000000000..bebff9fb3
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_v7_outcomes_pilot_N12_banked.json
@@ -0,0 +1,771 @@
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+}
\ No newline at end of file
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_v7_outcomes_pilot_N12_banked.npz b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_v7_outcomes_pilot_N12_banked.npz
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diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_v7_outcomes_pilot_banked.json b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_v7_outcomes_pilot_banked.json
new file mode 100644
index 000000000..05d140ef2
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_v7_outcomes_pilot_banked.json
@@ -0,0 +1,1411 @@
+{
+  "arrays_sha256": "5d61f53a39d334225700d6ecf42e48acc5b668a72bfed4a214a943d25891539d",
+  "checks": {
+    "complete_requested_grid": true,
+    "finite_outputs": true,
+    "registered_bootstrap_replicates": true,
+    "registered_null_replicates": true,
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+}
\ No newline at end of file
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_v7_outcomes_pilot_banked.npz b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_v7_outcomes_pilot_banked.npz
new file mode 100644
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diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_v7_outcomes_pilot_combined.json b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_v7_outcomes_pilot_combined.json
new file mode 100644
index 000000000..2ba1fadfb
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_v7_outcomes_pilot_combined.json
@@ -0,0 +1,3244 @@
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+  "registered_sizes": [
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+  "source_pilot_artifacts": [
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+    {
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+  },
+  "uncertainty_unit": "complete_disorder_realization",
+  "version": "v7"
+}
\ No newline at end of file
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_v7_outcomes_pilot_combined.npz b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_v7_outcomes_pilot_combined.npz
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diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/run_susy_hodge_delivery_v7.sh b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/run_susy_hodge_delivery_v7.sh
new file mode 100755
index 000000000..a28662215
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/run_susy_hodge_delivery_v7.sh
@@ -0,0 +1,22 @@
+#!/usr/bin/env bash
+set -euo pipefail
+
+SCRIPT_DIR="$(cd "$(dirname "$0")" && pwd)"
+REPO_DIR="$(cd "$SCRIPT_DIR/../../.." && pwd)"
+MANUSCRIPT_DIR="$REPO_DIR/overleaf_sync/cohomological_geometric_eth"
+PYTHON_BIN="${PYTHON_BIN:-python3}"
+
+export PYTHONPATH="$SCRIPT_DIR${PYTHONPATH:+:$PYTHONPATH}"
+
+"$PYTHON_BIN" "$SCRIPT_DIR/merge_susy_hodge_pilot_v7.py"
+"$PYTHON_BIN" "$SCRIPT_DIR/make_susy_hodge_figure_v7.py"
+"$PYTHON_BIN" "$SCRIPT_DIR/make_susy_hodge_manuscript_assets_v7.py"
+(
+  cd "$MANUSCRIPT_DIR"
+  latexmk -pdf -interaction=nonstopmode -halt-on-error main.tex
+  latexmk -pdf -interaction=nonstopmode -halt-on-error supplement.tex
+)
+cp "$MANUSCRIPT_DIR/main.pdf" "$SCRIPT_DIR/output/response_complex_memory_v7.pdf"
+cp "$MANUSCRIPT_DIR/supplement.pdf" "$SCRIPT_DIR/output/response_complex_memory_supplement_v7.pdf"
+"$PYTHON_BIN" "$SCRIPT_DIR/verify_susy_hodge_delivery_v7.py"
+"$PYTHON_BIN" "$SCRIPT_DIR/verify_susy_hodge_manuscript_v7.py"
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/run_susy_hodge_geometric_eth_v7.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/run_susy_hodge_geometric_eth_v7.py
new file mode 100644
index 000000000..cf46a371f
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/run_susy_hodge_geometric_eth_v7.py
@@ -0,0 +1,901 @@
+#!/usr/bin/env python3
+"""Checkpointed and sealed N=2 SYK Hodge-response runner v7."""
+
+from __future__ import annotations
+
+import argparse
+import hashlib
+import json
+from datetime import datetime, timezone
+from pathlib import Path
+from typing import Any
+
+import numpy as np
+
+from lgeth.hodge_response import (
+    coupling_panels,
+    hodge_response,
+    hodge_signature,
+    scalable_covariance_matched_wick,
+)
+from lgeth.hodge_response import HodgeSignature
+from lgeth.hodge_wick import hodge_gaussian_r4_reference
+from lgeth.susy_cohomology import (
+    BPSFrame,
+    charge_basis,
+    charge_hamiltonian,
+    cubic_supercharge,
+    expected_generic_bps_rank,
+    normalized_complex_couplings,
+    solve_bps_frame,
+)
+from lgeth.wick_channels import gaussian_r4_reference
+
+
+VERSION = "v7"
+SCRIPT_ROOT = Path(__file__).resolve().parent
+OUTPUT_ROOT = SCRIPT_ROOT / "output"
+CHECKPOINT_ROOT = OUTPUT_ROOT / "susy_hodge_v7_checkpoints"
+REGISTERED_SIZES = (8, 10, 12, 14)
+REGISTERED_SECTORS = ("central", "adjacent")
+REGISTERED_PANEL_KINDS = ("sparse", "isotropic")
+PANEL_SIZE = 8
+REALIZATION_COUNTS = {8: 64, 10: 48, 12: 32, 14: 24}
+NULL_REPLICATES = 2_000
+NULL_DRAWS_PER_REALIZATION = 128
+BASE_SEED = 2026080111
+FORBIDDEN_SAFE_TOKENS = ("r4", "four_point", "connected")
+PILOT_SAFE_JSON = OUTPUT_ROOT / "susy_hodge_v7_covariates_pilot.json"
+PILOT_JSON = OUTPUT_ROOT / "susy_hodge_v7_outcomes_pilot.json"
+PILOT_NPZ = OUTPUT_ROOT / "susy_hodge_v7_outcomes_pilot.npz"
+
+
+def _atomic_json(path: Path, payload: dict[str, Any]) -> None:
+    path = Path(path)
+    path.parent.mkdir(parents=True, exist_ok=True)
+    temporary = path.with_suffix(path.suffix + ".tmp")
+    temporary.write_text(
+        json.dumps(payload, indent=2, sort_keys=True),
+        encoding="utf-8",
+    )
+    temporary.replace(path)
+
+
+def _atomic_npz(path: Path, **arrays: np.ndarray) -> None:
+    path = Path(path)
+    path.parent.mkdir(parents=True, exist_ok=True)
+    temporary = path.with_suffix(path.suffix + ".tmp")
+    with temporary.open("wb") as handle:
+        np.savez_compressed(handle, **arrays)
+    temporary.replace(path)
+
+
+def _atomic_text(path: Path, value: str) -> None:
+    path = Path(path)
+    path.parent.mkdir(parents=True, exist_ok=True)
+    temporary = path.with_suffix(path.suffix + ".tmp")
+    temporary.write_text(value, encoding="utf-8")
+    temporary.replace(path)
+
+
+def sha256(path: Path) -> str:
+    digest = hashlib.sha256()
+    with Path(path).open("rb") as handle:
+        for block in iter(lambda: handle.read(1024 * 1024), b""):
+            digest.update(block)
+    return digest.hexdigest()
+
+
+def _json_hash(payload: dict[str, Any]) -> str:
+    return hashlib.sha256(
+        json.dumps(payload, sort_keys=True, separators=(",", ":")).encode()
+    ).hexdigest()
+
+
+def _derived_seed(*parts: object) -> int:
+    label = "|".join(str(item) for item in (BASE_SEED, VERSION, *parts))
+    return int.from_bytes(hashlib.sha256(label.encode()).digest()[:8], "big")
+
+
+def _source_hashes() -> dict[str, str]:
+    paths = (
+        Path(__file__).resolve(),
+        SCRIPT_ROOT / "lgeth" / "susy_cohomology.py",
+        SCRIPT_ROOT / "lgeth" / "hodge_response.py",
+        SCRIPT_ROOT / "lgeth" / "hodge_wick.py",
+        SCRIPT_ROOT / "lgeth" / "wick_channels.py",
+    )
+    return {str(path.relative_to(SCRIPT_ROOT)): sha256(path) for path in paths}
+
+
+def _sector_charge(N: int, sector: str) -> int:
+    modes = int(N)
+    label = str(sector)
+    if modes % 2:
+        raise ValueError("registered SUSY sequence requires even N")
+    if label == "central":
+        return modes // 2
+    if label == "adjacent":
+        return modes // 2 - 1
+    raise ValueError(f"sector must be one of {REGISTERED_SECTORS}")
+
+
+def _validate_case(
+    N: int,
+    sector: str,
+    realization: int,
+    *,
+    reduced: bool,
+) -> tuple[int, str, int, int]:
+    modes = int(N)
+    label = str(sector)
+    index = int(realization)
+    charge = _sector_charge(modes, label)
+    if not reduced:
+        if modes not in REGISTERED_SIZES:
+            raise ValueError(f"N must be one of {REGISTERED_SIZES}")
+        if not 0 <= index < REALIZATION_COUNTS[modes]:
+            raise ValueError("realization is outside the registered range")
+    elif modes < 6 or index < 0:
+        raise ValueError("invalid reduced realization")
+    return modes, label, index, charge
+
+
+def kernel_paths(
+    root: Path,
+    N: int,
+    sector: str,
+    realization: int,
+) -> tuple[Path, Path]:
+    stem = (
+        Path(root)
+        / "kernels"
+        / f"N{int(N)}_{sector}_seed{int(realization):03d}_{VERSION}"
+    )
+    return stem.with_suffix(".json"), stem.with_suffix(".npz")
+
+
+def panel_paths(
+    root: Path,
+    N: int,
+    sector: str,
+    realization: int,
+    panel_kind: str,
+) -> tuple[Path, Path, Path]:
+    stem = (
+        Path(root)
+        / "panels"
+        / (
+            f"N{int(N)}_{sector}_seed{int(realization):03d}_"
+            f"{panel_kind}_{VERSION}"
+        )
+    )
+    return (
+        stem.with_suffix(".json"),
+        stem.with_suffix(".npz"),
+        Path(str(stem) + ".outcome.json"),
+    )
+
+
+def prepare_realization(
+    N: int,
+    sector: str,
+    realization: int,
+    *,
+    root: Path = CHECKPOINT_ROOT,
+    reduced: bool = False,
+    force: bool = False,
+) -> dict[str, Any]:
+    """Solve and checkpoint one coupling realization without any four-point data."""
+
+    modes, label, index, charge = _validate_case(
+        N,
+        sector,
+        realization,
+        reduced=reduced,
+    )
+    coupling_seed = _derived_seed(modes, label, index, "couplings")
+    identity = {
+        "version": VERSION,
+        "N": modes,
+        "sector": label,
+        "charge": charge,
+        "realization": index,
+        "coupling_seed": coupling_seed,
+        "expected_rank": expected_generic_bps_rank(modes, charge),
+        "reduced": bool(reduced),
+        "sources": _source_hashes(),
+    }
+    identity_hash = _json_hash(identity)
+    metadata_path, arrays_path = kernel_paths(root, modes, label, index)
+    if not force and metadata_path.is_file() and arrays_path.is_file():
+        metadata = json.loads(metadata_path.read_text(encoding="utf-8"))
+        if (
+            metadata.get("identity") == identity
+            and metadata.get("identity_hash") == identity_hash
+            and metadata.get("arrays_sha256") == sha256(arrays_path)
+            and all(metadata.get("checks", {}).values())
+        ):
+            return metadata
+        raise ValueError("SUSY realization checkpoint identity mismatch")
+    couplings = normalized_complex_couplings(modes, coupling_seed)
+    frame = solve_bps_frame(modes, charge, couplings, dense_cutoff=4096)
+    _atomic_npz(
+        arrays_path,
+        couplings=couplings,
+        projector_frame=frame.projector_frame,
+        complement_frame=frame.complement_frame,
+        positive_energies=frame.positive_energies,
+    )
+    checks = {
+        "expected_bps_rank": frame.projector_frame.shape[1]
+        == identity["expected_rank"],
+        "open_external_gap": frame.gap > 1e-10,
+        "kernel_residual": frame.kernel_residual < 1e-8,
+        "orthonormal_frame": frame.orthogonality_error < 1e-10,
+        "unit_coupling_norm": abs(float(np.linalg.norm(couplings)) - 1.0)
+        < 1e-13,
+    }
+    metadata = {
+        "identity": identity,
+        "identity_hash": identity_hash,
+        "generated_utc": datetime.now(timezone.utc).isoformat(),
+        "hilbert_dimension": len(frame.basis),
+        "bps_rank": frame.projector_frame.shape[1],
+        "complement_rank": frame.complement_frame.shape[1],
+        "gap": frame.gap,
+        "kernel_residual": frame.kernel_residual,
+        "orthogonality_error": frame.orthogonality_error,
+        "arrays_sha256": sha256(arrays_path),
+        "checks": checks,
+        "passed": all(checks.values()),
+    }
+    if not metadata["passed"]:
+        raise RuntimeError(f"SUSY realization audit failed: {checks}")
+    _atomic_json(metadata_path, metadata)
+    return metadata
+
+
+def _load_frame(
+    root: Path,
+    N: int,
+    sector: str,
+    realization: int,
+) -> tuple[dict[str, Any], np.ndarray, BPSFrame]:
+    metadata_path, arrays_path = kernel_paths(root, N, sector, realization)
+    if not metadata_path.is_file() or not arrays_path.is_file():
+        raise FileNotFoundError("missing SUSY realization checkpoint")
+    metadata = json.loads(metadata_path.read_text(encoding="utf-8"))
+    if metadata.get("arrays_sha256") != sha256(arrays_path):
+        raise ValueError("SUSY realization array hash mismatch")
+    with np.load(arrays_path) as arrays:
+        couplings = np.asarray(arrays["couplings"], dtype=complex)
+        projector = np.asarray(arrays["projector_frame"], dtype=complex)
+        complement = np.asarray(arrays["complement_frame"], dtype=complex)
+        energies = np.asarray(arrays["positive_energies"], dtype=float)
+    charge = int(metadata["identity"]["charge"])
+    q_in = cubic_supercharge(N, charge - 3, couplings)
+    q_out = cubic_supercharge(N, charge, couplings)
+    hamiltonian = charge_hamiltonian(N, charge, couplings)
+    frame = BPSFrame(
+        N=int(N),
+        charge=charge,
+        basis=charge_basis(N, charge),
+        projector_frame=projector,
+        complement_frame=complement,
+        positive_energies=energies,
+        gap=float(energies[0]),
+        kernel_residual=float(metadata["kernel_residual"]),
+        orthogonality_error=float(metadata["orthogonality_error"]),
+        expected_rank=int(metadata["identity"]["expected_rank"]),
+        q_in=q_in,
+        q_out=q_out,
+        hamiltonian=hamiltonian,
+    )
+    return metadata, couplings, frame
+
+
+def _signature_arrays(signature: Any) -> dict[str, np.ndarray]:
+    return {
+        "minus_channel_covariance": signature.minus_channel_covariance,
+        "plus_channel_covariance": signature.plus_channel_covariance,
+        "minus_target_eigenvalues": signature.minus_target_eigenvalues,
+        "plus_target_eigenvalues": signature.plus_target_eigenvalues,
+        "minus_external_eigenvalues": signature.minus_external_eigenvalues,
+        "plus_external_eigenvalues": signature.plus_external_eigenvalues,
+    }
+
+
+def _signature_from_safe(
+    safe: dict[str, Any],
+    arrays: Any,
+) -> HodgeSignature:
+    scalars = safe["signature"]
+    return HodgeSignature(
+        channel_count=int(scalars["channel_count"]),
+        target_rank=int(scalars["target_rank"]),
+        minus_weight=float(scalars["minus_weight"]),
+        plus_weight=float(scalars["plus_weight"]),
+        hodge_balance=float(scalars["hodge_balance"]),
+        minus_channel_covariance=np.asarray(
+            arrays["minus_channel_covariance"], dtype=complex
+        ),
+        plus_channel_covariance=np.asarray(
+            arrays["plus_channel_covariance"], dtype=complex
+        ),
+        minus_target_eigenvalues=np.asarray(
+            arrays["minus_target_eigenvalues"], dtype=float
+        ),
+        plus_target_eigenvalues=np.asarray(
+            arrays["plus_target_eigenvalues"], dtype=float
+        ),
+        minus_external_eigenvalues=np.asarray(
+            arrays["minus_external_eigenvalues"], dtype=float
+        ),
+        plus_external_eigenvalues=np.asarray(
+            arrays["plus_external_eigenvalues"], dtype=float
+        ),
+        minus_target_effective_rank=float(
+            scalars["minus_target_effective_rank"]
+        ),
+        plus_target_effective_rank=float(scalars["plus_target_effective_rank"]),
+        minus_external_effective_rank=float(
+            scalars["minus_external_effective_rank"]
+        ),
+        plus_external_effective_rank=float(
+            scalars["plus_external_effective_rank"]
+        ),
+        minus_target_entropy=float(scalars["minus_target_entropy"]),
+        plus_target_entropy=float(scalars["plus_target_entropy"]),
+        minus_external_entropy=float(scalars["minus_external_entropy"]),
+        plus_external_entropy=float(scalars["plus_external_entropy"]),
+        orthogonality_relative_error=float(
+            scalars["orthogonality_relative_error"]
+        ),
+    )
+
+
+def _safe_serialization_check(payload: dict[str, Any]) -> bool:
+    serialized = json.dumps(payload, sort_keys=True).lower()
+    return not any(token in serialized for token in FORBIDDEN_SAFE_TOKENS)
+
+
+def _positive_covariance_spectrum(values: np.ndarray) -> np.ndarray:
+    spectrum = np.maximum(np.asarray(values, dtype=float), 0.0)
+    largest = float(np.max(spectrum))
+    if largest <= 0.0:
+        raise ValueError("covariance spectrum has no positive support")
+    return spectrum[spectrum > 1e-12 * largest]
+
+
+def _banked_complete_medians(
+    banks: np.ndarray,
+    replicates: int,
+    seed: int,
+) -> np.ndarray:
+    """Draw one bank entry per realization and aggregate by the median."""
+
+    values = np.asarray(banks, dtype=float)
+    count = int(replicates)
+    if values.ndim != 2 or min(values.shape) < 1 or count < 1:
+        raise ValueError("null banks and replicate count are invalid")
+    rng = np.random.default_rng(int(seed))
+    selections = rng.integers(
+        0,
+        values.shape[1],
+        size=(count, values.shape[0]),
+    )
+    realization_indices = np.arange(values.shape[0])[None, :]
+    draws = values[realization_indices, selections]
+    return np.median(draws, axis=1)
+
+
+def run_panel(
+    N: int,
+    sector: str,
+    realization: int,
+    panel_kind: str,
+    *,
+    root: Path = CHECKPOINT_ROOT,
+    reduced: bool = False,
+    force: bool = False,
+) -> dict[str, Any]:
+    """Evaluate one panel while isolating the physical statistic in a sidecar."""
+
+    modes, label, index, _ = _validate_case(
+        N,
+        sector,
+        realization,
+        reduced=reduced,
+    )
+    kind = str(panel_kind)
+    if kind not in REGISTERED_PANEL_KINDS:
+        raise ValueError(f"panel kind must be one of {REGISTERED_PANEL_KINDS}")
+    safe_path, arrays_path, outcome_path = panel_paths(
+        root,
+        modes,
+        label,
+        index,
+        kind,
+    )
+    if not force and safe_path.is_file() and arrays_path.is_file() and outcome_path.is_file():
+        safe = json.loads(safe_path.read_text(encoding="utf-8"))
+        outcome = json.loads(outcome_path.read_text(encoding="utf-8"))
+        if (
+            safe.get("arrays_sha256") == sha256(arrays_path)
+            and outcome.get("safe_identity_hash") == safe.get("identity_hash")
+            and all(safe.get("checks", {}).values())
+        ):
+            return {"safe": safe, "outcome": outcome}
+        raise ValueError("SUSY panel checkpoint identity mismatch")
+    kernel, couplings, frame = _load_frame(root, modes, label, index)
+    panel_seed = _derived_seed(modes, label, index, "panels")
+    tangents = coupling_panels(couplings, PANEL_SIZE, panel_seed)[kind]
+    response = hodge_response(frame, couplings, tangents)
+    signature = hodge_signature(response)
+    statistic = scalable_covariance_matched_wick(response.total)
+    safe_identity = {
+        "version": VERSION,
+        "N": modes,
+        "sector": label,
+        "charge": frame.charge,
+        "realization": index,
+        "panel_kind": kind,
+        "panel_seed": panel_seed,
+        "kernel_identity_hash": kernel["identity_hash"],
+        "sources": _source_hashes(),
+    }
+    safe_identity_hash = _json_hash(safe_identity)
+    arrays = {
+        "tangents": tangents,
+        **_signature_arrays(signature),
+        "total_target_eigenvalues": statistic.left_eigenvalues,
+        "total_external_eigenvalues": statistic.right_eigenvalues,
+    }
+    _atomic_npz(arrays_path, **arrays)
+    signature_scalars = {
+        "channel_count": signature.channel_count,
+        "target_rank": signature.target_rank,
+        "minus_weight": signature.minus_weight,
+        "plus_weight": signature.plus_weight,
+        "hodge_balance": signature.hodge_balance,
+        "minus_target_effective_rank": signature.minus_target_effective_rank,
+        "plus_target_effective_rank": signature.plus_target_effective_rank,
+        "minus_external_effective_rank": signature.minus_external_effective_rank,
+        "plus_external_effective_rank": signature.plus_external_effective_rank,
+        "minus_target_entropy": signature.minus_target_entropy,
+        "plus_target_entropy": signature.plus_target_entropy,
+        "minus_external_entropy": signature.minus_external_entropy,
+        "plus_external_entropy": signature.plus_external_entropy,
+        "orthogonality_relative_error": signature.orthogonality_relative_error,
+    }
+    checks = {
+        **response.checks,
+        "full_channel_support": len(statistic.channel_covariance_eigenvalues)
+        == PANEL_SIZE,
+        "safe_arrays_exclude_response_matrices": set(arrays)
+        == {
+            "tangents",
+            "minus_channel_covariance",
+            "plus_channel_covariance",
+            "minus_target_eigenvalues",
+            "plus_target_eigenvalues",
+            "minus_external_eigenvalues",
+            "plus_external_eigenvalues",
+            "total_target_eigenvalues",
+            "total_external_eigenvalues",
+        },
+        "finite_hodge_signature": all(
+            np.isfinite(value) for value in signature_scalars.values()
+        ),
+    }
+    safe = {
+        "identity": safe_identity,
+        "identity_hash": safe_identity_hash,
+        "generated_utc": datetime.now(timezone.utc).isoformat(),
+        "kernel": {
+            "bps_rank": kernel["bps_rank"],
+            "complement_rank": kernel["complement_rank"],
+            "gap": kernel["gap"],
+            "kernel_residual": kernel["kernel_residual"],
+        },
+        "signature": signature_scalars,
+        "spectrum_lengths": {
+            key: int(np.asarray(value).size)
+            for key, value in _signature_arrays(signature).items()
+        },
+        "arrays_sha256": sha256(arrays_path),
+        "checks": checks,
+        "passed": all(checks.values()),
+    }
+    safe["checks"]["no_outcome_leakage"] = _safe_serialization_check(safe)
+    safe["passed"] = all(safe["checks"].values())
+    if not safe["passed"]:
+        raise RuntimeError(f"safe SUSY panel audit failed: {safe['checks']}")
+    _atomic_json(safe_path, safe)
+    outcome = {
+        "version": VERSION,
+        "N": modes,
+        "sector": label,
+        "realization": index,
+        "panel_kind": kind,
+        "safe_identity_hash": safe_identity_hash,
+        "safe_arrays_sha256": safe["arrays_sha256"],
+        "R4": float(statistic.R4),
+    }
+    if not np.isfinite(outcome["R4"]):
+        raise RuntimeError("physical response statistic is not finite")
+    _atomic_json(outcome_path, outcome)
+    return {"safe": safe, "outcome": outcome}
+
+
+def write_safe_covariates(
+    cases: list[tuple[int, str, int, str]],
+    *,
+    root: Path = CHECKPOINT_ROOT,
+    output_json: Path,
+) -> dict[str, Any]:
+    """Aggregate safe panel records without opening outcome sidecars."""
+
+    records: list[dict[str, Any]] = []
+    for case in cases:
+        safe_path, arrays_path, _ = panel_paths(root, *case)
+        if not safe_path.is_file() or not arrays_path.is_file():
+            raise FileNotFoundError("missing safe SUSY panel checkpoint")
+        safe = json.loads(safe_path.read_text(encoding="utf-8"))
+        if safe.get("arrays_sha256") != sha256(arrays_path):
+            raise ValueError("safe SUSY panel array hash mismatch")
+        if not all(safe.get("checks", {}).values()):
+            raise ValueError("safe SUSY panel contains a failed check")
+        records.append(safe)
+    payload = {
+        "version": VERSION,
+        "records": records,
+        "checks": {
+            "complete_requested_grid": len(records) == len(cases),
+            "all_safe_checks": all(
+                all(record["checks"].values()) for record in records
+            ),
+        },
+    }
+    payload["checks"]["no_outcome_leakage"] = _safe_serialization_check(payload)
+    payload["passed"] = all(payload["checks"].values())
+    if not payload["passed"]:
+        raise RuntimeError(f"safe covariate audit failed: {payload['checks']}")
+    _atomic_json(output_json, payload)
+    return payload
+
+
+def aggregate_pilot(
+    cases: list[tuple[int, str, int, str]],
+    *,
+    root: Path = CHECKPOINT_ROOT,
+    null_samples: int = NULL_REPLICATES,
+    null_draws_per_realization: int = NULL_DRAWS_PER_REALIZATION,
+    seed: int = BASE_SEED,
+    safe_output_json: Path = PILOT_SAFE_JSON,
+    output_json: Path = PILOT_JSON,
+    output_npz: Path = PILOT_NPZ,
+) -> dict[str, Any]:
+    """Open sequential pilot outcomes after a complete safe-covariate audit."""
+
+    if (
+        int(null_samples) < 1
+        or int(null_draws_per_realization) < 1
+        or not cases
+    ):
+        raise ValueError("pilot aggregation requires cases and null samples")
+    write_safe_covariates(cases, root=root, output_json=safe_output_json)
+    grouped: dict[tuple[int, str, str], list[tuple[int, dict, Any, float]]] = {}
+    for case in sorted(cases):
+        safe_path, arrays_path, outcome_path = panel_paths(root, *case)
+        safe = json.loads(safe_path.read_text(encoding="utf-8"))
+        outcome = json.loads(outcome_path.read_text(encoding="utf-8"))
+        if (
+            outcome.get("safe_identity_hash") != safe.get("identity_hash")
+            or outcome.get("safe_arrays_sha256") != safe.get("arrays_sha256")
+            or safe.get("arrays_sha256") != sha256(arrays_path)
+        ):
+            raise ValueError("pilot outcome identity mismatch")
+        with np.load(arrays_path) as loaded:
+            copied = {key: np.asarray(loaded[key]) for key in loaded.files}
+        group = (int(case[0]), str(case[1]), str(case[3]))
+        grouped.setdefault(group, []).append(
+            (int(case[2]), safe, copied, float(outcome["R4"]))
+        )
+    output_arrays: dict[str, np.ndarray] = {}
+    summaries: list[dict[str, Any]] = []
+    for (N, sector, panel_kind), records in sorted(grouped.items()):
+        records.sort(key=lambda item: item[0])
+        physical = np.asarray([item[3] for item in records], dtype=float)
+        signatures = [
+            _signature_from_safe(item[1], item[2]) for item in records
+        ]
+        collapsed_draws = []
+        hodge_draws = []
+        for realization, _, arrays, _ in records:
+            collapsed_draws.append(
+                gaussian_r4_reference(
+                    _positive_covariance_spectrum(
+                        arrays["total_target_eigenvalues"]
+                    ),
+                    _positive_covariance_spectrum(
+                        arrays["total_external_eigenvalues"]
+                    ),
+                    PANEL_SIZE,
+                    int(null_draws_per_realization),
+                    _derived_seed(seed, N, sector, panel_kind, realization, "collapsed"),
+                )
+            )
+        for realization, signature in zip(
+            [item[0] for item in records],
+            signatures,
+            strict=True,
+        ):
+            hodge_draws.append(
+                hodge_gaussian_r4_reference(
+                    signature,
+                    PANEL_SIZE,
+                    int(null_draws_per_realization),
+                    _derived_seed(
+                        seed,
+                        N,
+                        sector,
+                        panel_kind,
+                        realization,
+                        "hodge_bank",
+                    ),
+                )
+            )
+        collapsed = _banked_complete_medians(
+            np.asarray(collapsed_draws),
+            int(null_samples),
+            _derived_seed(seed, N, sector, panel_kind, "collapsed_aggregate"),
+        )
+        hodge = _banked_complete_medians(
+            np.asarray(hodge_draws),
+            int(null_samples),
+            _derived_seed(seed, N, sector, panel_kind, "hodge_aggregate"),
+        )
+        key = f"N{N}_{sector}_{panel_kind}"
+        output_arrays[f"{key}_physical"] = physical
+        output_arrays[f"{key}_collapsed_null"] = collapsed
+        output_arrays[f"{key}_hodge_null"] = hodge
+        summaries.append(
+            {
+                "N": N,
+                "sector": sector,
+                "panel_kind": panel_kind,
+                "realizations": len(records),
+                "physical_quantiles": np.quantile(
+                    physical, [0.025, 0.5, 0.975]
+                ).tolist(),
+                "collapsed_null_quantiles": np.quantile(
+                    collapsed, [0.025, 0.5, 0.975]
+                ).tolist(),
+                "hodge_null_quantiles": np.quantile(
+                    hodge, [0.025, 0.5, 0.975]
+                ).tolist(),
+                "median_hodge_balance": float(
+                    np.median([item.hodge_balance for item in signatures])
+                ),
+            }
+        )
+    _atomic_npz(output_npz, **output_arrays)
+    checks = {
+        "complete_group_partition": sum(
+            item["realizations"] for item in summaries
+        )
+        == len(cases),
+        "finite_physical_and_nulls": all(
+            np.all(np.isfinite(values)) for values in output_arrays.values()
+        ),
+        "null_sample_counts": all(
+            values.shape == (int(null_samples),)
+            for key, values in output_arrays.items()
+            if key.endswith("_null")
+        ),
+        "safe_aggregate_preexists": Path(safe_output_json).is_file(),
+    }
+    payload = {
+        "version": VERSION,
+        "generated_utc": datetime.now(timezone.utc).isoformat(),
+        "uncertainty_unit": "complete_disorder_realization",
+        "null_samples": int(null_samples),
+        "null_draws_per_realization": int(null_draws_per_realization),
+        "cases": summaries,
+        "safe_covariates_sha256": sha256(safe_output_json),
+        "arrays_sha256": sha256(output_npz),
+        "checks": checks,
+        "passed": all(checks.values()),
+    }
+    if not payload["passed"]:
+        raise RuntimeError(f"SUSY pilot aggregation failed: {checks}")
+    _atomic_json(output_json, payload)
+    return payload
+
+
+def registered_case_grid(
+    sizes: tuple[int, ...] | list[int],
+) -> list[tuple[int, str, int, str]]:
+    """Return the frozen complete pilot grid for the requested sizes."""
+
+    cases: list[tuple[int, str, int, str]] = []
+    for N in tuple(int(value) for value in sizes):
+        if N not in REGISTERED_SIZES:
+            raise ValueError(f"N must be one of {REGISTERED_SIZES}")
+        for sector in REGISTERED_SECTORS:
+            for realization in range(REALIZATION_COUNTS[N]):
+                for panel_kind in REGISTERED_PANEL_KINDS:
+                    cases.append((N, sector, realization, panel_kind))
+    return cases
+
+
+def run_registered_pilot(
+    sizes: tuple[int, ...] | list[int],
+    *,
+    root: Path = CHECKPOINT_ROOT,
+    null_samples: int = NULL_REPLICATES,
+    force: bool = False,
+) -> dict[str, Any]:
+    """Run the complete registered grid and aggregate its sequential outcomes."""
+
+    requested = tuple(int(value) for value in sizes)
+    cases = registered_case_grid(requested)
+    for N in requested:
+        for sector in REGISTERED_SECTORS:
+            for realization in range(REALIZATION_COUNTS[N]):
+                prepare_realization(
+                    N,
+                    sector,
+                    realization,
+                    root=root,
+                    force=force,
+                )
+                for panel_kind in REGISTERED_PANEL_KINDS:
+                    run_panel(
+                        N,
+                        sector,
+                        realization,
+                        panel_kind,
+                        root=root,
+                        force=force,
+                    )
+    return aggregate_pilot(
+        cases,
+        root=root,
+        null_samples=int(null_samples),
+        seed=BASE_SEED,
+        safe_output_json=PILOT_SAFE_JSON,
+        output_json=PILOT_JSON,
+        output_npz=PILOT_NPZ,
+    )
+
+
+def _parser() -> argparse.ArgumentParser:
+    parser = argparse.ArgumentParser(description=__doc__)
+    subparsers = parser.add_subparsers(dest="command", required=True)
+    realization = subparsers.add_parser("realization")
+    realization.add_argument("--N", type=int, required=True)
+    realization.add_argument("--sector", choices=REGISTERED_SECTORS, required=True)
+    realization.add_argument("--realization", type=int, required=True)
+    realization.add_argument("--force", action="store_true")
+    panel = subparsers.add_parser("panel")
+    panel.add_argument("--N", type=int, required=True)
+    panel.add_argument("--sector", choices=REGISTERED_SECTORS, required=True)
+    panel.add_argument("--realization", type=int, required=True)
+    panel.add_argument("--panel-kind", choices=REGISTERED_PANEL_KINDS, required=True)
+    panel.add_argument("--force", action="store_true")
+    pilot = subparsers.add_parser("pilot")
+    pilot.add_argument("--sizes", type=int, nargs="+", required=True)
+    pilot.add_argument("--null-samples", type=int, default=NULL_REPLICATES)
+    pilot.add_argument("--force", action="store_true")
+    return parser
+
+
+def main() -> None:
+    args = _parser().parse_args()
+    if args.command == "realization":
+        payload = prepare_realization(
+            args.N,
+            args.sector,
+            args.realization,
+            force=args.force,
+        )
+    elif args.command == "panel":
+        payload = run_panel(
+            args.N,
+            args.sector,
+            args.realization,
+            args.panel_kind,
+            force=args.force,
+        )["safe"]
+    else:
+        payload = run_registered_pilot(
+            args.sizes,
+            null_samples=args.null_samples,
+            force=args.force,
+        )
+    print(json.dumps(payload, indent=2, sort_keys=True))
+
+
+if __name__ == "__main__":
+    main()
+
+
+def seal_file_hash(source: Path, seal: Path) -> str:
+    source = Path(source)
+    if not source.is_file():
+        raise FileNotFoundError("missing prediction file to seal")
+    digest = sha256(source)
+    _atomic_text(Path(seal), f"{digest}  {source.name}\n")
+    return digest
+
+
+def _validate_file_hash(source: Path, seal: Path) -> str:
+    source = Path(source)
+    seal = Path(seal)
+    if not seal.is_file():
+        raise FileNotFoundError("missing prediction hash seal")
+    if not source.is_file():
+        raise FileNotFoundError("missing sealed prediction file")
+    fields = seal.read_text(encoding="utf-8").strip().split()
+    if len(fields) != 2 or fields[1] != source.name:
+        raise ValueError("prediction hash seal format mismatch")
+    if fields[0] != sha256(source):
+        raise ValueError("prediction hash seal mismatch")
+    return fields[0]
+
+
+def unseal_outcomes(
+    cases: list[tuple[int, str, int, str]],
+    *,
+    root: Path = CHECKPOINT_ROOT,
+    prediction_json: Path,
+    prediction_seal: Path,
+    output_json: Path,
+    output_npz: Path,
+) -> dict[str, Any]:
+    """Open physical sidecars only after validating the prediction seal."""
+
+    prediction_hash = _validate_file_hash(prediction_json, prediction_seal)
+    records: list[dict[str, Any]] = []
+    values: list[float] = []
+    for case in cases:
+        safe_path, arrays_path, outcome_path = panel_paths(root, *case)
+        if not safe_path.is_file() or not arrays_path.is_file() or not outcome_path.is_file():
+            raise FileNotFoundError("missing sealed SUSY panel files")
+        safe = json.loads(safe_path.read_text(encoding="utf-8"))
+        outcome = json.loads(outcome_path.read_text(encoding="utf-8"))
+        if (
+            outcome.get("safe_identity_hash") != safe.get("identity_hash")
+            or outcome.get("safe_arrays_sha256") != safe.get("arrays_sha256")
+            or safe.get("arrays_sha256") != sha256(arrays_path)
+        ):
+            raise ValueError("outcome identity mismatch")
+        if tuple(
+            outcome[key]
+            for key in ("N", "sector", "realization", "panel_kind")
+        ) != tuple(case):
+            raise ValueError("outcome case identity mismatch")
+        value = float(outcome["R4"])
+        if not np.isfinite(value):
+            raise ValueError("unsealed outcome is not finite")
+        values.append(value)
+        records.append(outcome)
+    physical = np.asarray(values, dtype=float)
+    _atomic_npz(output_npz, physical_R4=physical)
+    payload = {
+        "version": VERSION,
+        "prediction_sha256": prediction_hash,
+        "unsealed_utc": datetime.now(timezone.utc).isoformat(),
+        "records": records,
+        "arrays_sha256": sha256(output_npz),
+        "checks": {
+            "complete_requested_grid": len(records) == len(cases),
+            "finite_outcomes": bool(np.all(np.isfinite(physical))),
+        },
+    }
+    payload["passed"] = all(payload["checks"].values())
+    _atomic_json(output_json, payload)
+    return payload
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/run_susy_hodge_null_bank_v7.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/run_susy_hodge_null_bank_v7.py
new file mode 100644
index 000000000..7fee669ac
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/run_susy_hodge_null_bank_v7.py
@@ -0,0 +1,204 @@
+#!/usr/bin/env python3
+"""Generate safe per-realization Gaussian null banks without opening outcomes."""
+
+from __future__ import annotations
+
+import argparse
+import hashlib
+import json
+from datetime import datetime, timezone
+from pathlib import Path
+from typing import Any
+
+import numpy as np
+
+from lgeth.hodge_wick import hodge_gaussian_r4_reference
+from lgeth.wick_channels import gaussian_r4_reference
+from run_susy_hodge_geometric_eth_v7 import (
+    CHECKPOINT_ROOT,
+    NULL_DRAWS_PER_REALIZATION,
+    PANEL_SIZE,
+    REGISTERED_PANEL_KINDS,
+    REGISTERED_SECTORS,
+    SCRIPT_ROOT,
+    VERSION,
+    _atomic_json,
+    _atomic_npz,
+    _derived_seed,
+    _positive_covariance_spectrum,
+    _signature_from_safe,
+    panel_paths,
+    sha256,
+)
+
+
+OUTPUT_ROOT = SCRIPT_ROOT / "output" / "susy_hodge_v7_null_banks"
+FORBIDDEN_SAFE_TOKENS = ("r4", "four_point", "connected")
+
+
+def _array_hash(values: np.ndarray) -> str:
+    array = np.ascontiguousarray(values)
+    return hashlib.sha256(array.view(np.uint8)).hexdigest()
+
+
+def _source_hashes() -> dict[str, str]:
+    paths = (
+        Path(__file__).resolve(),
+        SCRIPT_ROOT / "run_susy_hodge_geometric_eth_v7.py",
+        SCRIPT_ROOT / "lgeth" / "hodge_response.py",
+        SCRIPT_ROOT / "lgeth" / "hodge_wick.py",
+        SCRIPT_ROOT / "lgeth" / "wick_channels.py",
+    )
+    return {str(path.relative_to(SCRIPT_ROOT)): sha256(path) for path in paths}
+
+
+def null_bank_paths(
+    output_root: Path,
+    N: int,
+    sector: str,
+    realization: int,
+    panel_kind: str,
+) -> tuple[Path, Path]:
+    stem = Path(output_root) / (
+        f"N{int(N)}_{sector}_seed{int(realization):03d}_{panel_kind}_{VERSION}_null"
+    )
+    return stem.with_suffix(".json"), stem.with_suffix(".npz")
+
+
+def write_null_bank(
+    N: int,
+    sector: str,
+    realization: int,
+    panel_kind: str,
+    *,
+    checkpoint_root: Path = CHECKPOINT_ROOT,
+    output_root: Path = OUTPUT_ROOT,
+    draws: int = NULL_DRAWS_PER_REALIZATION,
+    force: bool = False,
+) -> dict[str, Any]:
+    """Write collapsed and Hodge null draws using only safe covariance data."""
+
+    count = int(draws)
+    if count < 1:
+        raise ValueError("null bank requires at least one draw")
+    safe_path, safe_arrays_path, _ = panel_paths(
+        checkpoint_root,
+        N,
+        sector,
+        realization,
+        panel_kind,
+    )
+    if not safe_path.is_file() or not safe_arrays_path.is_file():
+        raise FileNotFoundError("missing safe panel data for null bank")
+    safe = json.loads(safe_path.read_text(encoding="utf-8"))
+    if safe.get("arrays_sha256") != sha256(safe_arrays_path):
+        raise ValueError("safe panel array hash mismatch")
+    if not all(safe.get("checks", {}).values()):
+        raise ValueError("safe panel contains a failed gate")
+    metadata_path, arrays_path = null_bank_paths(
+        output_root,
+        N,
+        sector,
+        realization,
+        panel_kind,
+    )
+    identity = {
+        "version": VERSION,
+        "N": int(N),
+        "sector": str(sector),
+        "realization": int(realization),
+        "panel_kind": str(panel_kind),
+        "draws": count,
+        "safe_identity_hash": safe["identity_hash"],
+        "safe_arrays_sha256": safe["arrays_sha256"],
+        "sources": _source_hashes(),
+    }
+    identity_hash = hashlib.sha256(
+        json.dumps(identity, sort_keys=True, separators=(",", ":")).encode()
+    ).hexdigest()
+    if not force and metadata_path.is_file() and arrays_path.is_file():
+        metadata = json.loads(metadata_path.read_text(encoding="utf-8"))
+        if (
+            metadata.get("identity") == identity
+            and metadata.get("identity_hash") == identity_hash
+            and metadata.get("arrays_sha256") == sha256(arrays_path)
+            and all(metadata.get("checks", {}).values())
+        ):
+            return metadata
+        raise ValueError("null bank checkpoint identity mismatch")
+    with np.load(safe_arrays_path) as loaded:
+        copied = {key: np.asarray(loaded[key]) for key in loaded.files}
+    signature = _signature_from_safe(safe, copied)
+    collapsed = gaussian_r4_reference(
+        _positive_covariance_spectrum(copied["total_target_eigenvalues"]),
+        _positive_covariance_spectrum(copied["total_external_eigenvalues"]),
+        PANEL_SIZE,
+        count,
+        _derived_seed(N, sector, realization, panel_kind, "collapsed_bank"),
+    )
+    hodge = hodge_gaussian_r4_reference(
+        signature,
+        PANEL_SIZE,
+        count,
+        _derived_seed(N, sector, realization, panel_kind, "hodge_bank"),
+    )
+    _atomic_npz(
+        arrays_path,
+        collapsed_null=collapsed,
+        hodge_null=hodge,
+    )
+    checks = {
+        "finite_collapsed_null": bool(np.all(np.isfinite(collapsed))),
+        "finite_hodge_null": bool(np.all(np.isfinite(hodge))),
+        "registered_draw_count": collapsed.shape == (count,)
+        and hodge.shape == (count,),
+        "safe_source_hash": safe["arrays_sha256"] == sha256(safe_arrays_path),
+    }
+    metadata = {
+        "identity": identity,
+        "identity_hash": identity_hash,
+        "generated_utc": datetime.now(timezone.utc).isoformat(),
+        "draws": count,
+        "collapsed_sha256": _array_hash(collapsed),
+        "hodge_sha256": _array_hash(hodge),
+        "arrays_sha256": sha256(arrays_path),
+        "checks": checks,
+        "passed": all(checks.values()),
+    }
+    serialized = json.dumps(metadata, sort_keys=True).lower()
+    metadata["checks"]["no_outcome_leakage"] = not any(
+        token in serialized for token in FORBIDDEN_SAFE_TOKENS
+    )
+    metadata["passed"] = all(metadata["checks"].values())
+    if not metadata["passed"]:
+        raise RuntimeError(f"null bank audit failed: {metadata['checks']}")
+    _atomic_json(metadata_path, metadata)
+    return metadata
+
+
+def _parser() -> argparse.ArgumentParser:
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument("--N", type=int, required=True)
+    parser.add_argument("--sector", choices=REGISTERED_SECTORS, required=True)
+    parser.add_argument("--realization", type=int, required=True)
+    parser.add_argument("--panel-kind", choices=REGISTERED_PANEL_KINDS, required=True)
+    parser.add_argument("--draws", type=int, default=NULL_DRAWS_PER_REALIZATION)
+    parser.add_argument("--force", action="store_true")
+    return parser
+
+
+def main() -> None:
+    args = _parser().parse_args()
+    payload = write_null_bank(
+        args.N,
+        args.sector,
+        args.realization,
+        args.panel_kind,
+        draws=args.draws,
+        force=args.force,
+    )
+    print(json.dumps(payload, indent=2, sort_keys=True))
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/slurm/run_susy_hodge_N14_null_v7_array.sbatch b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/slurm/run_susy_hodge_N14_null_v7_array.sbatch
new file mode 100644
index 000000000..56a1e6a84
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/slurm/run_susy_hodge_N14_null_v7_array.sbatch
@@ -0,0 +1,54 @@
+#!/bin/bash
+#SBATCH --job-name=qgeom-susy-N14-null-v7
+#SBATCH --account=giggleliu
+#SBATCH --partition=xhacnormalb
+#SBATCH --nodes=1
+#SBATCH --ntasks=1
+#SBATCH --cpus-per-task=16
+#SBATCH --mem=32G
+#SBATCH --time=48:00:00
+#SBATCH --output=logs/%x-%A_%a.out
+#SBATCH --error=logs/%x-%A_%a.err
+
+set -euo pipefail
+umask 0002
+
+ARRAY_ID="${SLURM_ARRAY_TASK_ID:?submit with an N14 null array}"
+WORKER_COUNT="${N14_NULL_WORKERS:-48}"
+PROJECT_ROOT="${QGEOM_REMOTE_ROOT:-/work/share/giggleliu/Chaos-of-Quantum-Geometry}"
+
+if [[ "$WORKER_COUNT" -lt 1 || "$ARRAY_ID" -ge "$WORKER_COUNT" ]]; then
+    echo "invalid N14 null worker mapping" >&2
+    exit 2
+fi
+
+export PATH="/public/software/apps/anaconda3/2023.09/bin:$PATH"
+export LC_ALL=C
+export LANG=C
+export OMP_NUM_THREADS="${SLURM_CPUS_PER_TASK}"
+export OPENBLAS_NUM_THREADS="${SLURM_CPUS_PER_TASK}"
+export MKL_NUM_THREADS="${SLURM_CPUS_PER_TASK}"
+export NUMEXPR_NUM_THREADS="${SLURM_CPUS_PER_TASK}"
+export PYTHONPATH="$PROJECT_ROOT/01_task_folder/task_05/script"
+
+cd "$PROJECT_ROOT/01_task_folder/task_05/script"
+mkdir -p logs output/susy_hodge_v7_null_banks
+
+for ((LOGICAL_ID=ARRAY_ID; LOGICAL_ID<48; LOGICAL_ID+=WORKER_COUNT)); do
+    SECTOR_INDEX=$((LOGICAL_ID / 24))
+    REALIZATION=$((LOGICAL_ID % 24))
+    case "$SECTOR_INDEX" in
+        0) SECTOR="central" ;;
+        1) SECTOR="adjacent" ;;
+        *) exit 2 ;;
+    esac
+    echo "logical_task=${LOGICAL_ID} N=14 sector=${SECTOR} realization=${REALIZATION}"
+    for PANEL_KIND in sparse isotropic; do
+        python3 -u run_susy_hodge_null_bank_v7.py \
+            --N 14 \
+            --sector "$SECTOR" \
+            --realization "$REALIZATION" \
+            --panel-kind "$PANEL_KIND" \
+            --draws 128
+    done
+done
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/slurm/run_susy_hodge_N14_v7_array.sbatch b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/slurm/run_susy_hodge_N14_v7_array.sbatch
new file mode 100644
index 000000000..b1daf8e61
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/slurm/run_susy_hodge_N14_v7_array.sbatch
@@ -0,0 +1,61 @@
+#!/bin/bash
+#SBATCH --job-name=qgeom-susy-N14-v7
+#SBATCH --account=giggleliu
+#SBATCH --partition=xhacnormalb
+#SBATCH --nodes=1
+#SBATCH --ntasks=1
+#SBATCH --cpus-per-task=16
+#SBATCH --mem=32G
+#SBATCH --time=48:00:00
+#SBATCH --output=logs/%x-%A_%a.out
+#SBATCH --error=logs/%x-%A_%a.err
+
+set -euo pipefail
+umask 0002
+
+ARRAY_ID="${SLURM_ARRAY_TASK_ID:?submit with an N14 response array}"
+WORKER_COUNT="${N14_RESPONSE_WORKERS:-16}"
+PROJECT_ROOT="${QGEOM_REMOTE_ROOT:-/work/share/giggleliu/Chaos-of-Quantum-Geometry}"
+
+if [[ "$WORKER_COUNT" -lt 1 || "$ARRAY_ID" -ge "$WORKER_COUNT" ]]; then
+    echo "invalid N14 response worker mapping" >&2
+    exit 2
+fi
+
+export PATH="/public/software/apps/anaconda3/2023.09/bin:$PATH"
+export LC_ALL=C
+export LANG=C
+export OMP_NUM_THREADS="${SLURM_CPUS_PER_TASK}"
+export OPENBLAS_NUM_THREADS="${SLURM_CPUS_PER_TASK}"
+export MKL_NUM_THREADS="${SLURM_CPUS_PER_TASK}"
+export NUMEXPR_NUM_THREADS="${SLURM_CPUS_PER_TASK}"
+export PYTHONPATH="$PROJECT_ROOT/01_task_folder/task_05/script"
+
+cd "$PROJECT_ROOT/01_task_folder/task_05/script"
+mkdir -p logs output/susy_hodge_v7_checkpoints output/susy_hodge_v7_null_banks
+
+# Forty-eight realization jobs (24 per sector), quota-safely bundled into 16
+# workers.  This stage writes responses only; null banks run independently.
+for ((LOGICAL_ID=ARRAY_ID; LOGICAL_ID<48; LOGICAL_ID+=WORKER_COUNT)); do
+    SECTOR_INDEX=$((LOGICAL_ID / 24))
+    REALIZATION=$((LOGICAL_ID % 24))
+    case "$SECTOR_INDEX" in
+        0) SECTOR="central" ;;
+        1) SECTOR="adjacent" ;;
+        *) exit 2 ;;
+    esac
+
+    echo "logical_task=${LOGICAL_ID} N=14 sector=${SECTOR} realization=${REALIZATION}"
+    python3 -u run_susy_hodge_geometric_eth_v7.py realization \
+        --N 14 \
+        --sector "$SECTOR" \
+        --realization "$REALIZATION"
+
+    for PANEL_KIND in sparse isotropic; do
+        python3 -u run_susy_hodge_geometric_eth_v7.py panel \
+            --N 14 \
+            --sector "$SECTOR" \
+            --realization "$REALIZATION" \
+            --panel-kind "$PANEL_KIND"
+    done
+done
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/slurm/run_susy_hodge_pilot_v7_array.sbatch b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/slurm/run_susy_hodge_pilot_v7_array.sbatch
new file mode 100644
index 000000000..80ff00964
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/slurm/run_susy_hodge_pilot_v7_array.sbatch
@@ -0,0 +1,71 @@
+#!/bin/bash
+#SBATCH --job-name=qgeom-susy-pilot-v7
+#SBATCH --account=giggleliu
+#SBATCH --partition=xhacnormalb
+#SBATCH --nodes=1
+#SBATCH --ntasks=1
+#SBATCH --cpus-per-task=8
+#SBATCH --mem=16G
+#SBATCH --time=24:00:00
+#SBATCH --output=logs/%x-%A_%a.out
+#SBATCH --error=logs/%x-%A_%a.err
+
+set -euo pipefail
+umask 0002
+
+ARRAY_ID="${SLURM_ARRAY_TASK_ID:?submit with --array=0-7}"
+PROJECT_ROOT="${QGEOM_REMOTE_ROOT:-/work/share/giggleliu/Chaos-of-Quantum-Geometry}"
+
+export PATH="/public/software/apps/anaconda3/2023.09/bin:$PATH"
+export LC_ALL=C
+export LANG=C
+export OMP_NUM_THREADS="${SLURM_CPUS_PER_TASK}"
+export OPENBLAS_NUM_THREADS="${SLURM_CPUS_PER_TASK}"
+export MKL_NUM_THREADS="${SLURM_CPUS_PER_TASK}"
+export NUMEXPR_NUM_THREADS="${SLURM_CPUS_PER_TASK}"
+export PYTHONPATH="$PROJECT_ROOT/01_task_folder/task_05/script"
+
+cd "$PROJECT_ROOT/01_task_folder/task_05/script"
+mkdir -p logs output/susy_hodge_v7_checkpoints output/susy_hodge_v7_null_banks
+
+# The remote account is often close to its submitted-job cap.  Preserve the
+# registered 160 logical jobs but bundle them into eight quota-safe workers.
+for ((TASK_ID=ARRAY_ID; TASK_ID<160; TASK_ID+=8)); do
+    if [[ "$TASK_ID" -lt 96 ]]; then
+        N=10
+        COUNT=48
+        LOCAL_ID="$TASK_ID"
+    else
+        N=12
+        COUNT=32
+        LOCAL_ID=$((TASK_ID - 96))
+    fi
+
+    SECTOR_INDEX=$((LOCAL_ID / COUNT))
+    REALIZATION=$((LOCAL_ID % COUNT))
+    case "$SECTOR_INDEX" in
+        0) SECTOR="central" ;;
+        1) SECTOR="adjacent" ;;
+        *) exit 2 ;;
+    esac
+
+    echo "logical_task=${TASK_ID} N=${N} sector=${SECTOR} realization=${REALIZATION}"
+    python3 -u run_susy_hodge_geometric_eth_v7.py realization \
+        --N "$N" \
+        --sector "$SECTOR" \
+        --realization "$REALIZATION"
+
+    for PANEL_KIND in sparse isotropic; do
+        python3 -u run_susy_hodge_geometric_eth_v7.py panel \
+            --N "$N" \
+            --sector "$SECTOR" \
+            --realization "$REALIZATION" \
+            --panel-kind "$PANEL_KIND"
+        python3 -u run_susy_hodge_null_bank_v7.py \
+            --N "$N" \
+            --sector "$SECTOR" \
+            --realization "$REALIZATION" \
+            --panel-kind "$PANEL_KIND" \
+            --draws 128
+    done
+done
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/slurm/seal_susy_hodge_N14_v7.sbatch b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/slurm/seal_susy_hodge_N14_v7.sbatch
new file mode 100644
index 000000000..337b94056
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/slurm/seal_susy_hodge_N14_v7.sbatch
@@ -0,0 +1,30 @@
+#!/bin/bash
+#SBATCH --job-name=qgeom-susy-N14-seal-v7
+#SBATCH --account=giggleliu
+#SBATCH --partition=xhacnormalb
+#SBATCH --nodes=1
+#SBATCH --ntasks=1
+#SBATCH --cpus-per-task=8
+#SBATCH --mem=16G
+#SBATCH --time=02:00:00
+#SBATCH --output=logs/%x-%j.out
+#SBATCH --error=logs/%x-%j.err
+
+set -euo pipefail
+umask 0002
+
+PROJECT_ROOT="${QGEOM_REMOTE_ROOT:-/work/share/giggleliu/Chaos-of-Quantum-Geometry}"
+export PATH="/public/software/apps/anaconda3/2023.09/bin:$PATH"
+export LC_ALL=C
+export LANG=C
+export OMP_NUM_THREADS="${SLURM_CPUS_PER_TASK}"
+export OPENBLAS_NUM_THREADS="${SLURM_CPUS_PER_TASK}"
+export MKL_NUM_THREADS="${SLURM_CPUS_PER_TASK}"
+export NUMEXPR_NUM_THREADS="${SLURM_CPUS_PER_TASK}"
+export PYTHONPATH="$PROJECT_ROOT/01_task_folder/task_05/script"
+
+cd "$PROJECT_ROOT/01_task_folder/task_05/script"
+mkdir -p logs output
+python3 -u analyze_susy_hodge_geometric_eth_v7.py predict --null-replicates 2000
+sha256sum output/susy_hodge_v7_N14_prediction.json
+echo "prediction sealed; stop here for independent inspection"
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/slurm/submit_susy_hodge_N14_v7.sh b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/slurm/submit_susy_hodge_N14_v7.sh
new file mode 100644
index 000000000..5e106118c
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/slurm/submit_susy_hodge_N14_v7.sh
@@ -0,0 +1,13 @@
+#!/bin/bash
+set -euo pipefail
+
+mkdir -p logs
+ARRAY_JOB=$(sbatch --parsable --array=0-15%8 run_susy_hodge_N14_v7_array.sbatch)
+NULL_JOB=$(sbatch --parsable --dependency="afterok:${ARRAY_JOB}" --array=0-47%16 run_susy_hodge_N14_null_v7_array.sbatch)
+SEAL_JOB=$(sbatch --parsable --dependency="afterok:${NULL_JOB}" seal_susy_hodge_N14_v7.sbatch)
+
+echo "N14_response_array_job=${ARRAY_JOB}"
+echo "N14_null_array_job=${NULL_JOB}"
+echo "N14_prediction_seal_job=${SEAL_JOB}"
+echo "workflow stops after the prediction hash is printed"
+echo "opening outcome sidecars requires a separate, explicit command"
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/slurm/submit_susy_hodge_pilot_v7.sh b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/slurm/submit_susy_hodge_pilot_v7.sh
new file mode 100644
index 000000000..9bf16e4c6
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/slurm/submit_susy_hodge_pilot_v7.sh
@@ -0,0 +1,9 @@
+#!/bin/bash
+set -euo pipefail
+
+mkdir -p logs
+ARRAY_JOB=$(sbatch --parsable --array=0-7%8 run_susy_hodge_pilot_v7_array.sbatch)
+
+echo "response_and_null_array_job=${ARRAY_JOB}"
+echo "N10/N12 outcomes are sequential-pilot data; eight workers cover 160 registered logical jobs"
+echo "aggregate only after the complete array passes"
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_hodge_response_v7.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_hodge_response_v7.py
new file mode 100644
index 000000000..a68de084d
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_hodge_response_v7.py
@@ -0,0 +1,277 @@
+"""Exact/coexact response identities for the N=2 SYK BPS fiber."""
+
+from __future__ import annotations
+
+import numpy as np
+
+from lgeth.hodge_response import (
+    HodgeResponse,
+    coupling_panels,
+    decomposable_curvature,
+    external_covariance_eigenvalues_scalable,
+    hodge_response,
+    hodge_signature,
+    project_moduli_tangents,
+    projector_derivative_from_response,
+    scalable_covariance_matched_wick,
+)
+from lgeth.susy_cohomology import (
+    analytic_decomposable_curvature_multiplicities,
+    cubic_triples,
+    decomposable_couplings,
+    decomposable_tangent,
+    normalized_complex_couplings,
+    solve_bps_frame,
+)
+from lgeth.wick_channels import (
+    covariance_matched_wick,
+    external_covariance_eigenvalues,
+)
+
+
+def _generic_tangent(N: int, seed: int) -> np.ndarray:
+    rng = np.random.default_rng(seed)
+    tangent = rng.normal(size=len(cubic_triples(N))) + 1j * rng.normal(
+        size=len(cubic_triples(N))
+    )
+    return tangent / np.linalg.norm(tangent)
+
+
+def test_hodge_branches_are_orthogonal_and_equal_direct_resolvent() -> None:
+    couplings = normalized_complex_couplings(6, seed=29)
+    frame = solve_bps_frame(6, 3, couplings, dense_cutoff=64)
+    tangent = _generic_tangent(6, seed=31)
+    result = hodge_response(frame, couplings, tangent[None, :])
+    cross = result.minus[0].conj().T @ result.plus[0]
+    scale = np.linalg.norm(result.minus[0]) * np.linalg.norm(result.plus[0])
+    assert np.linalg.norm(cross) / scale < 2e-12
+    assert np.allclose(result.total, result.minus + result.plus, atol=2e-12)
+    assert np.allclose(result.total, result.direct, atol=2e-11)
+    assert result.branch_sum_relative_error < 2e-13
+    assert result.direct_relative_error < 2e-11
+    assert result.orthogonality_relative_error < 2e-12
+    assert result.target_leakage < 2e-12
+    assert all(result.checks.values())
+
+
+def test_response_reproduces_centered_projector_derivative() -> None:
+    couplings = normalized_complex_couplings(6, seed=37)
+    frame = solve_bps_frame(6, 3, couplings, dense_cutoff=64)
+    tangent = _generic_tangent(6, seed=41)
+    response = hodge_response(frame, couplings, tangent[None, :])
+    analytic = projector_derivative_from_response(
+        frame.projector_frame,
+        response.total[0],
+    )
+    errors: list[float] = []
+    for step in (2e-4, 1e-4):
+        plus = solve_bps_frame(
+            6,
+            3,
+            couplings + step * tangent,
+            dense_cutoff=64,
+        ).projector_frame
+        minus = solve_bps_frame(
+            6,
+            3,
+            couplings - step * tangent,
+            dense_cutoff=64,
+        ).projector_frame
+        finite = (
+            plus @ plus.conj().T - minus @ minus.conj().T
+        ) / (2.0 * step)
+        errors.append(float(np.linalg.norm(finite - analytic) / np.linalg.norm(analytic)))
+    assert errors[1] < 2e-6
+    assert errors[0] / errors[1] > 3.5
+
+
+def test_multiple_tangents_preserve_shapes_and_linearity() -> None:
+    couplings = normalized_complex_couplings(6, seed=43)
+    frame = solve_bps_frame(6, 2, couplings, dense_cutoff=64)
+    first = _generic_tangent(6, seed=47)
+    second = _generic_tangent(6, seed=53)
+    combined = hodge_response(
+        frame,
+        couplings,
+        np.stack([first, second, first + 2.0 * second]),
+    )
+    assert combined.total.shape == (3, 15, 9)
+    assert np.allclose(
+        combined.total[2],
+        combined.total[0] + 2.0 * combined.total[1],
+        atol=3e-11,
+    )
+
+
+def test_registered_panels_remove_radial_phase_and_have_full_support() -> None:
+    couplings = normalized_complex_couplings(8, seed=59)
+    panels = coupling_panels(couplings, panel_size=8, seed=61)
+    assert set(panels) == {"sparse", "isotropic"}
+    assert not np.allclose(panels["sparse"], panels["isotropic"])
+    for values in panels.values():
+        assert values.shape == (8, 56)
+        assert np.max(np.abs(values @ couplings.conj())) < 2e-13
+        assert np.allclose(
+            values @ values.conj().T,
+            np.eye(8),
+            atol=2e-13,
+        )
+
+
+def test_moduli_projection_rejects_rank_deficient_candidates() -> None:
+    couplings = normalized_complex_couplings(8, seed=67)
+    candidate = np.zeros(56, dtype=complex)
+    candidate[0] = 1.0
+    with np.testing.assert_raises_regex(ValueError, "full rank"):
+        project_moduli_tangents(
+            couplings,
+            np.stack([candidate, candidate]),
+        )
+
+
+def _synthetic_response(minus: np.ndarray, plus: np.ndarray) -> HodgeResponse:
+    total = minus + plus
+    return HodgeResponse(
+        minus=minus,
+        plus=plus,
+        total=total,
+        direct=total.copy(),
+        branch_sum_relative_error=0.0,
+        direct_relative_error=0.0,
+        orthogonality_relative_error=0.0,
+        target_leakage=0.0,
+        checks={"synthetic": True},
+    )
+
+
+def test_hodge_signature_resolves_one_sided_and_balanced_limits() -> None:
+    rng = np.random.default_rng(71)
+    minus = rng.normal(size=(8, 12, 5)) + 1j * rng.normal(size=(8, 12, 5))
+    zero = np.zeros_like(minus)
+    one_sided = hodge_signature(_synthetic_response(minus, zero))
+    assert one_sided.hodge_balance == 0.0
+    assert one_sided.minus_weight > 0.0
+    assert one_sided.plus_weight == 0.0
+    balanced = hodge_signature(_synthetic_response(minus, minus.copy()))
+    assert abs(balanced.hodge_balance - 1.0) < 2e-14
+
+
+def test_hodge_signature_is_gauge_invariant() -> None:
+    couplings = normalized_complex_couplings(6, seed=73)
+    frame = solve_bps_frame(6, 3, couplings, dense_cutoff=64)
+    panels = coupling_panels(couplings, panel_size=8, seed=79)
+    response = hodge_response(frame, couplings, panels["isotropic"])
+    reference = hodge_signature(response)
+    rng = np.random.default_rng(83)
+    ambient, _ = np.linalg.qr(
+        rng.normal(size=(20, 20)) + 1j * rng.normal(size=(20, 20))
+    )
+    target, _ = np.linalg.qr(
+        rng.normal(size=(18, 18)) + 1j * rng.normal(size=(18, 18))
+    )
+    rotated_minus = np.einsum(
+        "ij,mjk,kl->mil",
+        ambient,
+        response.minus,
+        target,
+        optimize=True,
+    )
+    rotated_plus = np.einsum(
+        "ij,mjk,kl->mil",
+        ambient,
+        response.plus,
+        target,
+        optimize=True,
+    )
+    rotated = hodge_signature(_synthetic_response(rotated_minus, rotated_plus))
+    assert np.isclose(reference.hodge_balance, rotated.hodge_balance, atol=1e-13)
+    assert np.allclose(
+        reference.minus_target_eigenvalues,
+        rotated.minus_target_eigenvalues,
+        atol=2e-12,
+    )
+    assert np.allclose(
+        reference.plus_external_eigenvalues,
+        rotated.plus_external_eigenvalues,
+        atol=2e-12,
+    )
+    assert np.allclose(
+        reference.minus_channel_covariance,
+        rotated.minus_channel_covariance,
+        atol=2e-12,
+    )
+
+
+def test_scalable_external_spectrum_and_statistic_match_immutable_code() -> None:
+    rng = np.random.default_rng(89)
+    # ambient=7 is much smaller than labels*rank=40, exercising the N=14 path.
+    channels = rng.normal(size=(8, 7, 5)) + 1j * rng.normal(size=(8, 7, 5))
+    reference_spectrum = external_covariance_eigenvalues(channels)
+    scalable_spectrum = external_covariance_eigenvalues_scalable(channels)
+    assert np.allclose(reference_spectrum, scalable_spectrum, atol=2e-12)
+    reference = covariance_matched_wick(channels)
+    scalable = scalable_covariance_matched_wick(channels)
+    assert np.isclose(reference.R4, scalable.R4, atol=2e-13)
+    assert np.isclose(reference.A_left, scalable.A_left, atol=2e-13)
+    assert np.isclose(reference.B_right, scalable.B_right, atol=2e-13)
+    assert np.allclose(reference.tensor, scalable.tensor, atol=2e-13)
+    assert np.allclose(
+        reference.right_eigenvalues,
+        scalable.right_eigenvalues,
+        atol=2e-12,
+    )
+
+
+def _assert_atomic_spectrum(
+    matrix: np.ndarray,
+    alpha: float,
+    multiplicities: dict[str, int],
+) -> None:
+    eigenvalues = np.linalg.eigvalsh(0.5 * (matrix + matrix.conj().T))
+    target = 1.0 / alpha**2
+    assert np.count_nonzero(np.isclose(eigenvalues, -target, atol=2e-11)) == (
+        multiplicities["negative"]
+    )
+    assert np.count_nonzero(np.isclose(eigenvalues, 0.0, atol=2e-11)) == (
+        multiplicities["zero"]
+    )
+    assert np.count_nonzero(np.isclose(eigenvalues, target, atol=2e-11)) == (
+        multiplicities["positive"]
+    )
+
+
+def test_decomposable_diagonal_curvature_recovers_exact_atoms() -> None:
+    alpha = 1.7
+    couplings = decomposable_couplings(6, alpha)
+    frame = solve_bps_frame(6, 3, couplings, dense_cutoff=64)
+    tangent = decomposable_tangent(6, "12", 3)
+    response = hodge_response(frame, couplings, tangent[None, :])
+    curvature = decomposable_curvature(response, 0)
+    _assert_atomic_spectrum(
+        curvature,
+        alpha,
+        analytic_decomposable_curvature_multiplicities(6, 3, "diagonal"),
+    )
+
+
+def test_decomposable_off_diagonal_curvature_recovers_exact_atoms() -> None:
+    alpha = 1.7
+    couplings = decomposable_couplings(6, alpha)
+    frame = solve_bps_frame(6, 3, couplings, dense_cutoff=64)
+    tangents = np.stack(
+        [
+            decomposable_tangent(6, "12", 3),
+            decomposable_tangent(6, "13", 4),
+        ]
+    )
+    response = hodge_response(frame, couplings, tangents)
+    curvature = decomposable_curvature(response, 0, 1)
+    _assert_atomic_spectrum(
+        curvature,
+        alpha,
+        analytic_decomposable_curvature_multiplicities(
+            6,
+            3,
+            "off_diagonal",
+        ),
+    )
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_hodge_wick_v7.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_hodge_wick_v7.py
new file mode 100644
index 000000000..9dddd9436
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_hodge_wick_v7.py
@@ -0,0 +1,132 @@
+"""Finite-size Gaussian nulls conditioned on safe Hodge signatures."""
+
+from __future__ import annotations
+
+from dataclasses import replace
+
+import numpy as np
+
+from lgeth.hodge_response import HodgeSignature
+from lgeth.hodge_wick import (
+    complete_realization_null,
+    hodge_gaussian_r4_reference,
+    sample_hodge_gaussian_channels,
+)
+from lgeth.wick_channels import gaussian_r4_reference
+
+
+def _signature(minus_weight: float, plus_weight: float) -> HodgeSignature:
+    minus_target = np.asarray([0.42, 0.27, 0.18, 0.09, 0.04])
+    plus_target = np.asarray([0.36, 0.25, 0.20, 0.12, 0.07])
+    minus_external = np.asarray([0.51, 0.31, 0.18])
+    plus_external = np.asarray([0.40, 0.28, 0.20, 0.12])
+    total = minus_weight + plus_weight
+    balance = 0.0 if total == 0 else 4.0 * minus_weight * plus_weight / total**2
+    return HodgeSignature(
+        channel_count=8,
+        target_rank=5,
+        minus_weight=minus_weight,
+        plus_weight=plus_weight,
+        hodge_balance=balance,
+        minus_channel_covariance=np.eye(8),
+        plus_channel_covariance=np.eye(8),
+        minus_target_eigenvalues=minus_target,
+        plus_target_eigenvalues=plus_target,
+        minus_external_eigenvalues=minus_external,
+        plus_external_eigenvalues=plus_external,
+        minus_target_effective_rank=3.5,
+        plus_target_effective_rank=4.0,
+        minus_external_effective_rank=2.5,
+        plus_external_effective_rank=3.2,
+        minus_target_entropy=0.8,
+        plus_target_entropy=0.9,
+        minus_external_entropy=0.8,
+        plus_external_entropy=0.9,
+        orthogonality_relative_error=0.0,
+    )
+
+
+def test_one_sided_hodge_reference_is_exact_existing_regression() -> None:
+    signature = _signature(1.0, 0.0)
+    observed = hodge_gaussian_r4_reference(signature, 8, 32, 89)
+    expected = gaussian_r4_reference(
+        signature.minus_target_eigenvalues,
+        signature.minus_external_eigenvalues,
+        8,
+        32,
+        89,
+    )
+    assert np.array_equal(observed, expected)
+
+
+def test_two_sided_sampler_has_direct_sum_shape_and_is_deterministic() -> None:
+    signature = _signature(0.4, 0.6)
+    first = sample_hodge_gaussian_channels(
+        signature,
+        8,
+        np.random.default_rng(97),
+    )
+    second = sample_hodge_gaussian_channels(
+        signature,
+        8,
+        np.random.default_rng(97),
+    )
+    assert first.shape == (8, 7, 5)
+    assert np.array_equal(first, second)
+    assert np.all(np.isfinite(first.real))
+    assert np.all(np.isfinite(first.imag))
+
+
+def test_common_branch_weight_rescaling_does_not_change_null_draws() -> None:
+    signature = _signature(0.4, 0.6)
+    scaled = replace(signature, minus_weight=4.0, plus_weight=6.0)
+    first = sample_hodge_gaussian_channels(
+        signature,
+        8,
+        np.random.default_rng(101),
+    )
+    second = sample_hodge_gaussian_channels(
+        scaled,
+        8,
+        np.random.default_rng(101),
+    )
+    assert np.array_equal(first, second)
+
+
+def test_branch_channel_covariance_changes_two_sided_null_draw() -> None:
+    signature = _signature(0.4, 0.6)
+    covariance = np.full((8, 8), 0.15, dtype=complex)
+    np.fill_diagonal(covariance, 1.0)
+    correlated = replace(signature, plus_channel_covariance=covariance)
+    first = sample_hodge_gaussian_channels(
+        signature,
+        8,
+        np.random.default_rng(102),
+    )
+    second = sample_hodge_gaussian_channels(
+        correlated,
+        8,
+        np.random.default_rng(102),
+    )
+    assert not np.allclose(first, second)
+
+
+def test_hodge_r4_and_complete_realization_nulls_are_reproducible() -> None:
+    first_signature = _signature(0.45, 0.55)
+    second_signature = _signature(0.30, 0.70)
+    first = hodge_gaussian_r4_reference(first_signature, 8, 24, 103)
+    second = hodge_gaussian_r4_reference(first_signature, 8, 24, 103)
+    assert np.array_equal(first, second)
+    assert np.all(np.isfinite(first))
+    aggregate_first = complete_realization_null(
+        [first_signature, second_signature],
+        samples=20,
+        seed=107,
+    )
+    aggregate_second = complete_realization_null(
+        [first_signature, second_signature],
+        samples=20,
+        seed=107,
+    )
+    assert aggregate_first.shape == (20,)
+    assert np.array_equal(aggregate_first, aggregate_second)
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_susy_cohomology_v7.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_susy_cohomology_v7.py
new file mode 100644
index 000000000..1c7b38a9d
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_susy_cohomology_v7.py
@@ -0,0 +1,111 @@
+"""Algebra and rank tests for the charge-resolved N=2 SYK complex."""
+
+from __future__ import annotations
+
+from math import comb
+
+import numpy as np
+
+from lgeth.susy_cohomology import (
+    analytic_decomposable_curvature_multiplicities,
+    charge_basis,
+    charge_hamiltonian,
+    cubic_supercharge,
+    cubic_triples,
+    decomposable_bps_rank,
+    decomposable_couplings,
+    decomposable_tangent,
+    expected_generic_bps_rank,
+    normalized_complex_couplings,
+    solve_bps_frame,
+)
+
+
+def test_charge_bases_and_cubic_triples_have_exact_counts() -> None:
+    assert len(charge_basis(8, 3)) == comb(8, 3)
+    assert charge_basis(8, -1) == ()
+    assert charge_basis(8, 9) == ()
+    triples = cubic_triples(8)
+    assert len(triples) == comb(8, 3)
+    assert triples[0] == (0, 1, 2)
+    assert triples[-1] == (5, 6, 7)
+
+
+def test_cubic_supercharge_is_nontrivially_nilpotent() -> None:
+    couplings = normalized_complex_couplings(8, seed=7)
+    q1 = cubic_supercharge(8, 1, couplings)
+    q4 = cubic_supercharge(8, 4, couplings)
+    product = (q4 @ q1).toarray()
+    assert product.shape == (8, 8)
+    assert np.linalg.norm(product) < 2e-14
+    assert np.linalg.norm(q1.toarray()) > 0.0
+    assert np.linalg.norm(q4.toarray()) > 0.0
+
+
+def test_charge_hamiltonian_is_positive_hermitian() -> None:
+    couplings = normalized_complex_couplings(6, seed=11)
+    hamiltonian = charge_hamiltonian(6, 3, couplings).toarray()
+    assert hamiltonian.shape == (20, 20)
+    assert np.allclose(hamiltonian, hamiltonian.conj().T, atol=1e-13)
+    eigenvalues = np.linalg.eigvalsh(hamiltonian)
+    assert float(eigenvalues[0]) > -1e-12
+    assert float(eigenvalues[-1]) > 1e-4
+
+
+def test_registered_even_charge_sectors_have_exact_generic_bps_ranks() -> None:
+    couplings = normalized_complex_couplings(6, seed=17)
+    central = solve_bps_frame(6, 3, couplings, dense_cutoff=64)
+    adjacent = solve_bps_frame(6, 2, couplings, dense_cutoff=64)
+    assert expected_generic_bps_rank(6, 3) == 18
+    assert expected_generic_bps_rank(6, 2) == 9
+    assert central.projector_frame.shape == (20, 18)
+    assert adjacent.projector_frame.shape == (15, 9)
+    for frame in (central, adjacent):
+        assert frame.gap > 1e-8
+        assert frame.kernel_residual < 1e-11
+        assert frame.orthogonality_error < 1e-12
+        assert frame.complement_frame.shape[1] == len(frame.positive_energies)
+
+
+def test_bps_projector_is_deterministic_at_fixed_couplings() -> None:
+    couplings = normalized_complex_couplings(6, seed=23)
+    first = solve_bps_frame(6, 3, couplings, dense_cutoff=64)
+    second = solve_bps_frame(6, 3, couplings, dense_cutoff=64)
+    first_projector = first.projector_frame @ first.projector_frame.conj().T
+    second_projector = second.projector_frame @ second.projector_frame.conj().T
+    assert np.allclose(first_projector, second_projector, atol=2e-13)
+
+
+def test_odd_system_size_is_outside_registered_rank_contract() -> None:
+    with np.testing.assert_raises_regex(ValueError, "even N"):
+        expected_generic_bps_rank(7, 3)
+
+
+def test_decomposable_rank_and_tangent_contracts() -> None:
+    couplings = decomposable_couplings(8, alpha=1.7)
+    triples = cubic_triples(8)
+    assert np.count_nonzero(couplings) == 1
+    assert couplings[triples.index((0, 1, 2))] == 1.7
+    tangent = decomposable_tangent(8, "12", 3)
+    assert np.count_nonzero(tangent) == 1
+    assert tangent[triples.index((0, 1, 3))] == 1.0
+    assert decomposable_bps_rank(8, 4) == 60
+    frame = solve_bps_frame(
+        8,
+        4,
+        couplings,
+        dense_cutoff=128,
+        expected_rank_override=decomposable_bps_rank(8, 4),
+    )
+    assert frame.projector_frame.shape == (70, 60)
+
+
+def test_decomposable_multiplicity_formulas_are_complete() -> None:
+    diagonal = analytic_decomposable_curvature_multiplicities(6, 3, "diagonal")
+    off_diagonal = analytic_decomposable_curvature_multiplicities(
+        6,
+        3,
+        "off_diagonal",
+    )
+    assert diagonal == {"negative": 1, "zero": 16, "positive": 1}
+    assert off_diagonal == {"negative": 2, "zero": 14, "positive": 2}
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_susy_hodge_analysis_v7.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_susy_hodge_analysis_v7.py
new file mode 100644
index 000000000..90560ef50
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_susy_hodge_analysis_v7.py
@@ -0,0 +1,214 @@
+"""Sealed prediction and complete-realization inference tests for v7."""
+
+from __future__ import annotations
+
+import json
+from pathlib import Path
+
+import numpy as np
+import pytest
+
+from analyze_susy_hodge_geometric_eth_v7 import (
+    aggregate_pilot_from_banks,
+    score_unsealed_n14,
+    select_frozen_branch,
+    write_n14_prediction,
+)
+from run_susy_hodge_geometric_eth_v7 import (
+    panel_paths,
+    prepare_realization,
+    run_panel,
+)
+from run_susy_hodge_null_bank_v7 import write_null_bank
+
+
+def _reduced_prediction_fixture(
+    tmp_path: Path,
+    *,
+    delete_outcomes: bool = True,
+) -> list[tuple[int, str, int, str]]:
+    checkpoint_root = tmp_path / "checkpoints"
+    bank_root = tmp_path / "banks"
+    cases: list[tuple[int, str, int, str]] = []
+    for sector in ("central", "adjacent"):
+        for realization in range(2):
+            prepare_realization(
+                6,
+                sector,
+                realization,
+                root=checkpoint_root,
+                reduced=True,
+                force=True,
+            )
+            case = (6, sector, realization, "sparse")
+            run_panel(*case, root=checkpoint_root, reduced=True, force=True)
+            write_null_bank(
+                *case,
+                checkpoint_root=checkpoint_root,
+                output_root=bank_root,
+                draws=8,
+                force=True,
+            )
+            if delete_outcomes:
+                # Prediction generation must succeed with no outcome sidecars.
+                _, _, outcome_path = panel_paths(checkpoint_root, *case)
+                outcome_path.unlink()
+            cases.append(case)
+    return cases
+
+
+def test_prediction_is_sealed_before_any_outcome_is_read(tmp_path: Path) -> None:
+    cases = _reduced_prediction_fixture(tmp_path)
+    prediction_json = tmp_path / "prediction.json"
+    prediction_npz = tmp_path / "prediction.npz"
+    prediction_seal = tmp_path / "prediction.sha256"
+    payload = write_n14_prediction(
+        cases,
+        checkpoint_root=tmp_path / "checkpoints",
+        null_bank_root=tmp_path / "banks",
+        safe_covariates_json=tmp_path / "safe.json",
+        output_json=prediction_json,
+        output_npz=prediction_npz,
+        seal_path=prediction_seal,
+        null_replicates=24,
+        seed=71,
+    )
+    assert payload["passed"]
+    assert prediction_seal.is_file()
+    serialized = prediction_json.read_text(encoding="utf-8").lower()
+    assert "r4" not in serialized
+    assert "four_point" not in serialized
+    assert "connected" not in serialized
+    assert {
+        (item["sector"], item["panel_kind"])
+        for item in payload["primary_pair"]
+    } == {("central", "sparse"), ("adjacent", "sparse")}
+    with np.load(prediction_npz) as arrays:
+        assert arrays["N6_central_sparse_collapsed"].shape == (24,)
+        assert arrays["N6_adjacent_sparse_hodge"].shape == (24,)
+
+
+def test_scoring_fails_closed_when_prediction_seal_is_corrupted(
+    tmp_path: Path,
+) -> None:
+    cases = _reduced_prediction_fixture(tmp_path)
+    prediction_json = tmp_path / "prediction.json"
+    prediction_npz = tmp_path / "prediction.npz"
+    prediction_seal = tmp_path / "prediction.sha256"
+    write_n14_prediction(
+        cases,
+        checkpoint_root=tmp_path / "checkpoints",
+        null_bank_root=tmp_path / "banks",
+        safe_covariates_json=tmp_path / "safe.json",
+        output_json=prediction_json,
+        output_npz=prediction_npz,
+        seal_path=prediction_seal,
+        null_replicates=12,
+        seed=73,
+    )
+    unsealed = {
+        "records": [
+            {
+                "N": N,
+                "sector": sector,
+                "realization": realization,
+                "panel_kind": panel,
+                "R4": float(0.1 + 0.01 * realization),
+            }
+            for N, sector, realization, panel in cases
+        ],
+        "passed": True,
+    }
+    unsealed_json = tmp_path / "unsealed.json"
+    unsealed_json.write_text(json.dumps(unsealed), encoding="utf-8")
+    prediction_seal.write_text("0" * 64 + "  prediction.json\n", encoding="utf-8")
+    with pytest.raises(ValueError, match="seal mismatch"):
+        score_unsealed_n14(
+            prediction_json,
+            prediction_seal,
+            unsealed_json,
+            output_json=tmp_path / "inference.json",
+            bootstrap_replicates=32,
+            seed=79,
+        )
+
+
+def test_frozen_branch_selection_is_exhaustive_and_fail_closed() -> None:
+    assert select_frozen_branch(True, True, False, True) == (
+        "strong_covariance_universality"
+    )
+    assert select_frozen_branch(False, True, False, True) == (
+        "hodge_resolved_geometric_eth"
+    )
+    assert select_frozen_branch(False, False, False, True) == (
+        "cohomological_non_gaussian_class"
+    )
+    assert select_frozen_branch(False, False, True, True) == (
+        "structured_cohomology"
+    )
+    assert select_frozen_branch(True, False, False, True) == (
+        "feasibility_failure"
+    )
+    assert select_frozen_branch(True, True, False, False) == (
+        "feasibility_failure"
+    )
+
+
+def test_scheduler_stops_after_the_prediction_seal() -> None:
+    script_root = Path(__file__).resolve().parents[1]
+    submit = (
+        script_root / "slurm" / "submit_susy_hodge_N14_v7.sh"
+    ).read_text(encoding="utf-8")
+    assert "seal_susy_hodge_N14_v7.sbatch" in submit
+    assert "run_susy_hodge_N14_null_v7_array.sbatch" in submit
+    assert 'dependency="afterok:${ARRAY_JOB}"' in submit
+    assert 'dependency="afterok:${NULL_JOB}"' in submit
+    assert "analyze_susy_hodge_geometric_eth_v7.py unseal" not in submit
+    seal_job = (
+        script_root / "slurm" / "seal_susy_hodge_N14_v7.sbatch"
+    ).read_text(encoding="utf-8")
+    assert " predict " in seal_job
+    assert " unseal" not in seal_job
+    response_job = (
+        script_root / "slurm" / "run_susy_hodge_N14_v7_array.sbatch"
+    ).read_text(encoding="utf-8")
+    assert 'WORKER_COUNT="${N14_RESPONSE_WORKERS:-16}"' in response_job
+    logical_ids = {
+        logical_id
+        for array_id in range(8)
+        for logical_id in range(array_id, 48, 8)
+    }
+    assert logical_ids == set(range(48))
+    null_job = (
+        script_root / "slurm" / "run_susy_hodge_N14_null_v7_array.sbatch"
+    ).read_text(encoding="utf-8")
+    assert 'WORKER_COUNT="${N14_NULL_WORKERS:-48}"' in null_job
+    null_logical_ids = {
+        logical_id
+        for array_id in range(8)
+        for logical_id in range(array_id, 48, 8)
+    }
+    assert null_logical_ids == set(range(48))
+
+
+def test_pilot_aggregate_resamples_complete_realizations(tmp_path: Path) -> None:
+    cases = _reduced_prediction_fixture(tmp_path, delete_outcomes=False)
+    payload = aggregate_pilot_from_banks(
+        cases,
+        checkpoint_root=tmp_path / "checkpoints",
+        null_bank_root=tmp_path / "banks",
+        safe_covariates_json=tmp_path / "pilot_safe.json",
+        output_json=tmp_path / "pilot.json",
+        output_npz=tmp_path / "pilot.npz",
+        null_replicates=12,
+        bootstrap_replicates=16,
+        seed=83,
+    )
+    assert payload["passed"]
+    assert payload["uncertainty_unit"] == "complete_disorder_realization"
+    assert len(payload["groups"]) == 2
+    with np.load(tmp_path / "pilot.npz") as arrays:
+        assert arrays["N6_central_sparse_physical"].shape == (2,)
+        assert arrays["N6_central_sparse_physical_bootstrap"].shape == (16,)
+        assert arrays["N6_central_sparse_collapsed_null"].shape == (12,)
+        assert arrays["N6_central_sparse_hodge_null"].shape == (12,)
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_susy_hodge_controls_v7.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_susy_hodge_controls_v7.py
new file mode 100644
index 000000000..7bd06bedf
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_susy_hodge_controls_v7.py
@@ -0,0 +1,30 @@
+"""Machine-readable analytic-control artifact tests for SUSY/Hodge v7."""
+
+from __future__ import annotations
+
+import json
+from pathlib import Path
+
+from generate_susy_hodge_controls_v7 import generate_controls
+
+
+def test_decomposable_atoms_and_one_sided_regression_are_audited(
+    tmp_path: Path,
+) -> None:
+    output = tmp_path / "controls.json"
+    payload = generate_controls(output)
+    assert payload["passed"]
+    assert payload["decomposable_N6"]["diagonal_multiplicities"] == {
+        "negative": 1,
+        "zero": 16,
+        "positive": 1,
+    }
+    assert payload["decomposable_N6"]["off_diagonal_multiplicities"] == {
+        "negative": 2,
+        "zero": 14,
+        "positive": 2,
+    }
+    assert payload["decomposable_N8"]["bps_rank"] == 60
+    assert payload["one_sided_regression"]["max_absolute_difference"] == 0.0
+    reloaded = json.loads(output.read_text(encoding="utf-8"))
+    assert reloaded["sources"] == payload["sources"]
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_susy_hodge_delivery_script_v7.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_susy_hodge_delivery_script_v7.py
new file mode 100644
index 000000000..254332142
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_susy_hodge_delivery_script_v7.py
@@ -0,0 +1,34 @@
+"""The delivery command must preserve the explicit held-out unseal boundary."""
+
+from __future__ import annotations
+
+from pathlib import Path
+
+
+def test_delivery_script_orders_assets_and_never_unseals() -> None:
+    script = (
+        Path(__file__).resolve().parents[1] / "run_susy_hodge_delivery_v7.sh"
+    ).read_text(encoding="utf-8")
+    merge = script.index("merge_susy_hodge_pilot_v7.py")
+    figure = script.index("make_susy_hodge_figure_v7.py")
+    assets = script.index("make_susy_hodge_manuscript_assets_v7.py")
+    compile_pdf = script.index("latexmk")
+    archive_pdf = script.index("response_complex_memory_v7.pdf")
+    supplement = script.index("supplement.tex")
+    archive_supplement = script.index("response_complex_memory_supplement_v7.pdf")
+    audit = script.index("verify_susy_hodge_delivery_v7.py")
+    manuscript = script.index("verify_susy_hodge_manuscript_v7.py")
+
+    assert (
+        merge
+        < figure
+        < assets
+        < compile_pdf
+        < supplement
+        < archive_pdf
+        < archive_supplement
+        < audit
+        < manuscript
+    )
+    assert " unseal" not in script.lower()
+    assert "analyze_susy_hodge_geometric_eth_v7.py unseal" not in script
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_susy_hodge_delivery_v7.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_susy_hodge_delivery_v7.py
new file mode 100644
index 000000000..1c5475d08
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_susy_hodge_delivery_v7.py
@@ -0,0 +1,196 @@
+"""Fail-closed delivery and corruption tests for SUSY/Hodge v7."""
+
+from __future__ import annotations
+
+import hashlib
+import json
+from datetime import datetime, timedelta, timezone
+from pathlib import Path
+
+import numpy as np
+
+from verify_susy_hodge_delivery_v7 import verify_delivery
+
+
+def _hash(path: Path) -> str:
+    return hashlib.sha256(path.read_bytes()).hexdigest()
+
+
+def _write_json(path: Path, payload: dict) -> None:
+    path.write_text(json.dumps(payload, indent=2, sort_keys=True), encoding="utf-8")
+
+
+def _synthetic_delivery(tmp_path: Path) -> dict[str, Path]:
+    now = datetime.now(timezone.utc)
+    pilot_groups = [
+        {
+            "N": N,
+            "sector": sector,
+            "panel_kind": panel,
+            "collapsed_covered": False,
+            "hodge_covered": False,
+        }
+        for N in (8, 10, 12)
+        for sector in ("central", "adjacent")
+        for panel in ("sparse", "isotropic")
+    ]
+    pilot = tmp_path / "pilot.json"
+    pilot_npz = tmp_path / "pilot.npz"
+    np.savez_compressed(pilot_npz, values=np.arange(3.0))
+    _write_json(
+        pilot,
+        {
+            "version": "v7",
+            "groups": pilot_groups,
+            "arrays_sha256": _hash(pilot_npz),
+            "checks": {"complete": True},
+            "passed": True,
+        },
+    )
+    safe = tmp_path / "safe.json"
+    _write_json(safe, {"version": "v7", "records": [], "passed": True})
+    prediction_npz = tmp_path / "prediction.npz"
+    np.savez_compressed(prediction_npz, central=np.arange(4.0))
+    primary_prediction = [
+        {
+            "N": 14,
+            "sector": sector,
+            "panel_kind": "sparse",
+            "realizations": 2,
+            "collapsed_interval": [0.10, 0.11, 0.12],
+            "hodge_interval": [0.13, 0.14, 0.15],
+        }
+        for sector in ("central", "adjacent")
+    ]
+    prediction = tmp_path / "prediction.json"
+    _write_json(
+        prediction,
+        {
+            "version": "v7",
+            "generated_utc": now.isoformat(),
+            "prediction_arrays_file": prediction_npz.name,
+            "prediction_arrays_sha256": _hash(prediction_npz),
+            "safe_covariates_sha256": _hash(safe),
+            "primary_pair": primary_prediction,
+            "checks": {"complete": True, "no_outcome_leakage": True},
+            "passed": True,
+        },
+    )
+    seal = tmp_path / "prediction.sha256"
+    seal.write_text(f"{_hash(prediction)}  {prediction.name}\n", encoding="utf-8")
+    unsealed = tmp_path / "unsealed.json"
+    _write_json(
+        unsealed,
+        {
+            "version": "v7",
+            "prediction_sha256": _hash(prediction),
+            "unsealed_utc": (now + timedelta(seconds=1)).isoformat(),
+            "checks": {"complete": True},
+            "passed": True,
+        },
+    )
+    primary_inference = [
+        {
+            "N": 14,
+            "sector": sector,
+            "panel_kind": "sparse",
+            "collapsed_covered": False,
+            "hodge_covered": False,
+            "robust_outside_both": True,
+        }
+        for sector in ("central", "adjacent")
+    ]
+    inference = tmp_path / "inference.json"
+    _write_json(
+        inference,
+        {
+            "version": "v7",
+            "prediction_sha256": _hash(prediction),
+            "selected_branch": "cohomological_non_gaussian_class",
+            "primary_pair": primary_inference,
+            "structured_indistinguishable": False,
+            "checks": {"registered_branch_resolved": True},
+            "passed": True,
+        },
+    )
+    controls = tmp_path / "controls.json"
+    _write_json(
+        controls,
+        {
+            "version": "v7",
+            "checks": {
+                "N6_curvature_atoms": True,
+                "one_sided_exact_regression": True,
+            },
+            "passed": True,
+        },
+    )
+    pdf = tmp_path / "figure.pdf"
+    png = tmp_path / "figure.png"
+    report = tmp_path / "report.md"
+    pdf.write_bytes(b"%PDF-1.4\nsynthetic\n")
+    png.write_bytes(b"synthetic-png")
+    report.write_text(
+        "## Established\ncohomological_non_gaussian_class\n"
+        "## Not established\n[Source](https://example.org)\n",
+        encoding="utf-8",
+    )
+    figure = tmp_path / "figure.json"
+    _write_json(
+        figure,
+        {
+            "version": "v7",
+            "selected_branch": "cohomological_non_gaussian_class",
+            "inputs": {
+                pilot.name: _hash(pilot),
+                inference.name: _hash(inference),
+            },
+            "outputs": {
+                pdf.name: _hash(pdf),
+                png.name: _hash(png),
+                report.name: _hash(report),
+            },
+            "checks": {"complete": True},
+            "passed": True,
+        },
+    )
+    return {
+        "pilot_json": pilot,
+        "pilot_npz": pilot_npz,
+        "safe_json": safe,
+        "prediction_json": prediction,
+        "prediction_npz": prediction_npz,
+        "prediction_seal": seal,
+        "unsealed_json": unsealed,
+        "inference_json": inference,
+        "controls_json": controls,
+        "figure_manifest": figure,
+        "figure_pdf": pdf,
+        "figure_png": png,
+        "report_md": report,
+    }
+
+
+def test_delivery_passes_then_rejects_seal_and_safe_leakage(tmp_path: Path) -> None:
+    paths = _synthetic_delivery(tmp_path)
+    output = tmp_path / "audit.json"
+    first = verify_delivery(**paths, output_json=output)
+    assert first["passed"]
+    paths["prediction_seal"].write_text(
+        "0" * 64 + f"  {paths['prediction_json'].name}\n",
+        encoding="utf-8",
+    )
+    second = verify_delivery(**paths, output_json=output)
+    assert not second["passed"]
+    assert not second["checks"]["valid_prediction_seal"]
+    paths = _synthetic_delivery(tmp_path)
+    leaked = json.loads(paths["prediction_json"].read_text(encoding="utf-8"))
+    leaked["R4"] = 0.3
+    _write_json(paths["prediction_json"], leaked)
+    paths["prediction_seal"].write_text(
+        f"{_hash(paths['prediction_json'])}  {paths['prediction_json'].name}\n",
+        encoding="utf-8",
+    )
+    third = verify_delivery(**paths, output_json=output)
+    assert not third["passed"]
+    assert not third["checks"]["prediction_has_no_outcome_leakage"]
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_susy_hodge_figure_v7.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_susy_hodge_figure_v7.py
new file mode 100644
index 000000000..7e7e5e749
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_susy_hodge_figure_v7.py
@@ -0,0 +1,98 @@
+"""Publication-figure and source-backed report tests for SUSY/Hodge v7."""
+
+from __future__ import annotations
+
+import json
+from pathlib import Path
+
+import matplotlib.image as mpimg
+
+from make_susy_hodge_figure_v7 import make_figure
+
+
+def _write_sources(tmp_path: Path) -> tuple[Path, Path]:
+    groups = []
+    for N in (8, 10, 12):
+        for sector, balance in (("central", 1.0), ("adjacent", 0.1)):
+            for panel_index, panel in enumerate(("sparse", "isotropic")):
+                observed = 0.34 - 0.01 * (N - 8) - 0.03 * panel_index
+                groups.append(
+                    {
+                        "N": N,
+                        "sector": sector,
+                        "panel_kind": panel,
+                        "observed_median": observed,
+                        "physical_bootstrap_interval": [
+                            observed - 0.01,
+                            observed + 0.01,
+                        ],
+                        "collapsed_prediction_interval": [0.12, 0.13, 0.14],
+                        "hodge_prediction_interval": [0.14, 0.15, 0.16],
+                        "collapsed_covered": False,
+                        "hodge_covered": False,
+                        "median_hodge_balance": balance,
+                    }
+                )
+    pilot = {
+        "version": "v7",
+        "uncertainty_unit": "complete_disorder_realization",
+        "groups": groups,
+        "checks": {"synthetic_complete_grid": True},
+        "passed": True,
+    }
+    primary = []
+    for sector, observed in (("central", 0.29), ("adjacent", 0.31)):
+        primary.append(
+            {
+                "N": 14,
+                "sector": sector,
+                "panel_kind": "sparse",
+                "observed_median": observed,
+                "physical_bootstrap_interval": [observed - 0.01, observed + 0.01],
+                "collapsed_prediction_interval": [0.10, 0.11, 0.12],
+                "hodge_prediction_interval": [0.13, 0.14, 0.15],
+                "collapsed_covered": False,
+                "hodge_covered": False,
+                "robust_outside_both": True,
+            }
+        )
+    inference = {
+        "version": "v7",
+        "prediction_sha256": "a" * 64,
+        "selected_branch": "cohomological_non_gaussian_class",
+        "primary_pair": primary,
+        "checks": {"valid_prediction_seal": True},
+        "passed": True,
+    }
+    pilot_path = tmp_path / "pilot.json"
+    inference_path = tmp_path / "inference.json"
+    pilot_path.write_text(json.dumps(pilot), encoding="utf-8")
+    inference_path.write_text(json.dumps(inference), encoding="utf-8")
+    return pilot_path, inference_path
+
+
+def test_figure_and_report_are_provenance_complete(tmp_path: Path) -> None:
+    pilot, inference = _write_sources(tmp_path)
+    pdf = tmp_path / "figure.pdf"
+    png = tmp_path / "figure.png"
+    manifest_path = tmp_path / "figure.json"
+    report_path = tmp_path / "report.md"
+    manifest = make_figure(
+        pilot_json=pilot,
+        inference_json=inference,
+        output_pdf=pdf,
+        output_png=png,
+        manifest_json=manifest_path,
+        report_md=report_path,
+    )
+    assert all(manifest["checks"].values())
+    assert manifest["selected_branch"] == "cohomological_non_gaussian_class"
+    assert manifest["pilot_group_count"] == 12
+    assert pdf.is_file() and png.is_file() and manifest_path.is_file()
+    image = mpimg.imread(png)
+    assert image.shape[1] >= 2000
+    report = report_path.read_text(encoding="utf-8")
+    assert "## Established" in report
+    assert "## Not established" in report
+    assert "cohomological_non_gaussian_class" in report
+    assert "](https://" in report
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_susy_hodge_manuscript_assets_v7.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_susy_hodge_manuscript_assets_v7.py
new file mode 100644
index 000000000..a75b1dfe7
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_susy_hodge_manuscript_assets_v7.py
@@ -0,0 +1,104 @@
+"""Fail-closed manuscript-asset tests for the SUSY/Hodge result."""
+
+from __future__ import annotations
+
+import json
+from pathlib import Path
+
+import pytest
+
+from make_susy_hodge_manuscript_assets_v7 import build_manuscript_assets
+from run_susy_hodge_geometric_eth_v7 import sha256
+
+
+def _write_json(path: Path, payload: dict) -> None:
+    path.write_text(json.dumps(payload), encoding="utf-8")
+
+
+def _sources(root: Path, *, branch: str = "hodge_resolved_geometric_eth") -> dict:
+    groups = [
+        {
+            "N": size,
+            "sector": sector,
+            "panel_kind": panel,
+            "collapsed_covered": False,
+            "hodge_covered": False,
+        }
+        for size in (8, 10, 12)
+        for sector in ("central", "adjacent")
+        for panel in ("sparse", "isotropic")
+    ]
+    primary = [
+        {
+            "N": 14,
+            "sector": sector,
+            "panel_kind": "sparse",
+            "observed_median": 0.3,
+            "physical_bootstrap_interval": [0.29, 0.31],
+            "collapsed_prediction_interval": [0.1, 0.12, 0.14],
+            "hodge_prediction_interval": [0.28, 0.30, 0.32],
+        }
+        for sector in ("central", "adjacent")
+    ]
+    pilot = root / "pilot.json"
+    inference = root / "inference.json"
+    figure = root / "figure.pdf"
+    figure_manifest = root / "figure.json"
+    common = {"version": "v7", "checks": {"passed": True}, "passed": True}
+    _write_json(pilot, {**common, "groups": groups})
+    _write_json(
+        inference,
+        {
+            **common,
+            "selected_branch": branch,
+            "prediction_sha256": "a" * 64,
+            "primary_pair": primary,
+        },
+    )
+    figure.write_bytes(b"%PDF-1.4\nsynthetic\n")
+    _write_json(
+        figure_manifest,
+        {
+            **common,
+            "selected_branch": branch,
+            "inputs": {
+                pilot.name: sha256(pilot),
+                inference.name: sha256(inference),
+            },
+            "outputs": {figure.name: sha256(figure)},
+        },
+    )
+    return {
+        "pilot_json": pilot,
+        "inference_json": inference,
+        "figure_manifest_json": figure_manifest,
+        "figure_pdf": figure,
+        "results_tex": root / "results.tex",
+        "figure_target": root / "copied.pdf",
+        "manifest_json": root / "assets.json",
+    }
+
+
+def test_build_manuscript_assets_enables_results_after_hash_audit(
+    tmp_path: Path,
+) -> None:
+    paths = _sources(tmp_path)
+    manifest = build_manuscript_assets(**paths)
+
+    assert manifest["passed"]
+    text = paths["results_tex"].read_text(encoding="utf-8")
+    assert r"\heldoutcompletetrue" in text
+    assert r"\heldoutcompletefalse" not in text
+    assert r"hodge\_resolved\_geometric\_eth" in text
+    assert r"\newcommand{\HeldoutAdjacentPhysical}" in text
+    assert r"\newcommand{\HeldoutCentralHodge}" in text
+    assert sha256(paths["figure_pdf"]) == sha256(paths["figure_target"])
+
+
+def test_build_manuscript_assets_rejects_feasibility_failure(
+    tmp_path: Path,
+) -> None:
+    paths = _sources(tmp_path, branch="feasibility_failure")
+
+    with pytest.raises(ValueError, match="not publishable"):
+        build_manuscript_assets(**paths)
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_susy_hodge_manuscript_audit_v7.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_susy_hodge_manuscript_audit_v7.py
new file mode 100644
index 000000000..616d8c23e
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_susy_hodge_manuscript_audit_v7.py
@@ -0,0 +1,105 @@
+"""Tests for the compiled response-complex manuscript audit."""
+
+from __future__ import annotations
+
+import json
+from pathlib import Path
+
+from run_susy_hodge_geometric_eth_v7 import sha256
+from verify_susy_hodge_manuscript_v7 import verify_manuscript
+
+
+def test_manuscript_audit_checks_activation_hashes_and_pdf(tmp_path: Path) -> None:
+    main = tmp_path / "main.tex"
+    results = tmp_path / "results_v7.tex"
+    figure = tmp_path / "figure.pdf"
+    pdf = tmp_path / "main.pdf"
+    archive = tmp_path / "archive.pdf"
+    log = tmp_path / "main.log"
+    supplement = tmp_path / "supplement.tex"
+    supplement_pdf = tmp_path / "supplement.pdf"
+    supplement_archive = tmp_path / "supplement-archive.pdf"
+    supplement_log = tmp_path / "supplement.log"
+    manifest = tmp_path / "assets.json"
+    output = tmp_path / "audit.json"
+    main.write_text(r"\input{generated/results_v7.tex}", encoding="utf-8")
+    supplement.write_text(
+        r"\input{generated/results_v7.tex}", encoding="utf-8"
+    )
+    results.write_text(
+        "\n".join(
+            (
+                r"\newif\ifheldoutcomplete",
+                r"\heldoutcompletetrue",
+                r"\newcommand{\HeldoutBranch}{hodge\_resolved\_geometric\_eth}",
+            )
+        ),
+        encoding="utf-8",
+    )
+    figure.write_bytes(b"%PDF-1.4\n" + b"x" * 2048 + b"\n%%EOF\n")
+    pdf.write_bytes(b"%PDF-1.4\n" + b"y" * 2048 + b"\n%%EOF\n")
+    archive.write_bytes(pdf.read_bytes())
+    log.write_text("Output written on main.pdf", encoding="utf-8")
+    supplement_pdf.write_bytes(
+        b"%PDF-1.4\n" + b"z" * 2048 + b"\n%%EOF\n"
+    )
+    supplement_archive.write_bytes(supplement_pdf.read_bytes())
+    supplement_log.write_text(
+        "Output written on supplement.pdf", encoding="utf-8"
+    )
+    manifest.write_text(
+        json.dumps(
+            {
+                "version": "v7",
+                "selected_branch": "hodge_resolved_geometric_eth",
+                "prediction_sha256": "a" * 64,
+                "outputs": {
+                    results.name: sha256(results),
+                    figure.name: sha256(figure),
+                },
+                "checks": {"assets": True},
+                "passed": True,
+            }
+        ),
+        encoding="utf-8",
+    )
+
+    payload = verify_manuscript(
+        asset_manifest_json=manifest,
+        main_tex=main,
+        results_tex=results,
+        figure_pdf=figure,
+        main_pdf=pdf,
+        archive_pdf=archive,
+        main_log=log,
+        supplement_tex=supplement,
+        supplement_pdf=supplement_pdf,
+        supplement_archive_pdf=supplement_archive,
+        supplement_log=supplement_log,
+        output_json=output,
+    )
+
+    assert payload["passed"]
+
+    results.write_text(
+        results.read_text(encoding="utf-8")
+        + "\n"
+        + r"\heldoutcompletefalse",
+        encoding="utf-8",
+    )
+    rejected = verify_manuscript(
+        asset_manifest_json=manifest,
+        main_tex=main,
+        results_tex=results,
+        figure_pdf=figure,
+        main_pdf=pdf,
+        archive_pdf=archive,
+        main_log=log,
+        supplement_tex=supplement,
+        supplement_pdf=supplement_pdf,
+        supplement_archive_pdf=supplement_archive,
+        supplement_log=supplement_log,
+        output_json=output,
+    )
+    assert not rejected["passed"]
+    assert not rejected["checks"]["heldout_result_enabled"]
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_susy_hodge_merge_v7.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_susy_hodge_merge_v7.py
new file mode 100644
index 000000000..675fcfd38
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_susy_hodge_merge_v7.py
@@ -0,0 +1,88 @@
+"""Tests for the compact sequential-pilot merge."""
+
+from __future__ import annotations
+
+import json
+from pathlib import Path
+
+import numpy as np
+import pytest
+
+from merge_susy_hodge_pilot_v7 import merge_pilot_artifacts
+from run_susy_hodge_geometric_eth_v7 import sha256
+
+
+def _source(root: Path, size: int) -> tuple[Path, Path]:
+    json_path = root / f"N{size}.json"
+    npz_path = root / f"N{size}.npz"
+    arrays = {}
+    groups = []
+    for sector in ("central", "adjacent"):
+        for panel in ("sparse", "isotropic"):
+            prefix = f"N{size}_{sector}_{panel}"
+            arrays[f"{prefix}_physical"] = np.arange(3.0) + size
+            arrays[f"{prefix}_physical_bootstrap"] = np.arange(5.0) + size
+            arrays[f"{prefix}_collapsed_null"] = np.arange(4.0) + size
+            arrays[f"{prefix}_hodge_null"] = np.arange(4.0) + size + 0.5
+            groups.append(
+                {
+                    "N": size,
+                    "sector": sector,
+                    "panel_kind": panel,
+                    "realizations": 3,
+                }
+            )
+    np.savez_compressed(npz_path, **arrays)
+    json_path.write_text(
+        json.dumps(
+            {
+                "version": "v7",
+                "uncertainty_unit": "complete_disorder_realization",
+                "null_replicates": 4,
+                "physical_bootstrap_replicates": 5,
+                "prediction_coverage": 0.975,
+                "groups": groups,
+                "safe_covariates_sha256": f"safe-{size}",
+                "arrays_sha256": sha256(npz_path),
+                "checks": {"source_passed": True},
+                "passed": True,
+            }
+        ),
+        encoding="utf-8",
+    )
+    return json_path, npz_path
+
+
+def test_merge_pilot_artifacts_preserves_complete_grid(tmp_path: Path) -> None:
+    first_json, first_npz = _source(tmp_path, 8)
+    second_json, second_npz = _source(tmp_path, 10)
+    output_json = tmp_path / "combined.json"
+    output_npz = tmp_path / "combined.npz"
+
+    result = merge_pilot_artifacts(
+        [first_json, second_json],
+        [first_npz, second_npz],
+        output_json=output_json,
+        output_npz=output_npz,
+        expected_sizes=(8, 10),
+    )
+
+    assert result["passed"]
+    assert len(result["groups"]) == 8
+    assert result["arrays_sha256"] == sha256(output_npz)
+    with np.load(output_npz) as arrays:
+        assert len(arrays.files) == 32
+
+
+def test_merge_pilot_artifacts_rejects_tampered_npz(tmp_path: Path) -> None:
+    json_path, npz_path = _source(tmp_path, 8)
+    np.savez_compressed(npz_path, changed=np.arange(2.0))
+
+    with pytest.raises(ValueError, match="hash mismatch"):
+        merge_pilot_artifacts(
+            [json_path],
+            [npz_path],
+            output_json=tmp_path / "combined.json",
+            output_npz=tmp_path / "combined.npz",
+            expected_sizes=(8,),
+        )
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_susy_hodge_null_bank_v7.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_susy_hodge_null_bank_v7.py
new file mode 100644
index 000000000..0e9b9f454
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_susy_hodge_null_bank_v7.py
@@ -0,0 +1,90 @@
+"""Safe per-realization null banks for parallel SUSY/Hodge production."""
+
+from __future__ import annotations
+
+import json
+from pathlib import Path
+
+import numpy as np
+
+from run_susy_hodge_geometric_eth_v7 import prepare_realization, run_panel
+from run_susy_hodge_null_bank_v7 import null_bank_paths, write_null_bank
+
+
+def test_null_bank_uses_only_safe_panel_files(tmp_path: Path) -> None:
+    case = (6, "central", 0, "sparse")
+    prepare_realization(6, "central", 0, root=tmp_path, reduced=True, force=True)
+    run_panel(*case, root=tmp_path, reduced=True, force=True)
+    outcome_path = (
+        tmp_path / "panels" / "N6_central_seed000_sparse_v7.outcome.json"
+    )
+    outcome_path.unlink()
+    result = write_null_bank(
+        *case,
+        checkpoint_root=tmp_path,
+        output_root=tmp_path / "banks",
+        draws=8,
+        force=True,
+    )
+    assert result["passed"]
+    metadata_path, arrays_path = null_bank_paths(
+        tmp_path / "banks",
+        *case,
+    )
+    text = metadata_path.read_text(encoding="utf-8").lower()
+    assert "r4" not in text
+    assert "four_point" not in text
+    assert "connected" not in text
+    metadata = json.loads(metadata_path.read_text(encoding="utf-8"))
+    assert metadata["draws"] == 8
+    with np.load(arrays_path) as arrays:
+        assert arrays["collapsed_null"].shape == (8,)
+        assert arrays["hodge_null"].shape == (8,)
+        assert np.all(np.isfinite(arrays["collapsed_null"]))
+        assert np.all(np.isfinite(arrays["hodge_null"]))
+
+
+def test_null_bank_is_deterministic_and_hash_checked(tmp_path: Path) -> None:
+    case = (6, "adjacent", 1, "isotropic")
+    prepare_realization(6, "adjacent", 1, root=tmp_path, reduced=True, force=True)
+    run_panel(*case, root=tmp_path, reduced=True, force=True)
+    first_root = tmp_path / "first"
+    second_root = tmp_path / "second"
+    first = write_null_bank(
+        *case,
+        checkpoint_root=tmp_path,
+        output_root=first_root,
+        draws=8,
+        force=True,
+    )
+    second = write_null_bank(
+        *case,
+        checkpoint_root=tmp_path,
+        output_root=second_root,
+        draws=8,
+        force=True,
+    )
+    assert first["collapsed_sha256"] == second["collapsed_sha256"]
+    assert first["hodge_sha256"] == second["hodge_sha256"]
+
+
+def test_pilot_slurm_array_maps_complete_n10_n12_grid() -> None:
+    slurm_root = Path(__file__).resolve().parents[1] / "slurm"
+    array = (slurm_root / "run_susy_hodge_pilot_v7_array.sbatch").read_text(
+        encoding="utf-8"
+    )
+    submit = (slurm_root / "submit_susy_hodge_pilot_v7.sh").read_text(
+        encoding="utf-8"
+    )
+    assert 'if [[ "$TASK_ID" -lt 96 ]]' in array
+    assert "COUNT=48" in array and "COUNT=32" in array
+    assert "LOCAL_ID=$((TASK_ID - 96))" in array
+    assert array.count("run_susy_hodge_null_bank_v7.py") == 1
+    assert "for PANEL_KIND in sparse isotropic" in array
+    assert "TASK_ID=ARRAY_ID; TASK_ID<160; TASK_ID+=8" in array
+    assert "--array=0-7%8" in submit
+    logical_ids = {
+        task_id for array_id in range(8) for task_id in range(array_id, 160, 8)
+    }
+    assert logical_ids == set(range(160))
+    assert "sbatch" in submit
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_susy_hodge_pilot_v7.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_susy_hodge_pilot_v7.py
new file mode 100644
index 000000000..45eca8e8a
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_susy_hodge_pilot_v7.py
@@ -0,0 +1,71 @@
+"""Reduced sequential-pilot aggregation for the SUSY/Hodge program."""
+
+from __future__ import annotations
+
+import json
+from pathlib import Path
+
+import numpy as np
+
+from run_susy_hodge_geometric_eth_v7 import (
+    aggregate_pilot,
+    prepare_realization,
+    run_panel,
+)
+
+
+def test_reduced_pilot_uses_complete_realizations_and_is_reproducible(
+    tmp_path: Path,
+) -> None:
+    cases: list[tuple[int, str, int, str]] = []
+    for sector in ("central", "adjacent"):
+        for realization in range(2):
+            prepare_realization(
+                6,
+                sector,
+                realization,
+                root=tmp_path,
+                reduced=True,
+                force=True,
+            )
+            for panel_kind in ("sparse", "isotropic"):
+                case = (6, sector, realization, panel_kind)
+                run_panel(*case, root=tmp_path, reduced=True, force=True)
+                cases.append(case)
+
+    first = aggregate_pilot(
+        cases,
+        root=tmp_path,
+        null_samples=12,
+        null_draws_per_realization=6,
+        seed=109,
+        safe_output_json=tmp_path / "safe_first.json",
+        output_json=tmp_path / "pilot_first.json",
+        output_npz=tmp_path / "pilot_first.npz",
+    )
+    second = aggregate_pilot(
+        cases,
+        root=tmp_path,
+        null_samples=12,
+        null_draws_per_realization=6,
+        seed=109,
+        safe_output_json=tmp_path / "safe_second.json",
+        output_json=tmp_path / "pilot_second.json",
+        output_npz=tmp_path / "pilot_second.npz",
+    )
+    assert first["passed"] and second["passed"]
+    assert len(first["cases"]) == 4
+    assert all(record["realizations"] == 2 for record in first["cases"])
+    with np.load(tmp_path / "pilot_first.npz") as first_arrays:
+        with np.load(tmp_path / "pilot_second.npz") as second_arrays:
+            assert set(first_arrays.files) == set(second_arrays.files)
+            for key in first_arrays.files:
+                assert np.array_equal(first_arrays[key], second_arrays[key])
+            assert first_arrays["N6_central_sparse_physical"].shape == (2,)
+            assert first_arrays["N6_central_sparse_collapsed_null"].shape == (12,)
+            assert first_arrays["N6_central_sparse_hodge_null"].shape == (12,)
+    safe_text = (tmp_path / "safe_first.json").read_text(encoding="utf-8").lower()
+    assert "r4" not in safe_text
+    payload = json.loads((tmp_path / "pilot_first.json").read_text(encoding="utf-8"))
+    assert payload["uncertainty_unit"] == "complete_disorder_realization"
+    assert payload["null_draws_per_realization"] == 6
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_susy_hodge_runner_v7.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_susy_hodge_runner_v7.py
new file mode 100644
index 000000000..f7dc69d97
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/tests/test_susy_hodge_runner_v7.py
@@ -0,0 +1,110 @@
+"""Reduced end-to-end tests for the sealed SUSY/Hodge runner."""
+
+from __future__ import annotations
+
+import json
+from pathlib import Path
+
+import pytest
+
+from run_susy_hodge_geometric_eth_v7 import (
+    panel_paths,
+    prepare_realization,
+    run_panel,
+    seal_file_hash,
+    unseal_outcomes,
+    write_safe_covariates,
+)
+
+
+def test_reduced_runner_splits_safe_hodge_data_from_r4(tmp_path: Path) -> None:
+    case = (6, "central", 0, "sparse")
+    kernel = prepare_realization(
+        6,
+        "central",
+        0,
+        root=tmp_path,
+        reduced=True,
+        force=True,
+    )
+    assert all(kernel["checks"].values())
+    summary = run_panel(
+        *case,
+        root=tmp_path,
+        reduced=True,
+        force=True,
+    )
+    assert all(summary["safe"]["checks"].values())
+    safe_json, safe_npz, outcome_json = panel_paths(tmp_path, *case)
+    safe_text = safe_json.read_text(encoding="utf-8")
+    safe_lower = safe_text.lower()
+    assert "r4" not in safe_lower
+    assert "four_point" not in safe_lower
+    assert "connected" not in safe_lower
+    assert '"R4"' in outcome_json.read_text(encoding="utf-8")
+    with pytest.raises(KeyError):
+        with __import__("numpy").load(safe_npz) as arrays:
+            _ = arrays["minus"]
+
+    covariate_path = tmp_path / "covariates.json"
+    covariates = write_safe_covariates(
+        [case],
+        root=tmp_path,
+        output_json=covariate_path,
+    )
+    assert covariates["checks"]["no_outcome_leakage"]
+    assert "r4" not in covariate_path.read_text(encoding="utf-8").lower()
+
+
+def test_unseal_requires_intact_prediction_and_outcome_identity(tmp_path: Path) -> None:
+    case = (6, "central", 0, "isotropic")
+    prepare_realization(6, "central", 0, root=tmp_path, reduced=True, force=True)
+    run_panel(*case, root=tmp_path, reduced=True, force=True)
+    prediction = tmp_path / "prediction.json"
+    prediction.write_text(json.dumps({"prediction": "frozen"}), encoding="utf-8")
+    seal = tmp_path / "prediction.sha256"
+    with pytest.raises(FileNotFoundError, match="prediction hash seal"):
+        unseal_outcomes(
+            [case],
+            root=tmp_path,
+            prediction_json=prediction,
+            prediction_seal=seal,
+            output_json=tmp_path / "outcomes.json",
+            output_npz=tmp_path / "outcomes.npz",
+        )
+    seal_file_hash(prediction, seal)
+    prediction.write_text(json.dumps({"prediction": "changed"}), encoding="utf-8")
+    with pytest.raises(ValueError, match="prediction hash seal mismatch"):
+        unseal_outcomes(
+            [case],
+            root=tmp_path,
+            prediction_json=prediction,
+            prediction_seal=seal,
+            output_json=tmp_path / "outcomes.json",
+            output_npz=tmp_path / "outcomes.npz",
+        )
+    prediction.write_text(json.dumps({"prediction": "frozen"}), encoding="utf-8")
+    seal_file_hash(prediction, seal)
+    result = unseal_outcomes(
+        [case],
+        root=tmp_path,
+        prediction_json=prediction,
+        prediction_seal=seal,
+        output_json=tmp_path / "outcomes.json",
+        output_npz=tmp_path / "outcomes.npz",
+    )
+    assert result["passed"]
+
+    _, _, outcome_path = panel_paths(tmp_path, *case)
+    outcome = json.loads(outcome_path.read_text(encoding="utf-8"))
+    outcome["safe_identity_hash"] = "0" * 64
+    outcome_path.write_text(json.dumps(outcome), encoding="utf-8")
+    with pytest.raises(ValueError, match="outcome identity mismatch"):
+        unseal_outcomes(
+            [case],
+            root=tmp_path,
+            prediction_json=prediction,
+            prediction_seal=seal,
+            output_json=tmp_path / "corrupt.json",
+            output_npz=tmp_path / "corrupt.npz",
+        )
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/verify_susy_hodge_delivery_v7.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/verify_susy_hodge_delivery_v7.py
new file mode 100644
index 000000000..1ab2d1592
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/verify_susy_hodge_delivery_v7.py
@@ -0,0 +1,302 @@
+#!/usr/bin/env python3
+"""Fail-closed scientific and provenance audit for SUSY/Hodge v7."""
+
+from __future__ import annotations
+
+import json
+from datetime import datetime, timezone
+from pathlib import Path
+from typing import Any
+
+from analyze_susy_hodge_geometric_eth_v7 import (
+    N14_INFERENCE_JSON,
+    N14_PREDICTION_JSON,
+    N14_PREDICTION_NPZ,
+    N14_PREDICTION_SEAL,
+    N14_SAFE_JSON,
+    N14_UNSEALED_JSON,
+    select_frozen_branch,
+)
+from generate_susy_hodge_controls_v7 import OUTPUT_JSON as CONTROLS_JSON
+from merge_susy_hodge_pilot_v7 import (
+    OUTPUT_JSON as PILOT_BANK_JSON,
+    OUTPUT_NPZ as PILOT_BANK_NPZ,
+)
+from make_susy_hodge_figure_v7 import (
+    FIGURE_PDF,
+    FIGURE_PNG,
+    MANIFEST_JSON as FIGURE_MANIFEST,
+    REPORT_MD,
+)
+from run_susy_hodge_geometric_eth_v7 import _atomic_json, sha256
+
+
+SCRIPT_ROOT = Path(__file__).resolve().parent
+OUTPUT_JSON = SCRIPT_ROOT / "output" / "susy_hodge_delivery_audit_v7.json"
+FORBIDDEN_SAFE_TOKENS = ("r4", "four_point", "connected")
+
+
+def _load(path: Path) -> dict[str, Any] | None:
+    try:
+        payload = json.loads(Path(path).read_text(encoding="utf-8"))
+    except (FileNotFoundError, json.JSONDecodeError, OSError):
+        return None
+    return payload if isinstance(payload, dict) else None
+
+
+def _passed(payload: dict[str, Any] | None) -> bool:
+    return bool(
+        payload
+        and payload.get("version") == "v7"
+        and payload.get("passed")
+        and all(payload.get("checks", {}).values())
+    )
+
+
+def _matches_hash(path: Path, expected: object) -> bool:
+    try:
+        return isinstance(expected, str) and sha256(path) == expected
+    except (FileNotFoundError, OSError):
+        return False
+
+
+def _seal_hash(source: Path, seal: Path) -> str | None:
+    try:
+        fields = Path(seal).read_text(encoding="utf-8").strip().split()
+    except (FileNotFoundError, OSError):
+        return None
+    if len(fields) != 2 or fields[1] != Path(source).name:
+        return None
+    return fields[0] if _matches_hash(source, fields[0]) else None
+
+
+def _safe_serialization(path: Path) -> bool:
+    try:
+        serialized = Path(path).read_text(encoding="utf-8").lower()
+    except (FileNotFoundError, OSError):
+        return False
+    return not any(token in serialized for token in FORBIDDEN_SAFE_TOKENS)
+
+
+def _timestamp_order(
+    prediction: dict[str, Any] | None,
+    unsealed: dict[str, Any] | None,
+) -> bool:
+    try:
+        prediction_time = datetime.fromisoformat(str(prediction["generated_utc"]))
+        unsealed_time = datetime.fromisoformat(str(unsealed["unsealed_utc"]))
+    except (KeyError, TypeError, ValueError):
+        return False
+    return unsealed_time > prediction_time
+
+
+def _exact_grid(payload: dict[str, Any] | None) -> bool:
+    if not payload:
+        return False
+    expected = {
+        (N, sector, panel)
+        for N in (8, 10, 12)
+        for sector in ("central", "adjacent")
+        for panel in ("sparse", "isotropic")
+    }
+    try:
+        observed = {
+            (int(item["N"]), str(item["sector"]), str(item["panel_kind"]))
+            for item in payload["groups"]
+        }
+    except (KeyError, TypeError, ValueError):
+        return False
+    return observed == expected
+
+
+def _primary_pair(payload: dict[str, Any] | None, key: str) -> bool:
+    if not payload:
+        return False
+    try:
+        observed = {
+            (int(item["N"]), str(item["sector"]), str(item["panel_kind"]))
+            for item in payload[key]
+        }
+    except (KeyError, TypeError, ValueError):
+        return False
+    return observed == {(14, "central", "sparse"), (14, "adjacent", "sparse")}
+
+
+def _recomputed_branch(inference: dict[str, Any] | None) -> str | None:
+    if not inference:
+        return None
+    try:
+        records = inference["primary_pair"]
+        collapsed = all(bool(item["collapsed_covered"]) for item in records)
+        hodge = all(bool(item["hodge_covered"]) for item in records)
+        structured = bool(inference.get("structured_indistinguishable", False))
+        resolved = bool(
+            inference.get("checks", {}).get("registered_branch_resolved", False)
+        )
+    except (KeyError, TypeError):
+        return None
+    return select_frozen_branch(collapsed, hodge, structured, resolved)
+
+
+def _figure_hashes(
+    manifest: dict[str, Any] | None,
+    *,
+    pilot_json: Path,
+    inference_json: Path,
+    figure_pdf: Path,
+    figure_png: Path,
+    report_md: Path,
+) -> bool:
+    if not manifest:
+        return False
+    inputs = manifest.get("inputs", {})
+    outputs = manifest.get("outputs", {})
+    return all(
+        (
+            _matches_hash(
+                pilot_json, inputs.get(Path(pilot_json).name)
+            ),
+            _matches_hash(
+                inference_json, inputs.get(Path(inference_json).name)
+            ),
+            _matches_hash(
+                figure_pdf, outputs.get(Path(figure_pdf).name)
+            ),
+            _matches_hash(
+                figure_png, outputs.get(Path(figure_png).name)
+            ),
+            _matches_hash(
+                report_md, outputs.get(Path(report_md).name)
+            ),
+        )
+    )
+
+
+def verify_delivery(
+    *,
+    pilot_json: Path = PILOT_BANK_JSON,
+    pilot_npz: Path = PILOT_BANK_NPZ,
+    safe_json: Path = N14_SAFE_JSON,
+    prediction_json: Path = N14_PREDICTION_JSON,
+    prediction_npz: Path = N14_PREDICTION_NPZ,
+    prediction_seal: Path = N14_PREDICTION_SEAL,
+    unsealed_json: Path = N14_UNSEALED_JSON,
+    inference_json: Path = N14_INFERENCE_JSON,
+    controls_json: Path = CONTROLS_JSON,
+    figure_manifest: Path = FIGURE_MANIFEST,
+    figure_pdf: Path = FIGURE_PDF,
+    figure_png: Path = FIGURE_PNG,
+    report_md: Path = REPORT_MD,
+    output_json: Path = OUTPUT_JSON,
+) -> dict[str, Any]:
+    """Audit every compact artifact and return checks instead of trusting prose."""
+
+    paths = {
+        "pilot_json": Path(pilot_json),
+        "pilot_npz": Path(pilot_npz),
+        "safe_json": Path(safe_json),
+        "prediction_json": Path(prediction_json),
+        "prediction_npz": Path(prediction_npz),
+        "prediction_seal": Path(prediction_seal),
+        "unsealed_json": Path(unsealed_json),
+        "inference_json": Path(inference_json),
+        "controls_json": Path(controls_json),
+        "figure_manifest": Path(figure_manifest),
+        "figure_pdf": Path(figure_pdf),
+        "figure_png": Path(figure_png),
+        "report_md": Path(report_md),
+    }
+    pilot = _load(paths["pilot_json"])
+    safe = _load(paths["safe_json"])
+    prediction = _load(paths["prediction_json"])
+    unsealed = _load(paths["unsealed_json"])
+    inference = _load(paths["inference_json"])
+    controls = _load(paths["controls_json"])
+    figure = _load(paths["figure_manifest"])
+    seal_hash = _seal_hash(paths["prediction_json"], paths["prediction_seal"])
+    recomputed_branch = _recomputed_branch(inference)
+    try:
+        report_text = paths["report_md"].read_text(encoding="utf-8")
+    except (FileNotFoundError, OSError):
+        report_text = ""
+    checks = {
+        "all_required_files_exist": all(path.is_file() for path in paths.values()),
+        "pilot_passed": _passed(pilot),
+        "complete_pilot_grid": _exact_grid(pilot),
+        "pilot_array_hash": bool(pilot)
+        and _matches_hash(paths["pilot_npz"], pilot.get("arrays_sha256")),
+        "safe_covariates_passed": bool(safe) and bool(safe.get("passed")),
+        "safe_covariates_have_no_outcome_leakage": _safe_serialization(
+            paths["safe_json"]
+        ),
+        "prediction_passed": _passed(prediction),
+        "complete_prediction_primary_pair": _primary_pair(prediction, "primary_pair"),
+        "prediction_array_hash": bool(prediction)
+        and _matches_hash(
+            paths["prediction_npz"], prediction.get("prediction_arrays_sha256")
+        ),
+        "prediction_safe_covariate_hash": bool(prediction)
+        and _matches_hash(paths["safe_json"], prediction.get("safe_covariates_sha256")),
+        "prediction_has_no_outcome_leakage": _safe_serialization(
+            paths["prediction_json"]
+        ),
+        "valid_prediction_seal": seal_hash is not None,
+        "unsealed_passed": _passed(unsealed),
+        "prediction_precedes_unseal": _timestamp_order(prediction, unsealed),
+        "unsealed_references_prediction": bool(unsealed)
+        and seal_hash is not None
+        and unsealed.get("prediction_sha256") == seal_hash,
+        "inference_passed": _passed(inference),
+        "complete_inference_primary_pair": _primary_pair(inference, "primary_pair"),
+        "inference_references_prediction": bool(inference)
+        and seal_hash is not None
+        and inference.get("prediction_sha256") == seal_hash,
+        "selected_branch_recomputed": bool(inference)
+        and recomputed_branch == inference.get("selected_branch"),
+        "analytic_controls_passed": _passed(controls),
+        "curvature_atom_control": bool(controls)
+        and bool(controls.get("checks", {}).get("N6_curvature_atoms")),
+        "one_sided_control": bool(controls)
+        and bool(controls.get("checks", {}).get("one_sided_exact_regression")),
+        "figure_manifest_passed": _passed(figure),
+        "figure_and_report_hashes": _figure_hashes(
+            figure,
+            pilot_json=paths["pilot_json"],
+            inference_json=paths["inference_json"],
+            figure_pdf=paths["figure_pdf"],
+            figure_png=paths["figure_png"],
+            report_md=paths["report_md"],
+        ),
+        "figure_branch_matches_inference": bool(figure and inference)
+        and figure.get("selected_branch") == inference.get("selected_branch"),
+        "report_has_claim_boundary_and_sources": bool(inference)
+        and "## Established" in report_text
+        and "## Not established" in report_text
+        and "](https://" in report_text
+        and str(inference.get("selected_branch")) in report_text,
+    }
+    payload = {
+        "version": "v7",
+        "generated_utc": datetime.now(timezone.utc).isoformat(),
+        "selected_branch": inference.get("selected_branch") if inference else None,
+        "recomputed_branch": recomputed_branch,
+        "prediction_sha256": seal_hash,
+        "artifact_hashes": {
+            key: sha256(path) for key, path in paths.items() if path.is_file()
+        },
+        "checks": checks,
+        "passed": all(checks.values()),
+    }
+    _atomic_json(output_json, payload)
+    return payload
+
+
+def main() -> None:
+    payload = verify_delivery()
+    print(json.dumps(payload, indent=2, sort_keys=True))
+    if not payload["passed"]:
+        raise SystemExit(1)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/verify_susy_hodge_manuscript_v7.py b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/verify_susy_hodge_manuscript_v7.py
new file mode 100644
index 000000000..66e77d5d7
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/verify_susy_hodge_manuscript_v7.py
@@ -0,0 +1,197 @@
+#!/usr/bin/env python3
+"""Verify the result-bearing v7 manuscript after compilation."""
+
+from __future__ import annotations
+
+import json
+from datetime import datetime, timezone
+from pathlib import Path
+from typing import Any
+
+from make_susy_hodge_manuscript_assets_v7 import (
+    FIGURE_TARGET,
+    MANIFEST_JSON as ASSET_MANIFEST_JSON,
+    MANUSCRIPT_ROOT,
+    RESULTS_TEX,
+)
+from run_susy_hodge_geometric_eth_v7 import _atomic_json, sha256
+
+
+SCRIPT_ROOT = Path(__file__).resolve().parent
+OUTPUT_JSON = SCRIPT_ROOT / "output" / "susy_hodge_manuscript_audit_v7.json"
+ARCHIVE_PDF = SCRIPT_ROOT / "output" / "response_complex_memory_v7.pdf"
+SUPPLEMENT_TEX = MANUSCRIPT_ROOT / "supplement.tex"
+SUPPLEMENT_PDF = MANUSCRIPT_ROOT / "supplement.pdf"
+SUPPLEMENT_LOG = MANUSCRIPT_ROOT / "supplement.log"
+SUPPLEMENT_ARCHIVE_PDF = (
+    SCRIPT_ROOT / "output" / "response_complex_memory_supplement_v7.pdf"
+)
+MAIN_TEX = MANUSCRIPT_ROOT / "main.tex"
+MAIN_PDF = MANUSCRIPT_ROOT / "main.pdf"
+MAIN_LOG = MANUSCRIPT_ROOT / "main.log"
+
+
+def _load(path: Path) -> dict[str, Any] | None:
+    try:
+        payload = json.loads(Path(path).read_text(encoding="utf-8"))
+    except (FileNotFoundError, json.JSONDecodeError, OSError):
+        return None
+    return payload if isinstance(payload, dict) else None
+
+
+def _valid_pdf(path: Path) -> bool:
+    try:
+        data = Path(path).read_bytes()
+    except (FileNotFoundError, OSError):
+        return False
+    return (
+        len(data) > 1024
+        and data.startswith(b"%PDF-")
+        and b"%%EOF" in data[-1024:]
+    )
+
+
+def _matches_hash(path: Path, expected: object) -> bool:
+    try:
+        return isinstance(expected, str) and sha256(path) == expected
+    except (FileNotFoundError, OSError):
+        return False
+
+
+def _same_hash(first: Path, second: Path) -> bool:
+    try:
+        return sha256(first) == sha256(second)
+    except (FileNotFoundError, OSError):
+        return False
+
+
+def verify_manuscript(
+    *,
+    asset_manifest_json: Path = ASSET_MANIFEST_JSON,
+    main_tex: Path = MAIN_TEX,
+    results_tex: Path = RESULTS_TEX,
+    figure_pdf: Path = FIGURE_TARGET,
+    main_pdf: Path = MAIN_PDF,
+    archive_pdf: Path = ARCHIVE_PDF,
+    main_log: Path = MAIN_LOG,
+    supplement_tex: Path = SUPPLEMENT_TEX,
+    supplement_pdf: Path = SUPPLEMENT_PDF,
+    supplement_archive_pdf: Path = SUPPLEMENT_ARCHIVE_PDF,
+    supplement_log: Path = SUPPLEMENT_LOG,
+    output_json: Path = OUTPUT_JSON,
+) -> dict[str, Any]:
+    """Audit source activation, copied assets, compilation, and claim branch."""
+
+    manifest = _load(asset_manifest_json)
+    try:
+        main_source = Path(main_tex).read_text(encoding="utf-8")
+        supplement_source = Path(supplement_tex).read_text(encoding="utf-8")
+        result_source = Path(results_tex).read_text(encoding="utf-8")
+        log_text = Path(main_log).read_text(encoding="utf-8").lower()
+        supplement_log_text = Path(supplement_log).read_text(
+            encoding="utf-8"
+        ).lower()
+    except (FileNotFoundError, OSError):
+        main_source = ""
+        supplement_source = ""
+        result_source = ""
+        log_text = ""
+        supplement_log_text = ""
+    outputs = manifest.get("outputs", {}) if manifest else {}
+    branch = str(manifest.get("selected_branch", "")) if manifest else ""
+    checks = {
+        "asset_manifest_passed": bool(
+            manifest
+            and manifest.get("version") == "v7"
+            and manifest.get("passed")
+            and all(manifest.get("checks", {}).values())
+        ),
+        "result_source_hash": bool(manifest)
+        and _matches_hash(
+            Path(results_tex), outputs.get(Path(results_tex).name)
+        ),
+        "figure_source_hash": bool(manifest)
+        and _matches_hash(
+            Path(figure_pdf), outputs.get(Path(figure_pdf).name)
+        ),
+        "main_uses_generated_results": r"\input{generated/results_v7.tex}"
+        in main_source,
+        "supplement_uses_generated_results": r"\input{generated/results_v7.tex}"
+        in supplement_source,
+        "heldout_result_enabled": r"\heldoutcompletetrue" in result_source
+        and r"\heldoutcompletefalse" not in result_source,
+        "selected_branch_in_source": bool(branch)
+        and branch.replace("_", r"\_") in result_source,
+        "compiled_pdf_structure": _valid_pdf(main_pdf),
+        "archived_pdf_exact": _valid_pdf(archive_pdf)
+        and _same_hash(Path(archive_pdf), Path(main_pdf)),
+        "compiled_supplement_structure": _valid_pdf(supplement_pdf),
+        "archived_supplement_exact": _valid_pdf(supplement_archive_pdf)
+        and _same_hash(Path(supplement_archive_pdf), Path(supplement_pdf)),
+        "clean_latex_log": bool(log_text)
+        and not any(
+            token in log_text
+            for token in (
+                "undefined citation",
+                "undefined references",
+                "overfull \\hbox",
+                "overfull \\vbox",
+                "underfull \\hbox",
+                "emergency stop",
+                "fatal error",
+            )
+        ),
+        "clean_supplement_log": bool(supplement_log_text)
+        and not any(
+            token in supplement_log_text
+            for token in (
+                "undefined citation",
+                "undefined references",
+                "overfull \\hbox",
+                "overfull \\vbox",
+                "underfull \\hbox",
+                "emergency stop",
+                "fatal error",
+            )
+        ),
+    }
+    payload = {
+        "version": "v7",
+        "generated_utc": datetime.now(timezone.utc).isoformat(),
+        "selected_branch": branch or None,
+        "prediction_sha256": (
+            manifest.get("prediction_sha256") if manifest else None
+        ),
+        "artifact_hashes": {
+            path.name: sha256(path)
+            for path in (
+                Path(asset_manifest_json),
+                Path(main_tex),
+                Path(results_tex),
+                Path(figure_pdf),
+                Path(main_pdf),
+                Path(archive_pdf),
+                Path(main_log),
+                Path(supplement_tex),
+                Path(supplement_pdf),
+                Path(supplement_archive_pdf),
+                Path(supplement_log),
+            )
+            if path.is_file()
+        },
+        "checks": checks,
+        "passed": all(checks.values()),
+    }
+    _atomic_json(output_json, payload)
+    return payload
+
+
+def main() -> None:
+    payload = verify_manuscript()
+    print(json.dumps(payload, indent=2, sort_keys=True))
+    if not payload["passed"]:
+        raise SystemExit(1)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/tracks/mps/solutions/Wander-276/research/README.md b/tracks/mps/solutions/Wander-276/research/README.md
index 62e85b34f..6b546d497 100644
--- a/tracks/mps/solutions/Wander-276/research/README.md
+++ b/tracks/mps/solutions/Wander-276/research/README.md
@@ -1,69 +1,107 @@
 # Chaos of Quantum Geometry
 
-> **Exact degeneracy turns quantum geometry into the signal.**
+> **Exact degeneracy removes spectral diagnostics, not state-space complexity.**
 
-![Exact spectral flatness and an emergent geometric ramp](01_task_folder/task_05/script/output/figure_1_spectral_silence_v2.png)
+![Hodge-resolved Geometric ETH evidence](01_task_folder/task_05/script/output/figure_susy_hodge_geometric_eth_v7.png)
 
-An exactly degenerate quantum manifold carries a flat internal energy spectrum. This project shows that its state-space geometry remains richly informative: non-Abelian Berry curvature, the quantum metric, response-channel cumulants, Chern numbers, and Wilson holonomy resolve a hierarchy of correlations hidden from energy spacings.
+This project studies quantum chaos as a property of how an exactly degenerate protected manifold moves over coupling space. The response amplitudes
 
-The project begins with Chen, Colin-Ellerin, Mamroud, and Papadodimas, [“Chaos of Berry curvature for BPS microstates”](https://arxiv.org/abs/2604.23287), and builds a complementary condensed-matter realization in an exactly degenerate bosonic Laughlin manifold.
+$$X_a=(1-P)\partial_aP$$
 
-## Featured Advance
+generate the non-Abelian quantum geometric tensor (\mathcal Q_{ab}=X_a^\dagger X_b), hence both the quantum metric and Berry curvature. They also retain higher correlations invisible to curvature eigenvalues alone.
 
-The task-05 release, [*Spectral Silence and Geometric Chaos in an Exactly Degenerate Topological Manifold*](01_task_folder/task_05/script/output/spectral_silence_and_geometric_chaos_v3.pdf), establishes three geometric scales inside one protected manifold:
+The starting point is Chen, Colin-Ellerin, Mamroud, and Papadodimas, [“Chaos of Berry curvature for BPS microstates”](https://arxiv.org/abs/2604.23287). The present release adds an independently protected many-body mechanism and an outcome-blind higher-moment test.
 
-| Scale | New capability | Result |
-|---|---|---|
-| Exact spectrum | Separate degeneracy from state-space complexity | \(K_{E,\mathrm{raw}}=D\), \(K_{E,c}=0\) exactly |
-| Local geometry | Compare curvature directly with a finite-rank analytic law | Jacobi-like level repulsion and a registered curvature ramp |
-| Higher/global geometry | Resolve operator memory and topological transport | A persistent four-channel cumulant and fixed-Chern, deformable Wilson holonomy |
+## Scientific Architecture
 
 ```mermaid
 flowchart LR
-    A["Exactly degenerate Laughlin manifold"] --> B["Exact energy identity"]
-    A --> C["Projector response P(dH)Q"]
-    C --> D["Finite-rank Jacobi curvature law"]
-    C --> E["Gauge-invariant four-channel Geometric ETH"]
-    C --> F["Fixed C1 with tunable Wilson holonomy"]
+    A["Exactly degenerate protected fiber P(lambda)"] --> B["Response X=(1-P)dP"]
+    B --> C["QGT: metric and Berry curvature"]
+    B --> D["Whitened four-channel tensor"]
+    E["Laughlin parent B-dagger B"] --> F["One-sided response"]
+    G["N=2 SYK {Q,Q-dagger}"] --> H["Exact plus coexact response"]
+    F --> D
+    H --> D
+    D --> I["Frozen covariance predictions"]
+    I --> J["SHA-256-sealed held-out N=14 test"]
 ```
 
 ## What Is New
 
-| Foundation | Advance delivered here |
+| Question | Delivered result |
 |---|---|
-| Berry curvature as a BPS chaos probe | A local, frustration-free fractional-topological parent with an exact, gapped zero-mode manifold |
-| Random-matrix comparison | A parameter-free finite-\(D\) complex-Jacobi kernel, connected form factor, and exact boundary-atom plateau theorem |
-| Curvature eigenvalue statistics | A covariance-whitened, gauge-invariant four-channel matrix-element test on the genuine \(N=3,4,5\) sequence |
-| Integrated Chern data | A closed-torus construction that preserves the complete spectrum and \(C_1\) while continuously tuning relative Wilson holonomy |
-| Numerical evidence | A hash-complete release contract connecting source, figures, compact artifacts, external production arrays, and the final PDF |
+| Is the phenomenon tied to the Kapit–Mueller/Laughlin parent? | No. Generic cubic (\mathcal N=2) SYK supplies a charge-resolved cohomological BPS manifold with a different protection mechanism. |
+| What replaces a one-sided parent response? | The exact identity (X=X_-\oplus X_+), with (X_-^\dagger X_+=0), resolves the response into exact and coexact Hodge branches. |
+| How is “Geometric ETH” made falsifiable? | Two covariance-only Gaussian predictions are frozen before the held-out four-channel outcome is opened. |
+| What is the statistical unit? | The complete disorder realization; no tangent entry or tensor component is treated as an independent sample. |
+| What prevents post-outcome tuning? | Safe covariates, numerical predictions, source identities, and the held-out state machine are hash sealed. |
 
-These advances become possible by combining exact parent-Hamiltonian kernels with metric-normalized signature compression. The resulting algorithm turns a large projector-response problem into a finite-rank Jacobi process, while gauge-invariant trace tensors and discrete Wilson transport capture structure beyond eigenvalue statistics.
+For an eight-channel tangent panel, the gauge-invariant diagnostic is
 
-## Reproduce
+$$\mathcal T_{abcd}=\frac1D\operatorname{Tr}(\widehat X_a^\dagger\widehat X_b\widehat X_c^\dagger\widehat X_d).$$
 
-The review path checks analytic identities, task isolation, release hashes, registered result branches, and 38 focused tests:
+The collapsed null matches registered marginal covariance data without a branch label. The Hodge null samples exact and coexact branches independently and combines their orthogonal direct sum. Both are fixed by safe two-point information.
+
+## Pilot Evidence
+
+The sequential (N=8,10,12) pilot contains central/adjacent sectors and sparse/isotropic tangent panels. All 12 size-sector-panel groups reject both registered separable covariance nulls. For the preregistered sparse panel, the physical-to-Hodge-null median ratio evolves as follows:
+
+| Sector | (N=8) | (N=10) | (N=12) |
+|---|---:|---:|---:|
+| Central | 1.467 | 2.790 | 3.328 |
+| Adjacent | 1.261 | 2.081 | 2.613 |
+
+These are strong finite-size deviations. They are not an asymptotic scaling theorem.
+
+## Sealed Held-Out Result
+
+The independent prediction seal passed before explicit outcome opening. The primary $N=14$ sparse pair gives:
+
+| Sector | Physical median (95% bootstrap) | Collapsed null (97.5% prediction) | Hodge null (97.5% prediction) |
+|---|---:|---:|---:|
+| Adjacent | 0.301529 [0.291527, 0.312061] | [0.111789, 0.111852] | [0.112344, 0.112513] |
+| Central | 0.374993 [0.368980, 0.380473] | [0.111338, 0.111353] | [0.111333, 0.111348] |
+
+Both registered nulls miss both primary sectors. The frozen selector returns `cohomological_non_gaussian_class`: two-point Hodge data do not close the observed four-channel response within the registered separable covariance family. The prediction SHA-256 is `fc300dc7e4bdc1be157919e458ac868d3468533cce31108f23c9fba4f7e9f102`; the inference SHA-256 is `177643e07fc6cf210362fc1077070bd1f0ba316b6805042a626de3f96c55a627`.
+
+## Exact Controls
+
+- A decomposable three-form reproduces the analytic curvature atoms (0,\pm\alpha^{-2}) with their predicted multiplicities.
+- A one-sided synthetic response reproduces the accepted Laughlin Gaussian null.
+- The Hodge formula agrees with a direct Hamiltonian resolvent derivative and a centered finite difference of the protected projector.
+- Exact scalable covariance diagonalization agrees with the dense reference within (2\times10^{-12}) in the regression regime.
+
+## Reproduce and Audit
+
+From `01_task_folder/task_05/script`:
 
 ```bash
-cd 01_task_folder/task_05/script
-python -m pip install -r requirements.txt
-bash run_quick_verify_v1.sh
+PYTHONPATH=. pytest -q $(rg --files tests | rg 'v7\.py$')
+bash run_susy_hodge_delivery_v7.sh
+python verify_susy_hodge_delivery_v7.py
+python verify_susy_hodge_manuscript_v7.py
 ```
 
-The task-level [release guide](01_task_folder/task_05/README.md) documents the article build, full numerical recomputation, artifact classes, exact commands, and growth roadmap. Machine-readable provenance lives in the [release manifest](01_task_folder/task_05/script/output/release_manifest_v1.json).
+The delivery script is fail-closed: it will not activate the paper macros unless the pilot, sealed (N=14) prediction, explicit unseal, frozen inference, controls, figures, and manuscript audits all pass.
 
 ## Start Here
 
 | Deliverable | Purpose |
 |---|---|
-| [Technical report](docs/2026-07-30-task05-technical-report.md) | Innovation, algorithm, equations, evidence, and research outlook |
-| [17-page PDF](01_task_folder/task_05/script/output/spectral_silence_and_geometric_chaos_v3.pdf) | Complete analytic and numerical article |
-| [Task release guide](01_task_folder/task_05/README.md) | Reproduction tiers and figure-by-figure map |
-| [Release notes](docs/2026-07-30-task05-release-notes.md) | Reviewer-facing summary |
-| [Quantum Harness challenge](docs/2026-07-30-quantum-geometry-harness-challenge-draft.md) | Public next-stage benchmark |
-| [Main dashboard](00_main/main_dashboard.md) | Global task ledger and provenance log |
+| [Letter source](overleaf_sync/cohomological_geometric_eth/main.tex) | Compact scientific argument and primary result |
+| [Supplement source](overleaf_sync/cohomological_geometric_eth/supplement.tex) | Derivation, controls, state machine, artifact contract, and limitations |
+| [Compiled Letter](01_task_folder/task_05/script/output/response_complex_memory_v7.pdf) | Four-page audited REVTeX paper; SHA-256 `9fe357a5bfce5e6efd60a3c8bf0a1b73a4eac4ee15f9bb8844f51d2f7e1252ee` |
+| [Compiled Supplemental Material](01_task_folder/task_05/script/output/response_complex_memory_supplement_v7.pdf) | Four-page audited methods and exact-statistics package; SHA-256 `e43a5a2f62494bb7595f790de5643d6244d782402478f36fdcc7c511176b79c5` |
+| [Result report](01_task_folder/task_05/script/output/susy_hodge_geometric_eth_report_v7.md) | Machine-generated verdict and numerical intervals |
+| [Figure manifest](01_task_folder/task_05/script/output/figure_susy_hodge_geometric_eth_v7.json) | Input/output hashes for the main evidence figure |
+| [Scientific ceiling memo](docs/2026-08-01-scientific-ceiling-strategy.md) | Novelty boundary, journal ceiling, and next-theorem roadmap |
+| [Legacy Laughlin article](01_task_folder/task_05/script/output/spectral_silence_and_geometric_chaos_v3.pdf) | One-sided topological benchmark and fixed-Chern holonomy results |
+
+## Claim Boundary and Research Horizon
 
-## Research Horizon
+The independent model/operator-class gate is now crossed: cohomological (\mathcal N=2) SYK is not a repackaged FQH parent Hamiltonian. The asymptotic gate remains open. The current release establishes only the tested finite-size sequence and only relative to the frozen separable covariance nulls.
 
-The current release establishes a finite-size geometric-chaos baseline with exact algebraic identities, high-statistics curvature results, a genuine many-body response sequence, and closed-surface topology. The next phase extends the sequence to \(N=6\), transfers the invariant test to a second exact-degeneracy mechanism, and derives the observed four-channel scaling from locality.
+The next high-ceiling steps are a controlled large-(N) response-tensor law and a spatially local nilpotent-supercharge model with a stable protected rank, open gap, and nontrivially moving harmonic projector.
 
 The code is released under the [GNU General Public License v3.0](LICENSE). Citation metadata are provided in [CITATION.cff](CITATION.cff).
diff --git a/tracks/mps/solutions/Wander-276/research/docs/2026-08-01-scientific-ceiling-strategy.md b/tracks/mps/solutions/Wander-276/research/docs/2026-08-01-scientific-ceiling-strategy.md
new file mode 100644
index 000000000..19eb3bb24
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/docs/2026-08-01-scientific-ceiling-strategy.md
@@ -0,0 +1,247 @@
+# 如何抬高 *Chaos of Quantum Geometry* 的科学上限
+
+Date: 2026-08-01
+
+Authoring agent: [Codex]
+
+## 2026-08-04 封存结果 closeout
+
+封存的 $N=14$ 主检验已经完成独立 hash/source 审计并显式解盲。Adjacent sparse 的物理中位数为 $0.301529$，complete-realization 95% 区间为 $[0.291527,0.312061]$；collapsed 与 Hodge 97.5% prediction intervals 分别为 $[0.111789,0.111852]$ 和 $[0.112344,0.112513]$。Central sparse 的对应结果为 $0.374993$、$[0.368980,0.380473]$，而两个 null 区间分别为 $[0.111338,0.111353]$ 和 $[0.111333,0.111348]$。两个主 sector 都拒绝两个冻结的 separable covariance null，选择 `cohomological_non_gaussian_class`。
+
+因此 `Independent model/operator class` 门槛已经从设计层面升级为封存验证后的有限尺寸结果：generic fixed-charge cubic $\mathcal N=2$ SYK 通过 exact/coexact cohomological response 实现了独立于 Kapit--Mueller/Laughlin 的保护机制，并在同一个 four-channel protocol 下保留结构记忆。`Asymptotic Geometric ETH` 仍未建立；完整 nonseparable entrywise covariance matching 也仍未完成。当前组合使 PRL 成为有逻辑依据的首投尝试，但 PRX Quantum 仍需要更强的 QIS consequence/capability，Nature Physics 仍需要受控大 $N$ 定律、BPS 新预测或同等级的广泛概念后果。
+
+## 2026-08-02 状态更新：两个上限门槛已经分化
+
+这份路线图中的一个关键前提已经改变。`Independent model/operator class` 不再是“没有”：当前 v7 工作使用 generic fixed-charge cubic $\mathcal N=2$ SYK 的 harmonic cohomology，实现了与 Kapit--Mueller/Laughlin $B^\dagger B$ parent 不同的 $H=\{Q,Q^\dagger\}$ 保护机制。其响应严格分成正交 exact/coexact 分支；$N=8,10,12$ 的 12 个 size/sector/panel 组都拒绝冻结的 collapsed 与 Hodge-separable Gaussian null。这里的新贡献不是再次发现 SYK Berry-curvature chaos，而是用同一个 gauge-invariant four-channel 统计量对不同保护复形进行 pre-outcome prediction test。
+
+`Asymptotic Geometric ETH` 仍然没有建立。即使封存的 $N=14$ 验证重复 pilot 分支，它也只把结论升级成受预注册保护的有限尺寸 cross-mechanism response class；它不能给出大 $N$ 集中定理、受控指数或 thermodynamic limit。两个主题因此都重要，但不是“做完两个 checkbox 就自动中好杂志”：独立机制回答“不是单个 parent 的巧合”，渐近理论回答“这是不是一个真正的普适律”。
+
+### 按期刊官方标准重新判断
+
+- [Physical Review Letters 的官方标准](https://journals.aps.org/prl/authors/publish/policies-and-practices-physical-review-letters-july-2013)要求工作构成一个领域中的重大进展或具有跨子领域影响，并且以广泛物理读者能理解的方式说明问题与主要成就。若 $N=14$ 封存检验通过全部门禁，当前组合——能谱沉默、量子几何替代诊断、独立拓扑与 SUSY 保护机制、精确 response-complex identity、无事后拟合的验证——已经形成一个可信的 PRL 尝试，而不是只有“多算了一个尺寸”。这仍是投稿判断，不是录用保证。
+- [PRX Quantum 的官方 acceptance criteria](https://journals.aps.org/prxquantum/about)要求至少体现 exceptional advance、exceptional connection、exceptional capability 或 exceptional insight；其[官方 scope](https://journals.aps.org/prxquantum/scope)明确包含 many-body quantum information、fundamental physics、verification/validation 与 benchmarking。当前工作的最佳匹配是 exceptional connection：把 BPS/SUSY cohomology、FQH parent geometry、随机矩阵高阶响应和 fail-closed computational validation 连接起来。要让它成为强 PRX Quantum 稿，而不是可尝试稿，需要把诊断明确连接到 quantum information observable、verification protocol 或参数空间信息传输后果。
+- [Nature Physics 的官方 scope](https://www.nature.com/nphys/submission-guidelines/about/aims)要求最高质量和显著性的广泛物理结果；其[审稿流程说明](https://www.nature.com/nphys/editorial-policies/peer-review)也明确只有最可能满足一般兴趣标准的稿件才会送外审。当前有限尺寸结果即使封存成功，也不足以把 Nature Physics 当作现实首投目标。合理的抬档条件是：受控大 $N$ 定律、一个参数无关的 geometric echo/holonomy/OTOC 后果，或对 BPS black-hole microstates 给出 seed paper 之外的新定理或预测；三者至少完成一个，最好完成两个。
+
+### 当前最诚实的期刊上限
+
+| 完成状态 | 科学含义 | 投稿判断 |
+|---|---|---|
+| 已完成 $N=8,10,12$ pilot 与封存 $N=14$ 主检验 | 独立 cohomological 机制 + outcome-blind finite-size falsification；两个主 sector 均拒绝两个冻结 null | PRL 是合理首投；PRX Quantum 可尝试但需强化 QIS consequence |
+| 再完成 full nonseparable covariance control 或可推导尺度律 | 排除“只是遗漏两点协方差”的主要替代解释，进入机制性 universality | 强 PRL / 实质性 PRX Quantum |
+| 再加局域 SUSY parent 或参数无关动力学/拓扑后果 | 跨保护、局域性与独立物理后果形成统一原则 | 强 PRX；Nature Physics 成为高风险但有逻辑依据的目标 |
+| 建立大 $N$ concentration theorem 并产生 BPS/black-hole 新预测 | Asymptotic Geometric ETH 与原始物理动机闭环 | Nature Physics/PRX 级真正高上限，仍无录用保证 |
+
+判断方法不是数关键词，而是问审稿人最难提出的替代解释还剩什么。现在最主要的替代解释已经从“只属于 Kapit--Mueller”变成“当前 null 没有匹配完整 nonseparable entrywise covariance”；最主要的量词缺口则仍是“$N\le14$ 不能决定 $N\to\infty$”。因此下一轮最值钱的工作不是立即堆 $N=16,18$，而是先导出或构造更强的 covariance-complete null，再用新增尺寸区分一个冻结的大 $N$ 预测。
+
+## 结论先行
+
+这篇工作的科学上限，不由还能多算几个粒子决定，而由论文标题中最强的量词决定。当前最稳妥的主张是：在一个 Kapit--Mueller bosonic Laughlin 精确零模家族中，能谱完全沉默时，非阿贝尔量子几何仍表现出局域 Jacobi 型相关和朝协方差匹配 Wick 零假设收敛的有限尺寸流，同时保留可分辨的非高斯结构记忆。要提高上限，需要把“一个构造中的有限尺寸观察”至少升级为以下三者之一：一个可推导的机制、一个跨模型的普适类、一个可检验的新后果。单纯扩大同一模型的 Monte Carlo 样本、增加曲率统计量或把随机矩阵维数推得更高，只会提高精度，不会改变主张的逻辑等级。
+
+最优研究组合是：现有 PRL 包不继续等待，保持其聚焦并进入投稿；随后以“机制优先、独立模型复现、可观测后果”为三个升级阶段发展一篇更高上限的后续工作。若只能选择一个下一步，应先做同一精确保护框架中的第二局域算符类，并同时推导以有效通道数为尺度的四点连通量衰减律。它最便宜，也最直接判断当前结果究竟是 Geometric ETH 普适性，还是仅属于密度型变形的特殊性质。
+
+## 一、先学会区分“算得更多”和“知道得更多”
+
+当前摘要中最弱的一句话可以抽象成：
+
+> 在一个工程化的精确简并拓扑 parent family 上，我们观察到五个粒子数的有限尺寸流。
+
+提高科学上限，本质上是改写这句话中的四个语法部件：
+
+| 维度 | 当前状态 | 真正的升级 |
+|---|---|---|
+| 名词 | 一个 Kapit--Mueller 家族 | 一类精确简并流形、两种不同保护机制、或 SUSY/BPS 扇区 |
+| 动词 | 数值观察 | 推导、证明、预测、分类 |
+| 量词 | \(N=3,\ldots,7\) 的有限尺寸趋势 | 受控渐近律、跨模型数据塌缩、或有假设的定理 |
+| 后果 | 一个新的诊断量 | 对慢驱动、参数回波、Wilson 传输、OTOC 或简并解除交叉的参数无关预测 |
+
+一个新计算如果不改变这四项中的任何一项，它通常只是精度工作。精度工作可能是投稿审计所必需的，却很少提高期刊上限。
+
+可以把科学主张分成五级：
+
+1. **存在性：** 能谱沉默时，几何仍然非平凡。
+2. **非冗余性：** 几何混沌与能谱混沌、Chern 数和秩可以独立变化。
+3. **机制性：** 局域响应通道为何产生 Jacobi 相关和特定的非高斯修正。
+4. **普适性：** 同一律跨算符类、模型或精确简并机制成立。
+5. **后果性：** 该几何律决定一个独立可计算的动力学、输运或信息论效应。
+
+现有论文已经可靠达到第二级，并且凭借精确 transported-kernel identity 进入了第三级的一部分。PRX 级别的自然目标是完整的第三级加第四级，或第三级加第五级。更宽领域的顶级期刊通常需要第四级和第五级至少有一个非常强，并且故事重新回到 BPS/黑洞问题或一个足够普遍的多体原则。实验不是硬门槛；没有机制、普适性和后果才是门槛。
+
+## 二、六种真正能提高上限的杠杆
+
+### 1. 从有限尺寸拟合升级为可推导的尺度律
+
+当前 \(\delta_4\) 随 \(D\) 单调下降，并且有限尺寸信息偏好零截距的 \(1/D\) 形式，但五个尺寸不能区分严格趋零和很小的平台。下一步不应只是把 \(N=8\) 接在曲线上，而应先问：为什么尺度变量应当是 \(D\)，而不是外部空间维数、可达响应秩、通道参与率或某个相关长度？
+
+理论目标是把响应写成受局域性和算符代数约束的协方差变形随机通道，
+
+$$X_a\simeq\sum_b(C_{\mathrm{op}}^{1/2})_{ab}G_bC_R^{1/2}+\delta X_a,$$
+
+然后在清楚写明的混合假设下，证明或推导连通四点量随有效独立通道数 \(M_{\mathrm{eff}}\) 抑制，例如给出 \(\delta_4\) 的上界、主导阶或可检验系数。这样，\(N=8\) 的作用才是区分理论预言，而不是帮助选择一个好看的拟合函数。
+
+成功后的摘要动词会从“观察到下降”变为“推导并验证一个有限尺寸律”。即使最后得到非零平台，只要平台由局域可达代数决定并能跨算符类预测，它仍然是一种 deformed Geometric ETH 普适类，而不是失败。
+
+### 2. 从单一密度变形升级为算符类普适性或分类
+
+这是性价比最高的下一步。保持同一个精确零模 projector、相同粒子数序列和相同统计流程，只更换保护家族的生成元：从当前类型扩展到键、流或更长程但仍准局域的一体生成元。精确 transported-kernel 定理使这些方向无需重新解决完整 resolvent 问题，因此计算资源主要用于零模 frame 和相同的 panel aggregation。
+
+关键结果不是“第二条曲线也下降”，而是下面两个互斥且都科学上有价值的分支：
+
+- 不同算符类在以 \(M_{\mathrm{eff}}\) 或可达秩重标度后塌缩到同一曲线：支持一个受局域协方差变形的普适 Geometric ETH。
+- 密度、键和流变形趋向不同的极限，但差异由可达算符代数或守恒律预测：得到 operator-class geometric phases 的分类。
+
+第二个分支不比第一个差。真正糟糕的是只看到不同曲线，却没有能解释差异的结构变量。
+
+### 3. 从一个工程化 parent family 升级为独立精确简并机制
+
+这是抬高 PRX 上限最直接的方式。第二个模型必须消除第一模型最可能的替代解释，而不是仅仅改一个晶格参数。候选按目标分成三类：
+
+- **近期最稳健：continuum LLL pseudopotential Laughlin 零模。** 它可以回答现象是否依赖 Kapit--Mueller 长程跳跃和晶格构造。若相同的白化四点律出现在 continuum torus 上，主张从“某个晶格 parent”升级为“Laughlin 零模流形”。
+- **拓扑上限最高：Moore--Read 或 Read--Rezayi quasihole parent。** 这些流形本身具有非阿贝尔编织结构。可以研究确定的拓扑 braid representation 与局域随机曲率能否共存，并把“固定 Chern”升级为“固定非阿贝尔拓扑数据与混沌几何分离”。已有 lattice Moore--Read parent Hamiltonian 可以通过耦合变化移动和编织 quasiholes，这给出了自然参数空间。[Manna et al.](https://arxiv.org/abs/1807.11222)
+- **与 seed paper 联系最强：SUSY/cohomological zero modes。** 构造 \(Q(\lambda)^2=0\)、\(H(\lambda)=\{Q,Q^\dagger\}\) 的精确零模流形，比较结构化和混沌超荷下的 Berry curvature。二维 supersymmetric lattice fermion 的零模可由 cohomology 精确描述，为此提供现成理论语言。[Huijse and Schoutens](https://arxiv.org/abs/0903.0784)
+
+选择原则很简单：如果目标是尽快增强当前 PRL 的自然性，先做 continuum LLL 或第二个 FQH parent；如果目标是发展一篇真正回到黑洞/BPS 动机的后续论文，应优先 SUSY/cohomological 模型。不要同时搭建三个新平台，因为那会把理论问题稀释成软件工程。
+
+### 4. 从“诊断”升级为“产生后果的定律”
+
+Geometric ETH 最容易被质疑为“又一个看起来像随机矩阵的统计量”。最强回应不是更多随机矩阵图，而是证明它控制一个独立响应。
+
+最自然的对象是小参数回路。沿 \((\lambda^a,\lambda^b)\) 平面走一个面积为 \(\mathcal A\) 的小矩形，简并子空间中的 holonomy 满足
+
+$$U_{\square}=\exp\!\left(iF_{ab}\mathcal A+O(\mathcal A^{3/2})\right).$$
+
+因此返回概率、\(\operatorname{Tr}U_{\square}\) 的矩、连续随机小回路的非阿贝尔扩散，以及非高斯修正，都可以由曲率二点和四点 cumulant 预测。若能从现有 \(X_a\) 的 Wick/connected decomposition 推出一个无额外拟合参数的 geometric echo 或 Wilson-loop 统计，并在独立数值演化中验证，论文就从“定义一个 chaos diagnostic”升级成“发现一个控制参数空间动力学的统计定律”。
+
+第二条桥梁是绝热规范势。\(X_a\) 正是 AGP 的 fiber-to-complement block；AGP 已被证明对可积性破缺和量子混沌敏感。[Pandey et al.](https://arxiv.org/abs/2004.05043) 可以尝试推导简并 projector 版本的 Kubo/AGP identity，并比较轻微解除简并后的谱统计交叉。重点必须是一个推导出来的 crossover relation，而不是两张相关性图。
+
+第三条桥梁是 generalized/full ETH。标准 ETH 的二点信息不足以决定 OTOC，高阶矩阵元相关和 free cumulants 才是关键。[Foini and Kurchan](https://arxiv.org/abs/1803.10658)；[Pappalardi, Foini, and Kurchan](https://arxiv.org/abs/2204.11679)；[Pappalardi, Fritzsch, and Prosen](https://arxiv.org/abs/2303.00713) 当前四通道残差可以被明确解释为简并几何版本的 connected free cumulant；若能证明它决定一个参数空间 OTOC 或 echo correction，就把 “Geometric ETH” 从命名提升为真正与 full ETH 同构的框架。
+
+### 5. 从固定 Chern 反例升级为 topology-constrained random process
+
+现有受控结果证明了完整能谱和 \(C_1\) 固定并不决定非阿贝尔 Wilson holonomy，但 ambient conjugation 是人为设计的，并且 holonomy 仍非 CUE。更高上限的版本应在自然物理 moduli 上研究 \(U(D)\) holonomy 的分解：拓扑约束控制 determinant/\(U(1)\) 扇区，而 traceless \(SU(D)\) 扇区是否趋向一个 Brownian、free-unitary 或 covariance-deformed 过程。
+
+一个值得追求的定理结构是：固定 Chern 数约束 \(\det U_\gamma\)，但在满足局域混合条件时，\(SU(D)\) holonomy 的低阶 cumulants 按独立规律衰减。数值上应使用 twist、interaction metric、quasihole position 或超对称 coupling 等自然参数，而不是仅使用 ambient orbit。若在 Moore--Read 或 \(\mathcal N=2\) SYK/SUSY 零模中实现，这条路线可直接承接 seed paper 关于 moduli-space topology 和大 Chern 数的主线。[Chen et al.](https://arxiv.org/abs/2604.23287)
+
+### 6. 从正面现象升级为必要性、充分性和 no-go 边界
+
+高水平理论论文不一定需要所有结果都“更随机”。一个严格的失败边界同样能提高上限，例如：证明有限范围、守恒律或低可达秩必然保留某个非高斯 cumulant；证明某类 frustration-free deformation 永远不可能达到完整 CUE；或者证明拓扑只约束 central sector 而不能约束 traceless curvature。这样的 no-go theorem 会把当前的“deformed”从有限尺寸不完美变成一个新 universality class 的定义特征。
+
+设计计算时要包含干预而不只是对照：固定 \(P\) 改变 \(PHP\)、固定能谱改变 \(P(\partial H)Q\)、固定拓扑改变局域连接、固定 covariance 改变高阶 cumulant。只有这种“保持其他量不变”的实验，才能回答必要性和充分性。
+
+## 三、三条完整路线及其取舍
+
+### 路线 A：机制优先——第二算符类加尺度理论
+
+这是推荐的下一步，也是单位计算资源信息增益最高的路线。
+
+**核心问题：** \(\delta_4\) 的下降是简单局域算符经过巨大外部通道混合后的中央极限定律，还是当前密度型变形的特殊性质？
+
+**理论工作：** 推导可达支持、左右协方差和 connected four-point tensor 的有限 \((D,M,m)\) 结构；定义从协方差谱得到的 \(M_{\mathrm{eff}}\)；给出 \(\delta_4(M_{\mathrm{eff}})\) 的主导预测或上界。
+
+**数值工作：** 在完全相同的 \(N=3,\ldots,7\) kernel 上运行固定的 bond/current panels；保持 whitening、Gaussian null、bootstrap 和阈值不变；比较按 \(D\) 和按 \(M_{\mathrm{eff}}\) 的 collapse；只有在两个候选渐近行为在 \(N=8\) 上给出可分辨差异时才启动 \(N=8\)。
+
+**成功主张：** “一类精确保护多体流形遵循由可达通道数控制的 covariance-deformed Geometric ETH。”
+
+**失败后的可发表主张：** “局域算符代数定义不同的 geometric universality classes。”
+
+**上限判断：** 足以明显稳固 PRL；若理论结果具有一般性并且跨算符类 collapse 成功，可成为 PRX 结构的核心，但单靠它通常还不足以支撑 Nature Physics 级别的广泛物理影响。
+
+### 路线 B：普适性优先——第二种精确简并机制
+
+**核心问题：** Geometric ETH 是 Laughlin/Kapit--Mueller 构造的性质，还是精确简并多体流形的一般现象？
+
+**近期版本：** continuum LLL Laughlin 或独立 CFT lattice parent，复用同一 gauge-invariant cumulant pipeline。
+
+**高风险高回报版本：** Moore--Read/Read--Rezayi 非阿贝尔 quasiholes，或 SUSY/cohomological zero modes。前者把拓扑编织与几何混沌放在同一框架中，后者把工作直接送回 BPS 黑洞动机。
+
+**成功主张：** “不同物理保护机制在 whitened response space 中共享同一几何统计律，而 central/topological data 保持模型特异。”
+
+**失败后的价值：** 若 FQH 成功而 SUSY 失败，或反之，结果会定位 Geometric ETH 的适用条件；这比盲目声称普适更有理论价值。
+
+**上限判断：** 独立模型复现加共同尺度变量是最清楚的 PRX 升级；若同时产生 BPS/黑洞新结论，则有资格把 Nature Physics 作为高风险目标，而不依赖实验。
+
+### 路线 C：后果优先——geometric echo、AGP 或 topology-constrained holonomy
+
+**核心问题：** 几何 cumulant 除了诊断混沌，还决定什么？
+
+**理论工作：** 从小回路展开或慢驱动 Kubo 公式导出可观测量，明确二点项、Wick 项和 connected four-point correction；给出不从验证数据重新拟合的预测。
+
+**数值工作：** 用独立的有限回路或时变 coupling 演化验证预测；构造结构化和混沌 family，在相同能谱/拓扑约束下比较回波扩散；必要时加入受控简并解除来连接普通 level statistics 和 OTOC。
+
+**成功主张：** “Geometric ETH 决定简并多体流形中的参数空间信息扩散/非阿贝尔回波。”
+
+**风险：** 如果最终只有 AGP、OTOC 和 \(R_4\) 的经验相关，这条路线不会抬高上限；必须有 identity、sum rule 或参数无关预测。
+
+**上限判断：** 一个清楚的新后果能显著扩大受众，并给 PRX 级故事提供第二条腿；若再与 BPS moduli 或非阿贝尔任意子结合，可能成为最有辨识度的长线方向。
+
+## 四、超算应该如何使用
+
+超算的价值不是“把所有尺寸都算一遍”，而是让互相竞争的理论预言变得可分辨。每个大任务提交前，必须能回答三句话：
+
+1. 如果成功，摘要中哪一个名词、动词或量词会变强？
+2. 它消灭哪一个具体替代解释？
+3. 如果失败，是否会自动落入另一个事先定义的科学分支？
+
+推荐的计算顺序是：
+
+1. 复用 \(N=3,\ldots,7\) kernels，完成第二 bond/current 算符类。它检验 universality，成本远低于新模型。
+2. 同时完成 \(M_{\mathrm{eff}}\) 理论和无需高阶数据拟合的曲率/四点预测。只有理论能区分候选趋势后，才决定是否需要 \(N=8\)。
+3. 若算符类 collapse 成功，选择一个独立自然机制。以近期论文为目标选 continuum LLL；以长线高上限为目标选 SUSY/cohomological 或 Moore--Read。
+4. 在普适结构明确后，推导并验证小回路 geometric echo。这样后果建立在一个稳定定律上，而不是建立在单个模型的漂亮图上。
+
+明确的止损条件：
+
+- 第二算符类不 collapse 时，不继续用更多尺寸强迫单一 \(1/D\) 拟合；转向 operator-class classification。
+- \(N=8\) 只有在零极限与平台模型对该点作出可分辨预测时才值得做；否则它只是更昂贵的第六个点。
+- 独立模型若无法维持精确简并、固定 nullity 和开隙，就不能承担“exact-degeneracy universality”的主张；应保留为解除保护的 crossover 对照。
+- 动力学路线若不能得到参数无关关系，就暂不进入主论文。
+
+## 五、如何预判审稿人的真正 objections
+
+把审稿人想象成依次提出五个问题：
+
+1. **这是数值或 gauge artifact 吗？** 现有 frame invariance、solver residual、结构化 control 和 fail-closed audit 已经较好解决。
+2. **这只是有限尺寸拟合吗？** 需要理论尺度变量、额外判别尺寸或严格界。
+3. **这只属于 Kapit--Mueller/这个生成元吗？** 需要第二算符类和独立模型。
+4. **为什么会出现这个统计律？** 需要 locality/accessibility/mixing 的机制。
+5. **除了新统计量，它改变了什么物理？** 需要 geometric echo、topology-constrained process、AGP/OTOC bridge 或 BPS 新预测。
+
+当前最值得花资源的是第二到第四个问题，而不是继续加固已经很强的第一个问题。
+
+## 六、期刊上限与项目组织
+
+现有 v5 Letter 已经是一个聚焦、可审计、适合立即尝试 PRL 的包。继续把所有长线路线塞进当前 Letter 会损害它的中心悖论，也会延迟一个已经形成闭环的结果。因此建议采用“双轨制”：
+
+- **当前论文：** 冻结 v5，完成作者元数据和公开归档后投稿 PRL。它的主张保持为 exact spectral silence 加 protected deformed Geometric ETH，并明确有限尺寸与单模型边界。
+- **上限论文：** 以路线 A 为起点；若跨算符类成立，进入路线 B；若得到共同定律，再做路线 C。这样每一步都能单独形成科学分支，失败不会摧毁整个项目。
+
+大致的上限映射不是录用保证，而是主张结构判断：
+
+| 新增内容 | 主张升级 | 合理上限 |
+|---|---|---|
+| 仅增加 \(N=8\)、样本数或曲率图 | 更精确的同一观察 | 不改变期刊层级 |
+| 第二算符类加理论尺度律 | 机制或 operator-class classification | 强化 PRL；广义定理可触及 PRX |
+| 独立精确简并模型加共同 collapse | 跨机制普适性 | PRX 成为实质性目标 |
+| 普适律加参数无关动力学/拓扑后果 | 新原则和新预测 | 强 PRX；更广期刊的必要条件之一 |
+| 回到 SUSY/BPS 并产生 seed paper 之外的新定理或预测 | 统一 condensed matter 与 black-hole microstates | Nature Physics 级高风险上限，不要求实验但要求广泛概念影响 |
+
+## 七、以后独立判断研究方向的方法
+
+每当出现一个新想法，先做“摘要句测试”，不要先写代码。把成功结果写成一句话，并检查它改变的是哪一个部件：
+
+> 我们在【什么对象】上【观察/推导/证明】了【多大范围成立的规律】，它【排除了什么替代解释】并【预测了什么新后果】。
+
+如果新想法只能填入“多算了一个尺寸”或“又画了一种分布”，它的科学信息增益通常低。若它能把“一个模型”改成“一类模型”，把“观察”改成“推导”，把“有限尺寸”改成“共同尺度律”，或者增加一个不能由原数据自动保证的新后果，它才真正提高上限。
+
+最后再做“反事实测试”：假如结果与预期相反，是否仍能形成清楚结论？好的研究设计至少有两个可发表分支；坏的设计只有在曲线朝想要的方向走时才有故事。当前项目的最好反事实正是：统一 collapse 对应 Geometric ETH，稳定分裂对应 operator-class geometric phases，非零平台对应 locality-protected deformed ETH。这样超算不是用来赌博，而是用来在有限个理论分支之间做决定。
+
+## 参考文献与原始来源
+
+- [Y. Chen et al., *Chaos of Berry curvature for BPS microstates*](https://arxiv.org/abs/2604.23287)
+- [E. Kapit and E. Mueller, *Exact Parent Hamiltonian for Quantum Hall States in a Lattice*](https://arxiv.org/abs/1005.3282)
+- [P. Pandey et al., *Adiabatic Eigenstate Deformations as a Sensitive Probe for Quantum Chaos*](https://arxiv.org/abs/2004.05043)
+- [L. Foini and J. Kurchan, *Eigenstate thermalization hypothesis and out of time order correlators*](https://arxiv.org/abs/1803.10658)
+- [S. Pappalardi, L. Foini, and J. Kurchan, *Eigenstate thermalization hypothesis and free probability*](https://arxiv.org/abs/2204.11679)
+- [S. Pappalardi, C. Fritzsch, and T. Prosen, *General Eigenstate Thermalization via Free Cumulants in Quantum Lattice Systems*](https://arxiv.org/abs/2303.00713)
+- [M. B. Hastings and X.-G. Wen, *Quasi-adiabatic continuation of quantum states*](https://arxiv.org/abs/cond-mat/0503554)
+- [S. Manna et al., *Non-Abelian quasiholes in lattice Moore--Read states and parent Hamiltonians*](https://arxiv.org/abs/1807.11222)
+- [L. Huijse and K. Schoutens, *Supersymmetry, lattice fermions, independence complexes and cohomology theory*](https://arxiv.org/abs/0903.0784)
diff --git a/tracks/mps/solutions/Wander-276/research/docs/literature/2026-08-01-susy-cohomological-third-model.md b/tracks/mps/solutions/Wander-276/research/docs/literature/2026-08-01-susy-cohomological-third-model.md
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+# SUSY/cohomological third-model source audit
+
+Date: 2026-08-01
+Status: discussion-stage literature and novelty audit; no numerical outcome has been inspected or generated.
+
+## Scientific question
+
+Can the covariance-whitened, gauge-invariant response statistic already used for the Kapit--Mueller and continuum-LLL Laughlin parents distinguish a one-sided frustration-free constraint kernel from a genuinely two-sided supersymmetric cohomology, without fitting the third model's four-point result?
+
+The intended third-model benchmark is the generic cubic $\mathcal N=2$ SYK complex,
+
+$$Q(C)=\sum_{i<j<k}C_{ijk}\psi_i\psi_j\psi_k,\qquad Q^2=0,\qquad H=\{Q,Q^\dagger\},$$
+
+in a fixed central $R$-charge sector. Its BPS fiber is the harmonic cohomology
+
+$$\mathcal H_{\mathrm{BPS},r}=\ker Q_r\cap\ker Q_{r-3}^\dagger.$$
+
+For a coupling tangent $\delta Q$, the complement response of a BPS state separates into the orthogonal exact and coexact Hodge branches
+
+$$X(\delta C)=-H_\perp^+\bigl[Q\,\delta Q^\dagger+Q^\dagger\delta Q\bigr]P\equiv X_-\oplus X_+,$$
+
+because $\operatorname{im}Q$ and $\operatorname{im}Q^\dagger$ are orthogonal when $Q^2=0$. By contrast, the two current Laughlin parents have a one-sided positive-constraint response. This makes branch number, Hodge balance, branch effective ranks, and branch covariance spectra available before any connected four-point statistic is opened.
+
+## Primary-source boundary
+
+- [Fu, Gaiotto, Maldacena, and Sachdev, *Supersymmetric SYK models*](https://arxiv.org/abs/1610.08917) introduced the supersymmetric SYK construction and its $\mathcal N=2$ version with exact supersymmetric ground states. It is the canonical model source.
+- [Chang, Chen, Sia, and Yang, *Fortuity in SYK Models*](https://arxiv.org/abs/2412.06902) established that generic-coupling $\mathcal N=2$ SYK BPS states are fortuitous and concentrated in central charge sectors, and formulated the supercharge-chaos conjecture. It supplies the physical reason to use the generic rather than decomposable supercharge.
+- [Chen, Lin, and Shenker, *BPS Chaos*](https://arxiv.org/abs/2407.19387) developed projected-operator diagnostics inside protected sectors and the smooth-state/black-hole-microstate contrast.
+- [Chen, Colin-Ellerin, Mamroud, and Papadodimas, *Chaos of Berry curvature for BPS microstates*](https://arxiv.org/abs/2604.23287) already computed non-Abelian Berry curvature in generic $\mathcal N=2$ SYK, including curvature level repulsion, number variance, spectral form factors, exact decomposable-three-form controls, and moduli-space topology. Reproducing only these curvature spectral statistics would not be a new result.
+- [Miyahara and Shibuya, *Chaos-Integrability Transition in the BPS Subspace of the $\mathcal N=2$ SYK Model*](https://arxiv.org/abs/2605.20913) already studied a projected-operator chaos-to-integrability crossover within the same BPS subspace. A generic-versus-integrable crossover alone is therefore also below the novelty threshold.
+- [Zhang, Sukeno, Ikeda, and Wei, *Local symmetries and extensive ground-state degeneracy of a 1D supersymmetric fermionic chain*](https://arxiv.org/abs/2412.17208) proves exponential zero-mode degeneracy in a spatially local SUSY chain and gives structured states built from immobile walls. This is a strong later negative control, but a stable multidimensional deformation with fixed charge-resolved cohomology and open gap must be demonstrated before it can replace the canonical SYK benchmark.
+- [Huijse and Schoutens, *Supersymmetry, lattice fermions, independence complexes and cohomology theory*](https://arxiv.org/abs/0903.0784) supplies the cohomological language for local lattice realizations and clarifies that cohomology counting alone does not determine how harmonic representatives move in parameter space.
+- [Jiang and Zhou, *Eigenvalue Statistics of Random Quantum Geometry*](https://arxiv.org/abs/2606.27809) raises the benchmark for claims based only on quantum-geometric eigenvalue statistics. The present extension must therefore operate at the response-matrix/four-point level and include a physical structural predictor.
+
+## Novelty conclusion
+
+The publishable unit is not “Berry curvature in $\mathcal N=2$ SYK.” That calculation exists. The distinct target is a common response-complex formalism across non-SUSY topological parents and SUSY cohomology, with a preregistered two-point Hodge signature and an unseen four-point test. A positive result would identify a mechanism-level geometric-chaos class; a negative result would delimit precisely which covariance information fails to predict higher-order quantum geometry.
+
+The lowest-risk benchmark is generic $\mathcal N=2$ SYK because its BPS degeneracy, charge sectors, fortuity, and curvature chaos are independently established. The higher-novelty follow-up is a spatially local nilpotent supercharge, but only after the exact zero-mode-count, gap, and nontrivial-projector-motion feasibility gates pass.
+
+## Proposed pre-outcome quantities
+
+For every accepted response panel, keep the four-point outcome in a sealed sidecar and expose only:
+
+1. the exact/coexact branch weights $T_\pm=\sum_a\lVert X_{a,\pm}\rVert_F^2$;
+2. the Hodge balance $\eta_H=4T_+T_-/(T_++T_-)^2$, with $\eta_H=0$ for a one-sided response and $\eta_H=1$ for exactly balanced branches;
+3. branch-resolved target and complement covariance spectra and their effective ranks;
+4. the numerical orthogonality residual between $\operatorname{im}Q$ and $\operatorname{im}Q^\dagger$;
+5. BPS nullity, external gap, charge-sector identity, and particle-hole/AZ symmetry class.
+
+These data may choose between a one-sided and a signed two-sided Gaussian null, but they may not be used to fit the sealed physical $R_4$. A third-model prediction is scientifically meaningful only if the null, channel panel, size split, aggregation unit, and branch decision are fixed first.
diff --git a/tracks/mps/solutions/Wander-276/research/docs/plans/2026-08-01-susy-cohomological-geometric-eth-design.md b/tracks/mps/solutions/Wander-276/research/docs/plans/2026-08-01-susy-cohomological-geometric-eth-design.md
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+++ b/tracks/mps/solutions/Wander-276/research/docs/plans/2026-08-01-susy-cohomological-geometric-eth-design.md
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+# Hodge-Resolved Geometric ETH Across Topological and SUSY Zero Modes
+
+**Status:** Approved by the human on 2026-08-01 with “做吧.”
+
+**Scientific target:** Determine whether the covariance-whitened response law developed for exactly degenerate Laughlin parent Hamiltonians extends to a genuinely different supersymmetric/cohomological protection mechanism, and whether a response-complex Hodge decomposition predicts the unseen higher-order geometry better than a collapsed covariance model.
+
+## Novelty boundary
+
+The third-model result must not be presented as the discovery of chaotic Berry curvature in $\mathcal N=2$ SYK. Chen, Colin-Ellerin, Mamroud, and Papadodimas already established random-matrix-like curvature statistics, number variance, spectral form factors, structured decomposable-three-form controls, and moduli-space topology in that model. Miyahara and Shibuya also studied a chaos--integrability crossover using operators projected into the BPS subspace.
+
+The new contribution is a common response-matrix and connected-four-point formalism across non-SUSY topological constraints and SUSY cohomology, with a prediction generated only from safe two-point Hodge data before the third model's physical $R_4$ is opened.
+
+## Model and protected fiber
+
+Use the generic cubic $\mathcal N=2$ SYK supercharge
+
+$$Q(C)=\sum_{1\leq i<j<k\leq N}C_{ijk}\psi_i\psi_j\psi_k,\qquad Q^2=0,$$
+
+with Hamiltonian
+
+$$H(C)=\{Q(C),Q(C)^\dagger\}.$$
+
+The computation is charge resolved. In the charge-$r$ Hilbert space $\mathcal H_r$, the protected fiber is the harmonic cohomology
+
+$$\mathcal H_{\mathrm{BPS},r}=\ker Q_r\cap\ker Q_{r-3}^\dagger.$$
+
+The primary sequence uses even $N$ and two sectors:
+
+1. the central sector $r=N/2$, where particle-hole symmetry constrains the curvature class and tests a balanced Hodge response;
+2. the adjacent sector $r=N/2-1$, which tests a generically unbalanced response without the central spectral pairing.
+
+The script-generated registered dimensions are:
+
+| $N$ | sector | $\dim\mathcal H_r$ | expected BPS rank | complement rank |
+|---:|---|---:|---:|---:|
+| 8 | $r=4$ | 70 | 54 | 16 |
+| 8 | $r=3$ | 56 | 27 | 29 |
+| 10 | $r=5$ | 252 | 162 | 90 |
+| 10 | $r=4$ | 210 | 81 | 129 |
+| 12 | $r=6$ | 924 | 486 | 438 |
+| 12 | $r=5$ | 792 | 243 | 549 |
+| 14 | $r=7$ | 3432 | 1458 | 1974 |
+| 14 | $r=6$ | 3003 | 729 | 2274 |
+| 16 | $r=8$ | 12870 | 4374 | 8496 |
+| 16 | $r=7$ | 11440 | 2187 | 9253 |
+
+Use $N=8,10,12$ for implementation and sequential validation. Keep every $N=14$ four-point outcome sealed until a numerical prediction is hashed. Run $N=16$ only if the accepted models give separated registered intervals and the $N=14$ calculation passes every numerical gate.
+
+## Exact Hodge response
+
+Let $P$ project onto $\mathcal H_{\mathrm{BPS},r}$ and $H_\perp^+$ denote the inverse of $H$ on the orthogonal complement of the BPS fiber. For a real coupling tangent $\delta Q+\delta Q^\dagger$, the complement-to-fiber response is
+
+$$X(\delta C)=-H_\perp^+\bigl(Q\,\delta Q^\dagger+Q^\dagger\delta Q\bigr)P=X_-\oplus X_+,$$
+
+with
+
+$$X_-=-H_\perp^+Q\,\delta Q^\dagger P,\qquad X_+=-H_\perp^+Q^\dagger\delta QP.$$
+
+Nilpotency gives $\operatorname{im}Q\perp\operatorname{im}Q^\dagger$, so the exact and coexact branches are orthogonal. This identity must be checked directly against a finite-difference projector derivative and against the full resolvent response at reduced size.
+
+The existing Kapit--Mueller and continuum-LLL parents enter the common formalism as one-sided positive-constraint complexes. Their current accepted outputs remain immutable. A new adapter may read their safe covariance artifacts but may not change their physical $R_4$ arrays.
+
+## Coupling ensemble and tangent panels
+
+Draw the independent complex coefficients $C_{ijk}$ from the standard isotropic Gaussian SYK ensemble and normalize the full three-form to unit norm. Overall normalization does not move the BPS projector, so it cannot affect the normalized response law.
+
+At every accepted base point construct two $m=8$ tangent panels:
+
+1. **Primary sparse panel:** individual cubic coupling coordinates, selected by a deterministic seed and orthogonalized after projection away from null moduli directions;
+2. **Secondary isotropic panel:** deterministic complex Gaussian coupling combinations, projected and orthonormalized in the same tangent metric.
+
+Project away the real radial direction $C$ and the overall phase direction $iC$. Both leave the BPS projector invariant. Reject any panel whose supported channel-label covariance has rank below eight; do not replace it after an $R_4$ outcome is inspected.
+
+The uncertainty unit is a complete disorder realization, not an individual tangent direction or tensor entry. Panels from the same realization remain grouped in every bootstrap.
+
+## Safe Hodge signature
+
+Before opening any connected four-point outcome, expose only:
+
+$$T_\pm=\sum_{a=1}^{m}\lVert X_{a,\pm}\rVert_F^2,\qquad \eta_H=\frac{4T_+T_-}{(T_++T_-)^2},$$
+
+plus:
+
+- branch-resolved target covariance spectra;
+- branch-resolved complement covariance spectra;
+- effective ranks and normalized spectral entropies derived from those spectra;
+- exact/coexact orthogonality residual;
+- charge-sector identity, BPS rank, external gap, and kernel residual;
+- particle-hole and expected Altland--Zirnbauer symmetry labels;
+- input seeds, source hashes, array hashes, and numerical tolerances.
+
+Safe JSON and NPZ artifacts must fail a serialized-key audit if they contain `R4`, `four_point`, `connected`, or an outcome-sidecar payload.
+
+## Competing finite-size nulls
+
+The existing collapsed null samples one separable Gaussian response using the combined target and complement covariance spectra. It remains a frozen competitor.
+
+The new Hodge-resolved null samples the two branches independently,
+
+$$G_{a,\pm}=R_\pm^{1/2}Z_{a,\pm}L_\pm^{1/2},$$
+
+forms the orthogonal direct sum $G_a=G_{a,-}\oplus G_{a,+}$, applies the same complete channel whitening, and evaluates the same gauge-invariant four-channel tensor and normalized $R_4$. The one-sided Laughlin null must be recovered exactly when one branch weight is zero.
+
+The null uses measured two-point covariance spectra but no physical four-point number. Random streams for safe covariance generation, Gaussian reference generation, and physical disorder are disjoint and recorded.
+
+## Information barrier and sequential test
+
+Every physical response checkpoint is split into:
+
+1. a safe metadata/array pair containing generators, Hodge branches, covariance spectra, gaps, residuals, and hashes;
+2. a separately hashed `.outcome.json` sidecar containing physical $R_4$ and only the metadata needed to identify the case.
+
+The $N=8,10,12$ outcomes may be opened sequentially after their internal gates pass, but they cannot change the observable, panel construction, null definitions, or $N=14$ identities. The $N=14$ safe covariates are aggregated first. Both collapsed-null and Hodge-null numerical intervals are written atomically and sealed with SHA-256 before the unseal command is permitted to read any $N=14$ sidecar.
+
+## Controls and falsification gates
+
+1. **Analytic decomposable control:** use $C_3=A_1^{(1)}\wedge A_1^{(2)}\wedge A_1^{(3)}$ and tangent directions preserving the decomposable locus. Recover the analytic curvature atoms $0,\pm1/\alpha^2$ and their multiplicities at reduced size.
+2. **Gauge covariance:** independent random basis rotations in the BPS fiber and both complement branches leave every scalar, covariance spectrum, and $R_4$ unchanged.
+3. **Projector derivative:** centered finite differences agree with $X_-\oplus X_+$ after optimal subspace alignment.
+4. **Resolvent identity:** the branch sum agrees with the direct $-H_\perp^+(\partial H)P$ computation.
+5. **Hodge orthogonality:** $\lVert X_-^\dagger X_+\rVert_F$ is below a registered relative tolerance.
+6. **One-sided regression:** setting either branch to zero reproduces the accepted one-sided Wick implementation at machine precision.
+7. **Corruption tests:** changed outcome identity, source hash, seed, prediction hash, or premature outcome access must fail closed.
+
+## Frozen result branches
+
+The final inference selects exactly one primary branch:
+
+- `strong_covariance_universality`: both the collapsed and Hodge-resolved nulls cover the registered $N=14$ central/adjacent primary cases;
+- `hodge_resolved_geometric_eth`: the Hodge-resolved null covers the complete registered $N=14$ primary pair while the collapsed null does not;
+- `cohomological_non_gaussian_class`: neither null covers the registered pair, but a reproducible non-Gaussian excess survives all numerical and disorder checks;
+- `structured_cohomology`: generic-coupling cases cannot be statistically separated from the decomposable structured control under the frozen diagnostics;
+- `feasibility_failure`: expected BPS rank, open gap, Hodge support, response identity, or prediction seal fails.
+
+Monotonic decrease with $N$ is secondary evidence only. No asymptotic exponent or thermodynamic limit may be claimed from four sizes without a successful held-out law.
+
+## Publication claim boundary
+
+A successful Hodge prediction supports a response-complex classification of geometric chaos across a non-SUSY topological zero-mode manifold and a SUSY cohomological BPS manifold. It does not establish conventional energy-resolved ETH, real-time chaos, a thermodynamic theorem, or a universal law for all parent Hamiltonians.
+
+The generic $\mathcal N=2$ SYK benchmark is a cross-protection-mechanism test, not an independent discovery of SYK Berry chaos. A later spatially local nilpotent-supercharge model is required to claim spatial-locality universality.
+
+## Deliverables
+
+- a task-local sparse fermionic supercharge and charge-sector backend;
+- exact BPS/Hodge response and validation tests;
+- safe/outcome checkpoint writer with an enforced information barrier;
+- collapsed and Hodge-resolved Gaussian null generators;
+- sequential $N=8,10,12$ inference and sealed $N=14$ predictor/unsealer;
+- analytic decomposable-three-form control;
+- generated JSON/NPZ inference artifacts and a publication figure;
+- a source-backed report stating the selected branch and claim boundary;
+- synchronized task and main dashboards;
+- a full task-local regression, corruption, provenance, and delivery audit.
diff --git a/tracks/mps/solutions/Wander-276/research/docs/plans/2026-08-01-susy-cohomological-geometric-eth-implementation-plan.md b/tracks/mps/solutions/Wander-276/research/docs/plans/2026-08-01-susy-cohomological-geometric-eth-implementation-plan.md
new file mode 100644
index 000000000..41a596d59
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/docs/plans/2026-08-01-susy-cohomological-geometric-eth-implementation-plan.md
@@ -0,0 +1,505 @@
+# SUSY/Cohomological Hodge-Resolved Geometric ETH Implementation Plan
+
+> **For agentic workers:** REQUIRED SUB-SKILL: Use superpowers:subagent-driven-development (recommended) or superpowers:executing-plans to implement this plan task-by-task. Steps use checkbox (`- [ ]`) syntax for tracking.
+
+**Goal:** Build, preregister, execute, and audit a charge-resolved $\mathcal N=2$ SYK benchmark that predicts a sealed four-channel response statistic from exact/coexact two-point Hodge data and compares it with the existing one-sided Laughlin response law.
+
+**Architecture:** New task-local v7 modules construct cubic fermionic cochain complexes, solve their harmonic BPS fibers, decompose projector responses into orthogonal exact/coexact branches, and generate both collapsed and Hodge-resolved covariance-matched Gaussian nulls. A split-checkpoint runner keeps physical $R_4$ in outcome sidecars, a sequential analyzer seals the complete $N=14$ prediction before unsealing, and independent figure/report/delivery scripts consume only accepted hashed artifacts. Existing v1--v6 source and outcome files remain immutable.
+
+**Tech Stack:** Python 3, NumPy, SciPy sparse/dense linear algebra, pytest, Matplotlib, JSON/NPZ/SHA-256 checkpointing, Bash/Slurm for $N=14$, and the existing task-local `lgeth.wick_channels` finite-size statistic.
+
+## Global Constraints
+
+- Work only inside `01_task_folder/task_05/` for executable code and task outputs; task scripts may not import another task folder.
+- Create new v7 files; do not modify accepted v1--v6 numerical artifacts or hash-anchored implementation modules.
+- Write tests before implementation and commit each independently reviewable task.
+- Generate every numerical result, table, and figure by script; do not enter measured values by hand.
+- Treat a complete disorder realization as the uncertainty unit; never resample tangent entries as independent observations.
+- Keep safe Hodge covariates and physical four-point outcomes in different files; safe serialization must reject `R4`, `four_point`, and `connected` keys.
+- Use $m=8$ channels, primary sparse and secondary isotropic coupling panels, $N=8,10,12$ sequential development, $N=14$ sealed validation, and $N=16$ only after an explicit separation gate.
+- Preserve the registered result branches and claim boundaries from `docs/plans/2026-08-01-susy-cohomological-geometric-eth-design.md`.
+- Keep task_05 and main-dashboard statuses synchronized at `🟡 Ongoing` until the human explicitly closes the task.
+
+## File map
+
+- Create `01_task_folder/task_05/script/lgeth/susy_cohomology.py`: charge bases, fermionic signs, cubic supercharge matrices, charge-sector Hamiltonians, BPS frames, and expected generic ranks.
+- Create `01_task_folder/task_05/script/lgeth/hodge_response.py`: coupling-tangent projection, sparse/isotropic panels, exact/coexact response branches, covariance summaries, and Hodge signatures.
+- Create `01_task_folder/task_05/script/lgeth/hodge_wick.py`: collapsed-versus-Hodge Gaussian samplers and complete-realization reference aggregation.
+- Create `01_task_folder/task_05/script/run_susy_hodge_geometric_eth_v7.py`: source-hashed kernel/response checkpoints, split safe/outcome files, pilot aggregation, prediction seals, and CLI.
+- Create `01_task_folder/task_05/script/analyze_susy_hodge_geometric_eth_v7.py`: sequential pilot summaries, sealed $N=14$ predictions, unseal scoring, and frozen branch selection.
+- Create `01_task_folder/task_05/script/make_susy_hodge_figure_v7.py`: one publication figure and machine-readable manifest.
+- Create `01_task_folder/task_05/script/verify_susy_hodge_delivery_v7.py`: full scientific, provenance, corruption, figure, and report audit.
+- Create `01_task_folder/task_05/script/slurm/run_susy_hodge_N14_v7_array.sbatch` and `submit_susy_hodge_N14_v7.sh`: safe production and prediction-only dependency chain; no automatic unseal.
+- Create focused tests named `test_susy_cohomology_v7.py`, `test_hodge_response_v7.py`, `test_hodge_wick_v7.py`, `test_susy_hodge_runner_v7.py`, `test_susy_hodge_analysis_v7.py`, and `test_susy_hodge_delivery_v7.py`.
+- Generate outputs under `01_task_folder/task_05/script/output/susy_hodge_v7_*` and `susy_hodge_v7_checkpoints/`; do not commit bulk frames or response arrays.
+
+---
+
+### Task 1: Cubic charge-resolved cochain complex
+
+**Files:**
+- Create: `01_task_folder/task_05/script/lgeth/susy_cohomology.py`
+- Test: `01_task_folder/task_05/script/tests/test_susy_cohomology_v7.py`
+
+**Interfaces:**
+- Produces: `charge_basis(N: int, charge: int) -> tuple[int, ...]`, `cubic_triples(N: int) -> tuple[tuple[int,int,int], ...]`, `cubic_supercharge(N: int, charge: int, couplings: np.ndarray) -> scipy.sparse.csr_matrix`, `charge_hamiltonian(...) -> csr_matrix`, `expected_generic_bps_rank(N: int, charge: int) -> int`, and `solve_bps_frame(...) -> BPSFrame`.
+- `BPSFrame` fields: `basis`, `projector_frame`, `complement_frame`, `positive_energies`, `gap`, `kernel_residual`, `orthogonality_error`, `expected_rank`, `q_in`, and `q_out`.
+
+- [ ] **Step 1: Write the failing algebra tests**
+
+```python
+def test_cubic_supercharge_is_nilpotent_and_has_registered_bps_rank():
+    rng = np.random.default_rng(7)
+    couplings = rng.normal(size=20) + 1j * rng.normal(size=20)
+    q1 = cubic_supercharge(6, 1, couplings)
+    q4 = cubic_supercharge(6, 4, couplings)
+    assert np.linalg.norm((q4 @ q1).toarray()) < 1e-12
+    frame = solve_bps_frame(6, 3, couplings, dense_cutoff=64)
+    assert frame.projector_frame.shape == (20, 18)
+    assert frame.gap > 0.0
+    assert frame.kernel_residual < 1e-10
+```
+
+- [ ] **Step 2: Run the focused test and verify the missing-module failure**
+
+Run: `PYTHONPATH=01_task_folder/task_05/script pytest -q 01_task_folder/task_05/script/tests/test_susy_cohomology_v7.py`
+
+Expected: collection fails because `lgeth.susy_cohomology` does not exist.
+
+- [ ] **Step 3: Implement fermionic creation signs and sparse supercharges**
+
+Use sorted bit-string bases and apply the ordered operator product from right to left:
+
+```python
+def _create(state: int, mode: int) -> tuple[int, int] | None:
+    bit = 1 << mode
+    if state & bit:
+        return None
+    sign = -1 if (state & (bit - 1)).bit_count() % 2 else 1
+    return state | bit, sign
+```
+
+Build `Q_r: H_r -> H_{r+3}` in COO form, convert to CSR, and define
+
+```python
+h_r = q_in @ q_in.getH() + q_out.getH() @ q_out
+```
+
+Solve the reduced dense cases with `scipy.linalg.eigh`; classify eigenvalues relative to `max(1.0, max_eigenvalue) * 1e-11`; verify the expected rank rather than inferring the scientific rank from a tolerance.
+
+- [ ] **Step 4: Run the algebra tests**
+
+Run: `PYTHONPATH=01_task_folder/task_05/script pytest -q 01_task_folder/task_05/script/tests/test_susy_cohomology_v7.py`
+
+Expected: all tests pass for basis counts, Hermiticity, positivity, nilpotency, central/adjacent rank formulas, and deterministic frames.
+
+- [ ] **Step 5: Commit the cochain backend**
+
+```bash
+git add 01_task_folder/task_05/script/lgeth/susy_cohomology.py 01_task_folder/task_05/script/tests/test_susy_cohomology_v7.py
+git commit -m "feat: add charge-resolved SUSY cochain backend"
+```
+
+### Task 2: Exact/coexact Hodge response theorem
+
+**Files:**
+- Create: `01_task_folder/task_05/script/lgeth/hodge_response.py`
+- Test: `01_task_folder/task_05/script/tests/test_hodge_response_v7.py`
+
+**Interfaces:**
+- Consumes: `BPSFrame`, `cubic_supercharge`, and an $m\times\binom N3$ tangent array.
+- Produces: `HodgeResponse(minus: np.ndarray, plus: np.ndarray, total: np.ndarray, direct: np.ndarray, checks: dict[str,bool])` and `hodge_response(frame, couplings, tangents) -> HodgeResponse` with arrays shaped `(m, dim(H_r), D)`.
+
+- [ ] **Step 1: Write failing response-identity tests**
+
+```python
+def test_hodge_branches_are_orthogonal_and_equal_direct_resolvent():
+    frame, couplings, tangent = reduced_generic_case(N=6, charge=3, seed=11)
+    result = hodge_response(frame, couplings, tangent[None, :])
+    assert np.linalg.norm(result.minus[0].conj().T @ result.plus[0]) < 1e-10
+    assert np.allclose(result.total, result.minus + result.plus, atol=1e-10)
+    assert np.allclose(result.total, result.direct, atol=1e-10)
+```
+
+Add a centered finite-difference test for the projector derivative `dP = X P^† + P X^†` at step sizes `2e-5` and `1e-5`; require the error ratio to be compatible with second-order convergence and the smaller-step relative error below `2e-5`.
+
+- [ ] **Step 2: Run the test to confirm failure**
+
+Run: `PYTHONPATH=01_task_folder/task_05/script pytest -q 01_task_folder/task_05/script/tests/test_hodge_response_v7.py`
+
+Expected: collection fails because `hodge_response` is undefined.
+
+- [ ] **Step 3: Implement branch right-hand sides and pseudoinverse action**
+
+For tangent supercharges `dq_in` and `dq_out`, compute
+
+```python
+rhs_minus = q_in @ dq_in.getH() @ P
+rhs_plus = q_out.getH() @ dq_out @ P
+solve = U @ ((U.conj().T @ rhs) / energies[:, None])
+x_minus = -solve(rhs_minus)
+x_plus = -solve(rhs_plus)
+```
+
+Compute the direct derivative from `dH = dq_in @ q_in.H + q_in @ dq_in.H + dq_out.H @ q_out + q_out.H @ dq_out` and require branch sum agreement. Do not project away a failed residual.
+
+- [ ] **Step 4: Run response and cochain regressions**
+
+Run: `PYTHONPATH=01_task_folder/task_05/script pytest -q 01_task_folder/task_05/script/tests/test_susy_cohomology_v7.py 01_task_folder/task_05/script/tests/test_hodge_response_v7.py`
+
+Expected: all tests pass.
+
+- [ ] **Step 5: Commit the response theorem**
+
+```bash
+git add 01_task_folder/task_05/script/lgeth/hodge_response.py 01_task_folder/task_05/script/tests/test_hodge_response_v7.py
+git commit -m "feat: implement exact SUSY Hodge response"
+```
+
+### Task 3: Physical tangent panels and safe Hodge signature
+
+**Files:**
+- Modify: `01_task_folder/task_05/script/lgeth/hodge_response.py`
+- Modify: `01_task_folder/task_05/script/tests/test_hodge_response_v7.py`
+
+**Interfaces:**
+- Produces: `project_moduli_tangents(couplings, candidates)`, `coupling_panels(couplings, panel_size, seed) -> dict[str,np.ndarray]`, `HodgeSignature`, and `hodge_signature(response) -> HodgeSignature`.
+- `HodgeSignature` records full nonnegative branch target spectra, positive complement spectra, branch weights, Hodge balance, effective ranks, spectral entropies, and orthogonality residual.
+
+- [ ] **Step 1: Add failing tangent and signature tests**
+
+```python
+def test_registered_panels_remove_radial_phase_and_have_full_support():
+    couplings = normalized_couplings(8, seed=13)
+    panels = coupling_panels(couplings, panel_size=8, seed=17)
+    assert set(panels) == {"sparse", "isotropic"}
+    for values in panels.values():
+        assert values.shape == (8, 56)
+        assert np.max(np.abs(values @ couplings.conj())) < 1e-12
+        assert np.allclose(values @ values.conj().T, np.eye(8), atol=1e-12)
+```
+
+Test `eta_H=0` for a one-sided synthetic response, `eta_H=1` for equal branch weights, invariance under independent ambient and target unitary rotations, and rejection of a singular eight-channel panel.
+
+- [ ] **Step 2: Run tests and observe the missing-interface failure**
+
+Run: `PYTHONPATH=01_task_folder/task_05/script pytest -q 01_task_folder/task_05/script/tests/test_hodge_response_v7.py`
+
+- [ ] **Step 3: Implement complex moduli projection and deterministic QR**
+
+Use the complex projection
+
+```python
+projected = candidates - np.outer(candidates @ couplings.conj(), couplings)
+q, r = np.linalg.qr(projected.T, mode="reduced")
+phases = np.exp(-1j * np.angle(np.diag(r)))
+tangents = (q * phases[None, :]).T
+```
+
+The one complex direction removed spans both real radial and phase directions. Select sparse coordinates from a deterministic permutation and generate isotropic candidates from an independent RNG stream.
+
+- [ ] **Step 4: Run the focused response suite**
+
+Run: `PYTHONPATH=01_task_folder/task_05/script pytest -q 01_task_folder/task_05/script/tests/test_hodge_response_v7.py`
+
+- [ ] **Step 5: Commit the safe signature layer**
+
+```bash
+git add 01_task_folder/task_05/script/lgeth/hodge_response.py 01_task_folder/task_05/script/tests/test_hodge_response_v7.py
+git commit -m "feat: add SUSY tangent panels and Hodge signatures"
+```
+
+### Task 4: Hodge-resolved covariance-matched Gaussian null
+
+**Files:**
+- Create: `01_task_folder/task_05/script/lgeth/hodge_wick.py`
+- Test: `01_task_folder/task_05/script/tests/test_hodge_wick_v7.py`
+
+**Interfaces:**
+- Consumes: branch spectra/weights from `HodgeSignature` and `covariance_matched_wick` from the immutable `lgeth.wick_channels` module.
+- Produces: `sample_hodge_gaussian_channels(signature, channel_count, rng) -> np.ndarray`, `hodge_gaussian_r4_reference(signature, channel_count, samples, seed) -> np.ndarray`, and `complete_realization_null(signatures, samples, seed) -> np.ndarray`.
+
+- [ ] **Step 1: Write failing Gaussian-null tests**
+
+```python
+def test_one_sided_hodge_sampler_matches_existing_distribution():
+    signature = synthetic_signature(minus_weight=1.0, plus_weight=0.0)
+    first = hodge_gaussian_r4_reference(signature, 8, 512, 23)
+    second = gaussian_r4_reference(
+        signature.minus_target_positive,
+        signature.minus_external_positive,
+        8,
+        512,
+        23,
+    )
+    assert abs(np.median(first) - np.median(second)) < 0.015
+```
+
+Also test deterministic seeds, nonnegative spectra, branch-weight rescaling invariance after channel whitening, and direct-sum output shape.
+
+- [ ] **Step 2: Run tests and confirm failure**
+
+Run: `PYTHONPATH=01_task_folder/task_05/script pytest -q 01_task_folder/task_05/script/tests/test_hodge_wick_v7.py`
+
+- [ ] **Step 3: Implement the signed two-branch sampler**
+
+For each nonzero branch, normalize its target/external spectra, generate complex standard Gaussian entries, apply square-root spectra, rotate the target by a deterministic Haar unitary drawn from the null RNG, scale by the square root of the branch weight fraction, concatenate branches along the external axis, and call the unchanged `covariance_matched_wick` implementation. If exactly one branch has positive weight, dispatch directly to the existing one-sided sampler.
+
+- [ ] **Step 4: Run null and immutable Wick regressions**
+
+Run: `PYTHONPATH=01_task_folder/task_05/script pytest -q 01_task_folder/task_05/script/tests/test_hodge_wick_v7.py 01_task_folder/task_05/script/tests/test_wick_channels_v3.py`
+
+- [ ] **Step 5: Commit the Hodge null**
+
+```bash
+git add 01_task_folder/task_05/script/lgeth/hodge_wick.py 01_task_folder/task_05/script/tests/test_hodge_wick_v7.py
+git commit -m "feat: add Hodge-resolved Gaussian response null"
+```
+
+### Task 5: Split-checkpoint runner and information barrier
+
+**Files:**
+- Create: `01_task_folder/task_05/script/run_susy_hodge_geometric_eth_v7.py`
+- Test: `01_task_folder/task_05/script/tests/test_susy_hodge_runner_v7.py`
+
+**Interfaces:**
+- Produces: `prepare_realization(N, sector, realization, ...)`, `run_panel(...)`, `write_safe_covariates(...)`, `seal_file_hash(...)`, `write_prediction(...)`, and `unseal_outcomes(...)`.
+- Registered constants: `SIZES=(8,10,12,14)`, `SECTORS=("central","adjacent")`, `PANEL_KINDS=("sparse","isotropic")`, `PANEL_SIZE=8`, realization counts `{8:64,10:48,12:32,14:24}`, and `NULL_REPLICATES=2000`.
+
+- [ ] **Step 1: Write the reduced split/seal test**
+
+```python
+def test_reduced_susy_runner_keeps_r4_out_of_safe_artifacts(tmp_path):
+    prepare_realization(6, "central", 0, root=tmp_path, reduced=True, force=True)
+    run_panel(6, "central", 0, "sparse", root=tmp_path, reduced=True, force=True)
+    safe = (tmp_path / "N6_central_seed000_sparse_v7.json").read_text()
+    outcome = (tmp_path / "N6_central_seed000_sparse_v7.outcome.json").read_text()
+    assert "R4" not in safe and "four_point" not in safe and "connected" not in safe
+    assert '"R4"' in outcome
+```
+
+Require `unseal_outcomes` to fail before a seal exists, after a one-byte prediction mutation, and after an outcome identity mutation.
+
+- [ ] **Step 2: Run the runner test and verify failure**
+
+Run: `PYTHONPATH=01_task_folder/task_05/script pytest -q 01_task_folder/task_05/script/tests/test_susy_hodge_runner_v7.py`
+
+- [ ] **Step 3: Implement atomic, source-hashed checkpoints**
+
+Follow the v6 continuum runner's `_atomic_json`, `_atomic_npz`, identity hash, array hash, and seal validation patterns in a new file. Serialize branch matrices only in NPZ; serialize derived safe scalars/spectra in JSON. Write the outcome sidecar only after all response identities pass, and never load it from a safe aggregation function.
+
+- [ ] **Step 4: Run reduced runner plus Hodge suites**
+
+Run: `PYTHONPATH=01_task_folder/task_05/script pytest -q 01_task_folder/task_05/script/tests/test_susy_hodge_runner_v7.py 01_task_folder/task_05/script/tests/test_susy_cohomology_v7.py 01_task_folder/task_05/script/tests/test_hodge_response_v7.py 01_task_folder/task_05/script/tests/test_hodge_wick_v7.py`
+
+- [ ] **Step 5: Commit the information barrier**
+
+```bash
+git add 01_task_folder/task_05/script/run_susy_hodge_geometric_eth_v7.py 01_task_folder/task_05/script/tests/test_susy_hodge_runner_v7.py
+git commit -m "feat: enforce sealed SUSY Hodge response outcomes"
+```
+
+### Task 6: Analytic decomposable-three-form control
+
+**Files:**
+- Modify: `01_task_folder/task_05/script/lgeth/susy_cohomology.py`
+- Modify: `01_task_folder/task_05/script/lgeth/hodge_response.py`
+- Modify: `01_task_folder/task_05/script/tests/test_susy_cohomology_v7.py`
+- Modify: `01_task_folder/task_05/script/tests/test_hodge_response_v7.py`
+
+**Interfaces:**
+- Produces: `decomposable_couplings(N, alpha)`, `decomposable_tangent(N, family, site)`, and `analytic_decomposable_curvature_multiplicities(N, charge, kind)`.
+
+- [ ] **Step 1: Add failing atomic-spectrum tests**
+
+At $C_{123}=\alpha$ and all other couplings zero, compute diagonal tangent $(12k)$ and off-diagonal Hermitian combination $(12k),(13l)$. Assert every numerical curvature eigenvalue lies within `1e-10` of `{-1/alpha**2, 0, 1/alpha**2}` and the nonzero multiplicities match Appendix D.2 of the seed paper.
+
+- [ ] **Step 2: Run the control tests and verify failure**
+
+Run: `PYTHONPATH=01_task_folder/task_05/script pytest -q 01_task_folder/task_05/script/tests/test_susy_cohomology_v7.py 01_task_folder/task_05/script/tests/test_hodge_response_v7.py`
+
+- [ ] **Step 3: Implement the exact control and multiplicity formulas**
+
+Generate the decomposable coupling vector by the canonical triple lookup. Construct curvature from the response branches as the antisymmetrized Gram combination and compare it with the analytic $0,\pm1/\alpha^2$ support. Preserve zero eigenvalues rather than removing them in this structural test.
+
+- [ ] **Step 4: Run all v7 unit tests**
+
+Run: `PYTHONPATH=01_task_folder/task_05/script pytest -q $(rg --files 01_task_folder/task_05/script/tests | rg 'v7\.py$')`
+
+- [ ] **Step 5: Commit the analytic negative control**
+
+```bash
+git add 01_task_folder/task_05/script/lgeth/susy_cohomology.py 01_task_folder/task_05/script/lgeth/hodge_response.py 01_task_folder/task_05/script/tests/test_susy_cohomology_v7.py 01_task_folder/task_05/script/tests/test_hodge_response_v7.py
+git commit -m "test: certify decomposable SUSY curvature atoms"
+```
+
+### Task 7: Sequential $N=8,10,12$ pilot production
+
+**Files:**
+- Modify: `01_task_folder/task_05/script/run_susy_hodge_geometric_eth_v7.py`
+- Create: `01_task_folder/task_05/script/tests/test_susy_hodge_pilot_v7.py`
+
+**Interfaces:**
+- Produces: `script/output/susy_hodge_v7_covariates_pilot.json`, `susy_hodge_v7_outcomes_pilot.{json,npz}`, and per-realization checkpoints.
+
+- [ ] **Step 1: Add a reduced aggregation test**
+
+Generate two reduced realizations in each sector and panel kind. Require complete case grids, finite physical and both-null $R_4$ arrays, full source identity, complete-realization grouping, and deterministic regeneration.
+
+- [ ] **Step 2: Run the reduced pilot test**
+
+Run: `PYTHONPATH=01_task_folder/task_05/script pytest -q 01_task_folder/task_05/script/tests/test_susy_hodge_pilot_v7.py`
+
+- [ ] **Step 3: Implement resumable pilot aggregation**
+
+Use independent seeds derived from `(VERSION, N, sector, realization, purpose)`. The safe aggregate must be written before any pilot outcome aggregate. Opening pilot outcomes is allowed only after every kernel, gap, Hodge, panel-support, gauge, and source-hash gate passes.
+
+- [ ] **Step 4: Run the registered local sizes sequentially**
+
+Run:
+
+```bash
+PYTHONPATH=01_task_folder/task_05/script python 01_task_folder/task_05/script/run_susy_hodge_geometric_eth_v7.py pilot --sizes 8 10 12
+```
+
+Expected: 64/48/32 complete disorder realizations per sector and both panel kinds, with safe artifacts written before the pilot outcome aggregate.
+
+- [ ] **Step 5: Run v7 regressions and commit compact pilot code/metadata**
+
+```bash
+PYTHONPATH=01_task_folder/task_05/script pytest -q $(rg --files 01_task_folder/task_05/script/tests | rg 'v7\.py$')
+git add 01_task_folder/task_05/script/run_susy_hodge_geometric_eth_v7.py 01_task_folder/task_05/script/tests/test_susy_hodge_pilot_v7.py
+git commit -m "data: complete SUSY Hodge pilot sequence"
+```
+
+Do not stage bulk checkpoint NPZ files.
+
+### Task 8: Sealed $N=14$ prediction and Slurm workflow
+
+**Files:**
+- Create: `01_task_folder/task_05/script/analyze_susy_hodge_geometric_eth_v7.py`
+- Create: `01_task_folder/task_05/script/slurm/run_susy_hodge_N14_v7_array.sbatch`
+- Create: `01_task_folder/task_05/script/slurm/submit_susy_hodge_N14_v7.sh`
+- Test: `01_task_folder/task_05/script/tests/test_susy_hodge_analysis_v7.py`
+
+**Interfaces:**
+- Produces: `write_n14_prediction(covariates, ...)`, `score_unsealed_n14(...)`, `susy_hodge_v7_N14_prediction.json`, and `susy_hodge_v7_N14_prediction.sha256`.
+
+- [ ] **Step 1: Write failing prediction-before-outcome tests**
+
+Use synthetic safe covariates and hidden sidecars. Assert prediction creation succeeds when sidecars are unreadable, the serialized prediction contains no physical $R_4$, scoring fails without a valid SHA-256 seal, and the primary simultaneous pair is central/adjacent sparse panels only.
+
+- [ ] **Step 2: Run analysis tests and verify failure**
+
+Run: `PYTHONPATH=01_task_folder/task_05/script pytest -q 01_task_folder/task_05/script/tests/test_susy_hodge_analysis_v7.py`
+
+- [ ] **Step 3: Implement complete-realization prediction intervals and frozen branch logic**
+
+For each of 2000 reference replicates, draw one covariance-conditioned Gaussian tensor per disorder realization and take the realization median. Use per-case 97.5% intervals for the two-case primary pair. Score `strong_covariance_universality`, `hodge_resolved_geometric_eth`, `cohomological_non_gaussian_class`, `structured_cohomology`, or `feasibility_failure` exactly as frozen in the design.
+
+- [ ] **Step 4: Implement the scheduler stop point**
+
+The array maps 24 realizations × two sectors × two panel kinds. The dependent aggregate writes safe covariates and the two numerical null predictions, seals the JSON, prints the seal, and exits. The submission script must not invoke the unseal subcommand.
+
+- [ ] **Step 5: Run tests, shell syntax checks, and submit when the remote allocation is live**
+
+```bash
+PYTHONPATH=01_task_folder/task_05/script pytest -q 01_task_folder/task_05/script/tests/test_susy_hodge_analysis_v7.py 01_task_folder/task_05/script/tests/test_susy_hodge_runner_v7.py
+bash -n 01_task_folder/task_05/script/slurm/submit_susy_hodge_N14_v7.sh
+```
+
+After the prediction seal is independently visible, run the separate unseal command and commit only code, compact JSON summaries, and seals:
+
+```bash
+git add 01_task_folder/task_05/script/analyze_susy_hodge_geometric_eth_v7.py 01_task_folder/task_05/script/slurm/run_susy_hodge_N14_v7_array.sbatch 01_task_folder/task_05/script/slurm/submit_susy_hodge_N14_v7.sh 01_task_folder/task_05/script/tests/test_susy_hodge_analysis_v7.py
+git commit -m "analysis: seal SUSY Hodge held-out prediction"
+```
+
+### Task 9: Inference figure and source-backed result report
+
+**Files:**
+- Create: `01_task_folder/task_05/script/make_susy_hodge_figure_v7.py`
+- Create: `01_task_folder/task_05/script/tests/test_susy_hodge_figure_v7.py`
+- Generate: `01_task_folder/task_05/script/output/figure_susy_hodge_geometric_eth_v7.{pdf,png,json}`
+- Generate: `01_task_folder/task_05/script/output/susy_hodge_geometric_eth_report_v7.md`
+
+**Interfaces:**
+- Consumes only accepted pilot inference, sealed $N=14$ inference, decomposable-control audit, and immutable v6 cross-parent report.
+- Produces a four-panel figure: response-complex schematic; Hodge balance/effective-rank flow; physical versus collapsed/Hodge null; and held-out branch/structured-control verdict.
+
+- [ ] **Step 1: Write failing figure/report provenance tests**
+
+Require every plotted scalar to be recoverable from hashed JSON/NPZ input, the selected branch to appear verbatim in figure JSON and report, the literature links to be clickable Markdown, and the report to contain established/not-established sections.
+
+- [ ] **Step 2: Run figure tests and confirm missing outputs**
+
+Run: `PYTHONPATH=01_task_folder/task_05/script pytest -q 01_task_folder/task_05/script/tests/test_susy_hodge_figure_v7.py`
+
+- [ ] **Step 3: Implement generated assets**
+
+Use uncertainty bands from complete realizations, distinguish pilot from held-out points visually, mark the prediction-seal boundary, and place the analytic decomposable control in a separate style. Do not draw an asymptotic fit unless the registered $N=16$ separation gate later passes.
+
+- [ ] **Step 4: Generate and visually inspect both PDF and PNG**
+
+```bash
+PYTHONPATH=01_task_folder/task_05/script python 01_task_folder/task_05/script/make_susy_hodge_figure_v7.py
+pdftoppm -png -r 180 -f 1 -singlefile 01_task_folder/task_05/script/output/figure_susy_hodge_geometric_eth_v7.pdf tmp/susy_hodge_v7_figure
+```
+
+Inspect `tmp/susy_hodge_v7_figure.png` at original resolution and correct clipping, overlaps, unreadable labels, or misleading axes before acceptance.
+
+- [ ] **Step 5: Commit code and compact publication artifacts**
+
+```bash
+git add 01_task_folder/task_05/script/make_susy_hodge_figure_v7.py 01_task_folder/task_05/script/tests/test_susy_hodge_figure_v7.py 01_task_folder/task_05/script/output/figure_susy_hodge_geometric_eth_v7.pdf 01_task_folder/task_05/script/output/figure_susy_hodge_geometric_eth_v7.png 01_task_folder/task_05/script/output/figure_susy_hodge_geometric_eth_v7.json 01_task_folder/task_05/script/output/susy_hodge_geometric_eth_report_v7.md
+git commit -m "docs: report Hodge-resolved geometric ETH verdict"
+```
+
+### Task 10: Fail-closed delivery audit and dashboard synchronization
+
+**Files:**
+- Create: `01_task_folder/task_05/script/verify_susy_hodge_delivery_v7.py`
+- Create: `01_task_folder/task_05/script/tests/test_susy_hodge_delivery_v7.py`
+- Modify: `01_task_folder/task_05/task_05_dashboard.md`
+- Modify: `00_main/main_dashboard.md`
+
+**Interfaces:**
+- Produces: `script/output/susy_hodge_delivery_audit_v7.json` with individual checks and one top-level `passed` boolean.
+
+- [ ] **Step 1: Write the failing delivery and corruption tests**
+
+Require exact registered case grids, all source/array/seal hashes, no safe-outcome leakage, prediction timestamp before unseal timestamp, analytic curvature atoms, one-sided regression, selected branch consistency, figure/report provenance, and the complete v7 pytest command. Copy accepted metadata to a temporary directory, corrupt one seal and one safe JSON key, and require both audits to fail.
+
+- [ ] **Step 2: Run the delivery test and confirm failure**
+
+Run: `PYTHONPATH=01_task_folder/task_05/script pytest -q 01_task_folder/task_05/script/tests/test_susy_hodge_delivery_v7.py`
+
+- [ ] **Step 3: Implement the audit and one-command verifier**
+
+The verifier must recompute branch selection from arrays rather than trust the report, scan safe serialized data for forbidden keys, compare every referenced SHA-256, and include exact test counts and result provenance in its JSON.
+
+- [ ] **Step 4: Run the complete v7 and immutable v6 regressions**
+
+```bash
+PYTHONPATH=01_task_folder/task_05/script pytest -q $(rg --files 01_task_folder/task_05/script/tests | rg '(v6|v7)\.py$')
+PYTHONPATH=01_task_folder/task_05/script python 01_task_folder/task_05/script/verify_susy_hodge_delivery_v7.py
+```
+
+- [ ] **Step 5: Synchronize dashboards and commit the delivery**
+
+Append a `[Codex]` version-log entry with the selected branch, main numerical intervals, source hashes, prediction seal, test count, report, and figure. Embed `![Hodge-resolved Geometric ETH](script/output/figure_susy_hodge_geometric_eth_v7.png)` in the task canvas and add the same status/result to the main session log. Keep both statuses `🟡 Ongoing` unless the human explicitly closes the task.
+
+```bash
+git add 01_task_folder/task_05/script/verify_susy_hodge_delivery_v7.py 01_task_folder/task_05/script/tests/test_susy_hodge_delivery_v7.py 01_task_folder/task_05/script/output/susy_hodge_delivery_audit_v7.json
+git commit -m "science: deliver Hodge-resolved SUSY benchmark"
+```
+
+## Self-review result
+
+- **Spec coverage:** The ten tasks cover the cubic cochain, expected BPS ranks, exact/coexact theorem, tangent panels, pre-outcome Hodge signature, two competing nulls, information barrier, decomposable control, sequential pilot, sealed $N=14$, branch inference, figure/report, corruption tests, and dashboard delivery. The conditional $N=16$ extension remains gated exactly as specified rather than being silently omitted.
+- **Placeholder scan:** No red-flag placeholder or unspecified error-handling step remains. Every code task has a named failing test, exact command, implementation rule, passing command, and commit boundary.
+- **Type consistency:** `BPSFrame` flows from `susy_cohomology` into `hodge_response`; `HodgeSignature` flows into `hodge_wick` and the safe runner; only the analyzer may validate a seal and open outcome sidecars; figure and delivery scripts consume the analyzer's accepted artifacts.
+
+## Execution handoff
+
+Plan saved at `docs/plans/2026-08-01-susy-cohomological-geometric-eth-implementation-plan.md`. Execution mode is **inline**: the human already authorized execution with “做吧,” and the active repository instructions prohibit unrequested subagent delegation. Work proceeds task by task with the commit and regression checkpoints above.
diff --git a/tracks/mps/solutions/Wander-276/research/overleaf_sync/cohomological_geometric_eth/figures/figure_susy_hodge_geometric_eth_v7.pdf b/tracks/mps/solutions/Wander-276/research/overleaf_sync/cohomological_geometric_eth/figures/figure_susy_hodge_geometric_eth_v7.pdf
new file mode 100644
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diff --git a/tracks/mps/solutions/Wander-276/research/overleaf_sync/cohomological_geometric_eth/generated/results_v7.tex b/tracks/mps/solutions/Wander-276/research/overleaf_sync/cohomological_geometric_eth/generated/results_v7.tex
new file mode 100644
index 000000000..f3b90bfc7
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/overleaf_sync/cohomological_geometric_eth/generated/results_v7.tex
@@ -0,0 +1,16 @@
+% Generated from audited v7 inference; do not edit.
+\newif\ifheldoutcomplete
+\heldoutcompletetrue
+\newcommand{\HeldoutAbstract}{Exactly degenerate quantum manifolds have no internal level statistics, but their projectors move over coupling space. We formulate this motion as a response complex and compare one-sided frustration-free constraints with the orthogonal exact/coexact response of charge-resolved cubic $\mathcal N=2$ Sachdev--Ye--Kitaev cohomology. In the sequential $N=8,10,12$ pilot, 12 of 12 size/sector/panel groups reject both registered separable covariance nulls. A prediction sealed before the held-out $N=14$ opening is rejected by both nulls for the central/adjacent sparse pair, establishing structured four-point memory beyond the frozen separable Hodge-covariance law, without claiming complete entrywise covariance matching.}
+\newcommand{\HeldoutBranch}{cohomological\_non\_gaussian\_class}
+\newcommand{\HeldoutResultSentence}{The held-out adjacent and central medians are 0.301529 and 0.374993; their complete-realization confidence intervals do not overlap either sealed covariance prediction.}
+\newcommand{\PilotResultSentence}{Across the complete $N=8,10,12$ pilot, 12 of 12 groups reject both registered separable covariance nulls under complete-realization resampling.}
+\newcommand{\HeldoutSeal}{fc300dc7e4bd}
+\newcommand{\HeldoutAdjacentObserved}{0.301529}
+\newcommand{\HeldoutAdjacentPhysical}{$[0.291527,\,0.312061]$}
+\newcommand{\HeldoutAdjacentCollapsed}{$[0.111789,\,0.111852]$}
+\newcommand{\HeldoutAdjacentHodge}{$[0.112344,\,0.112513]$}
+\newcommand{\HeldoutCentralObserved}{0.374993}
+\newcommand{\HeldoutCentralPhysical}{$[0.368980,\,0.380473]$}
+\newcommand{\HeldoutCentralCollapsed}{$[0.111338,\,0.111353]$}
+\newcommand{\HeldoutCentralHodge}{$[0.111333,\,0.111348]$}
diff --git a/tracks/mps/solutions/Wander-276/research/overleaf_sync/cohomological_geometric_eth/main.log b/tracks/mps/solutions/Wander-276/research/overleaf_sync/cohomological_geometric_eth/main.log
new file mode 100644
index 000000000..82dd1ad43
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/overleaf_sync/cohomological_geometric_eth/main.log
@@ -0,0 +1,586 @@
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diff --git a/tracks/mps/solutions/Wander-276/research/overleaf_sync/cohomological_geometric_eth/main.tex b/tracks/mps/solutions/Wander-276/research/overleaf_sync/cohomological_geometric_eth/main.tex
new file mode 100644
index 000000000..99f334113
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/overleaf_sync/cohomological_geometric_eth/main.tex
@@ -0,0 +1,53 @@
+\documentclass[aps,prl,reprint,superscriptaddress,longbibliography,floatfix]{revtex4-2}
+
+\usepackage{amsmath,amssymb,bm}
+\usepackage{booktabs}
+\usepackage{graphicx}
+\usepackage{microtype}
+\usepackage{xcolor}
+\usepackage[colorlinks=true,citecolor=blue!55!black,linkcolor=blue!55!black,urlcolor=blue!55!black]{hyperref}
+\hypersetup{pdftitle={Response-Complex Memory in Exactly Degenerate Quantum Matter},pdfauthor={Thomas J. Wang; OKongOYangO},pdfsubject={Hodge-resolved quantum geometry and chaos under exact degeneracy}}
+
+\graphicspath{{figures/}}
+\input{generated/results_v7.tex}
+\newcommand{\Tr}{\operatorname{Tr}}
+\newcommand{\dd}{\mathrm d}
+\newcommand{\cH}{\mathcal H}
+\newcommand{\cM}{\mathcal M}
+
+\begin{document}
+
+\title{Response-Complex Memory in Exactly Degenerate Quantum Matter}
+
+\author{Thomas J. Wang}
+\email{WangTheoPhys@outlook.com}
+\affiliation{Tsinghua University, Beijing 100084, China}
+
+\author{OKongOYangO}
+\affiliation{The Pennsylvania State University, University Park, Pennsylvania 16802, USA}
+
+\date{\today}
+
+\begin{abstract}
+\ifheldoutcomplete
+\HeldoutAbstract
+\else
+This source tree freezes the response-complex formalism and the prediction protocol before the held-out calculation is opened. The result-bearing abstract is generated only after a valid prediction seal, explicit unseal, and fail-closed inference audit exist. No held-out scientific branch is claimed in this draft state.
+\fi
+\end{abstract}
+
+\maketitle
+
+\input{sections/01-introduction.tex}
+\input{sections/02-response-complex.tex}
+\input{sections/03-sealed-protocol.tex}
+\input{sections/04-results.tex}
+\input{sections/05-discussion.tex}
+
+\begin{acknowledgments}
+The numerical artifacts, complete-realization resampling records, source hashes, and prediction seals are retained with the reproducibility package. We thank the Quantum Harness community for discussions motivating fail-closed computational tests.
+\end{acknowledgments}
+
+\bibliography{references}
+
+\end{document}
diff --git a/tracks/mps/solutions/Wander-276/research/overleaf_sync/cohomological_geometric_eth/references.bib b/tracks/mps/solutions/Wander-276/research/overleaf_sync/cohomological_geometric_eth/references.bib
new file mode 100644
index 000000000..143301513
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/overleaf_sync/cohomological_geometric_eth/references.bib
@@ -0,0 +1,94 @@
+@article{berry1984,
+  author = {Berry, Michael V.},
+  title = {Quantal phase factors accompanying adiabatic changes},
+  journal = {Proceedings of the Royal Society of London A},
+  volume = {392},
+  pages = {45--57},
+  year = {1984},
+  doi = {10.1098/rspa.1984.0023}
+}
+
+@article{wilczekzee1984,
+  author = {Wilczek, Frank and Zee, A.},
+  title = {Appearance of gauge structure in simple dynamical systems},
+  journal = {Physical Review Letters},
+  volume = {52},
+  pages = {2111--2114},
+  year = {1984},
+  doi = {10.1103/PhysRevLett.52.2111}
+}
+
+@article{provostvallee1980,
+  author = {Provost, J. P. and Vall{\'e}e, G.},
+  title = {Riemannian structure on manifolds of quantum states},
+  journal = {Communications in Mathematical Physics},
+  volume = {76},
+  pages = {289--301},
+  year = {1980},
+  doi = {10.1007/BF02193559}
+}
+
+@article{kato1950,
+  author = {Kato, Tosio},
+  title = {On the adiabatic theorem of quantum mechanics},
+  journal = {Journal of the Physical Society of Japan},
+  volume = {5},
+  pages = {435--439},
+  year = {1950},
+  doi = {10.1143/JPSJ.5.435}
+}
+
+@article{fu2017susy,
+  author = {Fu, Wenbo and Gaiotto, Davide and Maldacena, Juan and Sachdev, Subir},
+  title = {Supersymmetric Sachdev--Ye--Kitaev models},
+  journal = {Physical Review D},
+  volume = {95},
+  pages = {026009},
+  year = {2017},
+  doi = {10.1103/PhysRevD.95.026009},
+  eprint = {1610.08917},
+  archivePrefix = {arXiv}
+}
+
+@misc{chang2024fortuity,
+  author = {Chang, Chi-Ming and Chen, Ying-Hsuan and Sia, Gregory and Yang, Zhenbin},
+  title = {Fortuity in {SYK} models},
+  year = {2024},
+  eprint = {2412.06902},
+  archivePrefix = {arXiv}
+}
+
+@misc{chen2024bps,
+  author = {Chen, Yiming and Lin, Henry W. and Shenker, Stephen H.},
+  title = {{BPS} chaos},
+  year = {2024},
+  eprint = {2407.19387},
+  archivePrefix = {arXiv}
+}
+
+@misc{chen2026berry,
+  author = {Chen, Yiming and Colin-Ellerin, Sean and Mamroud, Ohad and Papadodimas, Kyriakos},
+  title = {Chaos of Berry curvature for {BPS} microstates},
+  year = {2026},
+  eprint = {2604.23287},
+  archivePrefix = {arXiv}
+}
+
+@article{huijse2009cohomology,
+  author = {Huijse, Liza and Schoutens, Kareljan},
+  title = {Supersymmetry, lattice fermions, independence complexes and cohomology theory},
+  journal = {Advances in Theoretical and Mathematical Physics},
+  volume = {14},
+  pages = {643--694},
+  year = {2010},
+  eprint = {0903.0784},
+  archivePrefix = {arXiv}
+}
+
+@misc{zhang2024local,
+  author = {Zhang, Zhiyuan and Sukeno, Hikaru and Ikeda, Tatsuhiko N. and Wei, Tzu-Chieh},
+  title = {Local symmetries and extensive ground-state degeneracy of a one-dimensional supersymmetric fermionic chain},
+  year = {2024},
+  eprint = {2412.17208},
+  archivePrefix = {arXiv}
+}
diff --git a/tracks/mps/solutions/Wander-276/research/overleaf_sync/cohomological_geometric_eth/sections/01-introduction.tex b/tracks/mps/solutions/Wander-276/research/overleaf_sync/cohomological_geometric_eth/sections/01-introduction.tex
new file mode 100644
index 000000000..4774045ab
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/overleaf_sync/cohomological_geometric_eth/sections/01-introduction.tex
@@ -0,0 +1,8 @@
+\section{Spectral silence and response complexity}
+\label{sec:introduction}
+
+Exact degeneracy removes the level spacings on which conventional quantum-chaos diagnostics are built. If a protected multiplet contains \(D\) states at the same energy, its raw energy spectral form factor is constant and its connected form factor vanishes. This is a structural blind spot in supersymmetric sectors, frustration-free zero-mode manifolds, and other problems where lifting the degeneracy would destroy the object of interest. The missing information is carried by the motion of the protected projector \(P(\bm\lambda)\) over a coupling or moduli space, through its non-Abelian Berry curvature and quantum metric \cite{berry1984,wilczekzee1984,provostvallee1980,kato1950}.
+
+Random-matrix-like Berry curvature in supersymmetric black-hole microstates and in generic \(\mathcal N=2\) Sachdev--Ye--Kitaev (SYK) models is already established \cite{chen2026berry,chen2024bps}. The question addressed here is different. Does random-matrix-like local curvature exhaust the information in the protected response, or do higher gauge-invariant correlations retain the mechanism by which the degeneracy is protected? Equivalently, can a two-point law predict a four-point response observable across distinct protection mechanisms? We compare one-sided positive-constraint Laughlin parents with a two-sided supersymmetric cohomology. The comparison uses the same covariance-whitened four-channel statistic, the same complete-realization uncertainty unit, and a prediction constructed before the held-out four-point outcome is opened.
+
+The organizing object is a \emph{response complex}. For a frustration-free parent \(H=B^\dagger B\), the zero-mode response is one-sided. For \(H=\{Q,Q^\dagger\}\) with \(Q^2=0\), it decomposes into orthogonal exact and coexact branches. Their weights, covariance spectra, and effective ranks form a safe Hodge signature that is available without reading the four-channel outcome. We ask whether this signature selects a finite-size Gaussian response law. Coverage would support a two-point-controlled form of Geometric ETH; reproducible rejection would instead identify response-complex memory beyond that law. The protocol retains either outcome rather than fitting the held-out statistic after the fact.
diff --git a/tracks/mps/solutions/Wander-276/research/overleaf_sync/cohomological_geometric_eth/sections/02-response-complex.tex b/tracks/mps/solutions/Wander-276/research/overleaf_sync/cohomological_geometric_eth/sections/02-response-complex.tex
new file mode 100644
index 000000000..0620e3b86
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/overleaf_sync/cohomological_geometric_eth/sections/02-response-complex.tex
@@ -0,0 +1,59 @@
+\section{Hodge-resolved protected response}
+\label{sec:response-complex}
+
+The generic cubic \(\mathcal N=2\) SYK supercharge is
+\begin{equation}
+ \begin{split}
+ Q(C)&=\sum_{i<j<k}C_{ijk}\psi_i\psi_j\psi_k,\qquad Q^2=0,\\
+ H&=\{Q,Q^\dagger\}.
+ \end{split}
+ \label{eq:supercharge}
+\end{equation}
+In charge sector \(r\), the protected fiber is the harmonic cohomology
+\begin{equation}
+ \cH_{\mathrm{BPS},r}=\ker Q_r\cap\ker Q_{r-3}^\dagger.
+ \label{eq:harmonic-fiber}
+\end{equation}
+We use generic isotropic complex three-forms \(C\), rather than the decomposable locus, because the generic BPS states are fortuitous and concentrated near the central charge sectors \cite{fu2017susy,chang2024fortuity}.
+
+Let \(P\) project onto Eq.~\eqref{eq:harmonic-fiber}, and let \(H_\perp^+\) be the inverse of \(H\) on its positive-energy complement. For a real coupling tangent represented by \(\delta Q+\delta Q^\dagger\), the complement-to-fiber response is
+\begin{align}
+ X(\delta C)&=-H_\perp^+\left(Q\,\delta Q^\dagger+Q^\dagger\delta Q\right)P
+ \nonumber\\
+ &=X_-\oplus X_+,
+ \label{eq:hodge-response}\\
+ X_-&=-H_\perp^+Q\,\delta Q^\dagger P,
+ \qquad
+ X_+=-H_\perp^+Q^\dagger\delta QP.
+ \nonumber
+\end{align}
+Nilpotency implies \(\operatorname{im}Q\perp\operatorname{im}Q^\dagger\), hence \(X_-^\dagger X_+=0\). We verify Eq.~\eqref{eq:hodge-response} against the direct resolvent derivative and a centered finite difference of \(P\). This identity turns the qualitative distinction between constraint and cohomological protection into a measurable branch structure.
+
+The response is the quantum geometry, not an auxiliary diagnostic. In a local frame of the protected fiber, the matrix-valued quantum geometric tensor, metric, and Berry curvature are
+\begin{equation}
+ \begin{aligned}
+ \mathcal Q_{ab}&=X_a^\dagger X_b,\qquad
+ g_{ab}=\frac{\mathcal Q_{ab}+\mathcal Q_{ba}}{2},\\
+ F_{ab}&=i\left(\mathcal Q_{ab}-\mathcal Q_{ba}\right).
+ \end{aligned}
+ \label{eq:qgt-response}
+\end{equation}
+Thus all gauge-invariant contractions used below are correlations of the same complement-resolved amplitudes that generate \(g\) and \(F\). For a one-sided parent \(H=B^\dagger B\) with \(BP=0\), the corresponding derivative is \(X=-H_\perp^+B^\dagger\delta B P\) and lies in a single response branch. Equation~\eqref{eq:hodge-response} is therefore an independent, two-sided protection mechanism rather than a change of basis within the Laughlin construction.
+
+For an eight-channel tangent panel, define branch weights and Hodge balance by
+\begin{equation}
+ T_\pm=\sum_{a=1}^{8}\lVert X_{a,\pm}\rVert_F^2,
+ \qquad
+ \eta_H=\frac{4T_+T_-}{(T_++T_-)^2}.
+ \label{eq:hodge-balance}
+\end{equation}
+The pre-outcome signature also contains branch-resolved channel, target, and complement covariance spectra. The collapsed null discards the branch label, whereas the Hodge null samples the two branches independently and forms their orthogonal direct sum. Both are parameter-free once the safe two-point data are fixed.
+
+After complete channel whitening, the physical diagnostic is the gauge-invariant tensor
+\begin{equation}
+ \mathcal T_{abcd}=\frac{1}{D}\Tr\!\left(
+ \widehat X_a^\dagger\widehat X_b
+ \widehat X_c^\dagger\widehat X_d\right),
+ \label{eq:four-channel}
+\end{equation}
+and its normalized Frobenius distance from the registered Gaussian Wick contraction. Independent target and complement basis rotations leave Eq.~\eqref{eq:four-channel} unchanged. The label ``non-Gaussian class'' below refers operationally to rejection of these frozen separable covariance models; it does not assert that the complete entrywise covariance operator has been matched.
diff --git a/tracks/mps/solutions/Wander-276/research/overleaf_sync/cohomological_geometric_eth/sections/03-sealed-protocol.tex b/tracks/mps/solutions/Wander-276/research/overleaf_sync/cohomological_geometric_eth/sections/03-sealed-protocol.tex
new file mode 100644
index 000000000..13fd28e5b
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/overleaf_sync/cohomological_geometric_eth/sections/03-sealed-protocol.tex
@@ -0,0 +1,10 @@
+\section{Sequential and sealed protocol}
+\label{sec:protocol}
+
+We study central \(r=N/2\) and adjacent \(r=N/2-1\) sectors at even \(N\). Each coupling realization supplies a sparse coordinate panel and an independent isotropic panel, both projected away from the complex radial line and orthonormalized before any four-channel result is inspected. The complete disorder realization is the uncertainty unit: tangent entries and tensor components are never resampled as independent observations.
+
+The sequential pilot uses \(N=8,10,12\). Each realization is split into a safe metadata/array checkpoint and an outcome sidecar. The safe checkpoint contains the BPS rank, positive gap, numerical residuals, Hodge signature, covariance spectra, seeds, and source hashes, but no four-channel value. Per-realization Gaussian banks are generated from this safe file. A null replicate selects one bank draw per realization and takes their median; the physical uncertainty is a nonparametric bootstrap of complete-realization medians.
+
+The held-out \(N=14\) computation is more restrictive. All safe response and null checkpoints must pass before the collapsed and Hodge numerical prediction intervals are written atomically. The prediction JSON is sealed by SHA-256. No scheduler dependency invokes the unseal command. Only a separate explicit action may validate the seal, open the sidecars, and score the central/adjacent sparse pair. The isotropic pair is secondary and cannot change the primary branch.
+
+The registered branches are: simultaneous coverage by both nulls; coverage only by the Hodge null; rejection of both with reproducible response memory; statistical indistinguishability from the decomposable structured control; or feasibility failure. A decomposable three-form recovers exact curvature atoms \(0,\pm\alpha^{-2}\) with analytic multiplicities, and a one-sided synthetic response reproduces the accepted Laughlin Gaussian null exactly. These controls test the algebra and implementation independently of the generic-coupling outcome.
diff --git a/tracks/mps/solutions/Wander-276/research/overleaf_sync/cohomological_geometric_eth/sections/04-results.tex b/tracks/mps/solutions/Wander-276/research/overleaf_sync/cohomological_geometric_eth/sections/04-results.tex
new file mode 100644
index 000000000..a88b4797e
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/overleaf_sync/cohomological_geometric_eth/sections/04-results.tex
@@ -0,0 +1,16 @@
+\section{Response-complex inference}
+\label{sec:results}
+
+\PilotResultSentence
+
+\ifheldoutcomplete
+\begin{figure*}[t]
+ \includegraphics[width=\textwidth]{figure_susy_hodge_geometric_eth_v7.pdf}
+ \caption{\textbf{Hodge-resolved response-complex test.} The panels show the one-sided/two-sided protection map, charge-resolved Hodge balance, complete-realization pilot intervals, and the sealed \(N=14\) central/adjacent sparse validation. Every plotted scalar is recoverable from the associated hash manifest.}
+ \label{fig:hodge-inference}
+\end{figure*}
+
+\HeldoutResultSentence The frozen decision therefore selects structured cohomological response memory beyond the registered separable covariance laws. Figure~\ref{fig:hodge-inference} separates the exact two-point Hodge structure from the higher response memory tested by Eq.~\eqref{eq:four-channel}; the exact branch identifier and prediction hash are retained in the audited Supplemental Material and machine-readable artifact.
+\else
+The result-bearing figure and paragraph are disabled until the prediction seal, unsealed aggregate, and inference artifact pass the delivery audit. This fail-closed draft cannot state a held-out branch.
+\fi
diff --git a/tracks/mps/solutions/Wander-276/research/overleaf_sync/cohomological_geometric_eth/sections/05-discussion.tex b/tracks/mps/solutions/Wander-276/research/overleaf_sync/cohomological_geometric_eth/sections/05-discussion.tex
new file mode 100644
index 000000000..100c80437
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/overleaf_sync/cohomological_geometric_eth/sections/05-discussion.tex
@@ -0,0 +1,8 @@
+\section{Discussion}
+\label{sec:discussion}
+
+The response-complex construction changes the object being classified. Spectral chaos asks how eigenvalues fluctuate after a degeneracy is resolved. Here the protected energies remain exactly equal, and the diagnostic asks how the degenerate fiber moves over coupling space. Equation~\eqref{eq:qgt-response} makes the replacement exact: two-point response generates the quantum metric and Berry curvature, while Eq.~\eqref{eq:four-channel} tests whether their underlying amplitudes obey a Gaussian higher-moment closure. The exact/coexact split supplies a mechanism-level coordinate on that motion. One-sided positive constraints and two-sided cohomology need not share the same higher response law even when their local curvature spectra are random-matrix-like.
+
+The claim is deliberately finite-size and geometric. It is not conventional ETH, thermalization, a real-time chaos diagnostic, or a thermodynamic theorem. In particular, a successful sealed finite-size prediction would establish covariance-controlled Geometric ETH only on the tested sequence; it would not supply an asymptotic concentration law. Conversely, rejection localizes the missing information above the registered separable two-point structure without proving that every more general Gaussian covariance model fails. Generic \(\mathcal N=2\) SYK supplies a genuinely supersymmetric protection mechanism but not spatial locality. Establishing locality universality requires a later nilpotent lattice-supercharge model with a fixed charge-resolved zero-mode count, an open gap, and a nontrivially moving harmonic projector \cite{huijse2009cohomology,zhang2024local}.
+
+There is also a covariance boundary. The collapsed and Hodge nulls match the registered marginal covariance data under a separable matrix-normal ansatz. If they are rejected, the result establishes structured memory beyond that ansatz. A stronger statement of intrinsic non-Gaussianity would require matching or independently constraining the complete nonseparable entrywise covariance operator. This distinction is not a weakness of the sealed test; it identifies the next theoretical target without allowing a post-outcome refit to rewrite the primary result.
diff --git a/tracks/mps/solutions/Wander-276/research/overleaf_sync/cohomological_geometric_eth/supplement.log b/tracks/mps/solutions/Wander-276/research/overleaf_sync/cohomological_geometric_eth/supplement.log
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@@ -0,0 +1,556 @@
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diff --git a/tracks/mps/solutions/Wander-276/research/overleaf_sync/cohomological_geometric_eth/supplement.tex b/tracks/mps/solutions/Wander-276/research/overleaf_sync/cohomological_geometric_eth/supplement.tex
new file mode 100644
index 000000000..93f7ec4a9
--- /dev/null
+++ b/tracks/mps/solutions/Wander-276/research/overleaf_sync/cohomological_geometric_eth/supplement.tex
@@ -0,0 +1,172 @@
+\documentclass[aps,prl,onecolumn,superscriptaddress,longbibliography,floatfix]{revtex4-2}
+
+\usepackage{amsmath,amssymb,bm}
+\usepackage{booktabs}
+\usepackage{microtype}
+\usepackage{xcolor}
+\usepackage[colorlinks=true,citecolor=blue!55!black,linkcolor=blue!55!black,urlcolor=blue!55!black]{hyperref}
+\hypersetup{pdftitle={Supplemental Material for Response-Complex Memory in Exactly Degenerate Quantum Matter},pdfauthor={Thomas J. Wang; OKongOYangO}}
+
+\input{generated/results_v7.tex}
+\newcommand{\Tr}{\operatorname{Tr}}
+\newcommand{\cH}{\mathcal H}
+
+\begin{document}
+
+\title{Supplemental Material for ``Response-Complex Memory in Exactly Degenerate Quantum Matter''}
+
+\author{Thomas J. Wang}
+\email{WangTheoPhys@outlook.com}
+\affiliation{Tsinghua University, Beijing 100084, China}
+
+\author{OKongOYangO}
+\affiliation{The Pennsylvania State University, University Park, Pennsylvania 16802, USA}
+
+\maketitle
+
+\section{Finite cochain complex and harmonic fiber}
+\label{sec:supp-cochain}
+
+Let \(V_r=\bigwedge^r\mathbb C^N\) be the fixed-charge sector with the occupation basis ordered lexicographically. A complex antisymmetric three-form \(C\) defines the degree-lowering maps
+\begin{equation}
+ Q_r(C):V_r\longrightarrow V_{r-3},\qquad Q_r(C)=\sum_{i<j<k}C_{ijk}\psi_i\psi_j\psi_k.
+ \label{eq:supp-qr}
+\end{equation}
+Fermionic antisymmetry gives \(Q_{r-3}Q_r=0\) exactly. The charge-resolved Hamiltonian and harmonic subspace are
+\begin{align}
+ H_r&=Q_r^\dagger Q_r+Q_{r-3}Q_{r-3}^\dagger,\label{eq:supp-hr}\\
+ \cH_{\mathrm{BPS},r}&=\ker Q_r\cap\ker Q_{r-3}^\dagger.
+ \label{eq:supp-harmonic}
+\end{align}
+The implementation constructs the sparse cochain matrices from the signed occupation action and obtains the harmonic frame from the numerical kernel of Eq.~\eqref{eq:supp-hr}. Every accepted realization passes nilpotency, Hermiticity, projector idempotency, harmonic-residual, and positive-gap gates. No zero-mode count is inferred from an energy histogram.
+
+The generic ensemble uses isotropic complex Gaussian coefficients followed by normalization. The decomposable control instead takes \(C=u\wedge v\wedge w\). It is analytically reducible to one occupied three-mode block and produces the registered exact curvature atoms and multiplicities. This separates the generic cohomological response from an algebraically structured locus without changing the cochain conventions.
+
+\section{Hodge-resolved projector derivative}
+\label{sec:supp-response}
+
+Let \(P\) be the harmonic projector, \(R=1-P\), and \(H_\perp^+=RH^+R\). Differentiating \(HP=0\), multiplying by \(R\) on the left, and imposing the parallel-frame convention \(P\,\delta P\,P=0\) gives
+\begin{equation}
+ X\equiv R\,\delta P\,P=-H_\perp^+\,\delta H\,P.
+ \label{eq:supp-resolvent}
+\end{equation}
+For a real coupling tangent \(\delta Q+\delta Q^\dagger\), the terms in \(\delta H\) that survive on the harmonic fiber yield
+\begin{equation}
+ X=-H_\perp^+\left(Q\delta Q^\dagger+Q^\dagger\delta Q\right)P=X_-+X_+.
+ \label{eq:supp-hodge}
+\end{equation}
+Here \(X_-\) lies in \(\operatorname{im}Q\), whereas \(X_+\) lies in \(\operatorname{im}Q^\dagger\). Since \(Q^2=0\),
+\begin{equation}
+ \langle Q a,Q^\dagger b\rangle=\langle Q^2a,b\rangle=0,
+ \qquad X_-^\dagger X_+=0.
+ \label{eq:supp-orthogonal}
+\end{equation}
+The code compares Eq.~\eqref{eq:supp-hodge} with Eq.~\eqref{eq:supp-resolvent} and with a centered finite difference of the full harmonic projector. These are independent numerical paths.
+
+For comparison, a one-sided positive parent \(H=B^\dagger B\) with \(BP=0\) has
+\begin{equation}
+ X=-H_\perp^+B^\dagger\delta B P,
+ \label{eq:supp-one-sided}
+\end{equation}
+because the \(\delta B^\dagger BP\) term vanishes. Equations~\eqref{eq:supp-hodge} and \eqref{eq:supp-one-sided} therefore distinguish protection complexes, not merely coordinate choices.
+
+\section{Quantum geometry and gauge-invariant higher response}
+\label{sec:supp-geometry}
+
+For tangent labels \(a,b\), the protected-fiber quantum geometric tensor is
+\begin{equation}
+ \mathcal Q_{ab}=X_a^\dagger X_b,
+ \label{eq:supp-qgt}
+\end{equation}
+whose symmetric and antisymmetric parts give the matrix-valued metric and non-Abelian Berry curvature. Under independent basis changes \(U\) in the protected fiber and \(V\) in its complement, \(X_a\mapsto VX_aU^\dagger\). Consequently \(\mathcal Q_{ab}\mapsto U\mathcal Q_{ab}U^\dagger\), and every trace contraction below is gauge invariant.
+
+An eight-channel panel has Gram matrix
+\begin{equation}
+ G_{ab}=\frac{1}{D}\Tr(X_a^\dagger X_b).
+ \label{eq:supp-gram}
+\end{equation}
+The accepted panels are projected away from the complex radial direction, orthonormalized in coupling space, and whitened on the numerical support of \(G\). The registered four-channel tensor is
+\begin{equation}
+ \mathcal T_{abcd}=\frac{1}{D}\Tr\!\left(
+ \widehat X_a^\dagger\widehat X_b
+ \widehat X_c^\dagger\widehat X_d\right).
+ \label{eq:supp-four-channel}
+\end{equation}
+The scalar outcome is the normalized Frobenius distance between Eq.~\eqref{eq:supp-four-channel} and its registered complex-Gaussian Wick contraction. Channel entries and tensor components are not treated as independent observations.
+
+\section{Safe Hodge signature and frozen nulls}
+\label{sec:supp-nulls}
+
+Before any four-channel outcome is opened, each panel writes a safe checkpoint containing the harmonic dimension, gap, residuals, branch weights, Hodge balance, covariance spectra, seeds, code hashes, and array hash. Outcome tokens are forbidden from the serialized safe checkpoint. The Hodge balance is
+\begin{equation}
+ \eta_H=\frac{4T_+T_-}{(T_++T_-)^2},\qquad
+ T_\pm=\sum_a\lVert X_{a,\pm}\rVert_F^2.
+ \label{eq:supp-balance}
+\end{equation}
+
+Two parameter-free nulls are frozen from safe information. The collapsed null matches the registered channel, target, and complement covariance spectra after forgetting the branch label. The Hodge null samples exact and coexact matrix-normal responses independently using their branch-resolved covariance spectra, then combines them as an orthogonal direct sum. Both nulls are separable covariance models. They do not match the complete nonseparable covariance operator of every response entry; rejection therefore establishes higher response memory beyond the registered null family, not the failure of every possible Gaussian model.
+
+Null draws are generated separately for each complete coupling realization. A group-level null replicate selects one precomputed draw for every realization and takes their median. Physical confidence intervals resample complete realizations and also take the median. This hierarchy preserves disorder dependence within all tangent channels and tensor components.
+
+\section{Sequential pilot and prediction seal}
+\label{sec:supp-seal}
+
+The sequential pilot contains the complete \(N=8,10,12\) grid, two charge sectors, and sparse-coordinate plus isotropic panels. It is used to freeze the qualitative branch definitions but not to read the held-out \(N=14\) outcome. The held-out workflow has four ordered states:
+\begin{enumerate}
+ \item response jobs write safe checkpoints and physically separate outcome sidecars;
+ \item safe covariance data generate all collapsed and Hodge null banks;
+ \item a prediction-only process aggregates the safe files, writes numerical prediction intervals, and seals the prediction JSON by SHA-256;
+ \item a separate explicit command validates the seal, opens the outcome sidecars, and scores the frozen branch.
+\end{enumerate}
+No scheduler dependency invokes step 4. The delivery audit also requires the prediction timestamp to precede the unseal timestamp, the unsealed aggregate to cite the exact prediction hash, and the selected branch to equal a fresh recomputation from the two primary sparse-sector records.
+
+\ifheldoutcomplete
+\HeldoutResultSentence The frozen decision selects the cohomological response-memory branch; the prediction-hash prefix is \texttt{\HeldoutSeal}.
+\begin{table}[h]
+\caption{Held-out sparse-panel statistic. Physical brackets are complete-realization 95\% bootstrap intervals; the remaining brackets are sealed 97.5\% prediction intervals.}
+\label{tab:supp-heldout}
+\begin{ruledtabular}
+\begin{tabular}{lcccc}
+Sector & Observed & Physical & Collapsed null & Hodge null \\
+\hline
+Adjacent & \HeldoutAdjacentObserved & \HeldoutAdjacentPhysical & \HeldoutAdjacentCollapsed & \HeldoutAdjacentHodge \\
+Central & \HeldoutCentralObserved & \HeldoutCentralPhysical & \HeldoutCentralCollapsed & \HeldoutCentralHodge \\
+\end{tabular}
+\end{ruledtabular}
+\end{table}
+\else
+The result paragraph remains disabled in the pre-unseal source state.
+\fi
+
+\section{Controls and falsification gates}
+\label{sec:supp-controls}
+
+The response and inference implementations are tested by four controls with distinct failure modes. First, the decomposable three-form admits an analytic unitary reduction and fixes the expected harmonic rank and curvature-atom multiplicities; this catches fermionic signs and charge-block errors. Second, a synthetic one-sided response is generated with a covariance law whose Wick contraction is known, and the collapsed null reproduces it. Third, independent protected-fiber and complement basis rotations leave the whitened tensor and scalar outcome invariant. Fourth, negative delivery tests alter a seal, remove a grid element, change an array hash, or introduce an outcome token into safe serialization; each modification must stop the workflow rather than select a scientific branch.
+
+The following compact artifacts are sufficient to audit the public result without retaining the large per-realization working tree:
+\begin{center}
+\begin{tabular}{@{}l@{\hspace{1.2em}}l@{}}
+\toprule
+Artifact & Audited role \\
+\midrule
+\texttt{susy\_hodge\_v7\_controls.json} & analytic and one-sided controls \\
+\texttt{susy\_hodge\_v7\_outcomes\_pilot\_combined.*} & complete \(N=8,10,12\) pilot \\
+\texttt{susy\_hodge\_v7\_N14\_prediction.*} & pre-outcome intervals and seal \\
+\texttt{susy\_hodge\_v7\_N14\_unsealed.*} & post-seal outcome aggregate \\
+\texttt{susy\_hodge\_v7\_N14\_inference.json} & recomputable frozen branch \\
+\texttt{susy\_hodge\_delivery\_audit\_v7.json} & end-to-end scientific hashes \\
+\bottomrule
+\end{tabular}
+\end{center}
+
+\section{Reproducibility contract and claim boundary}
+\label{sec:supp-reproducibility}
+\mbox{}\par
+
+The release retains source hashes, safe and outcome array hashes, per-realization null-bank identities, the prediction seal, the unsealed aggregate, a machine-recomputed inference branch, figure hashes, and compiled-paper audits. The focused test suite covers cochain nilpotency, analytic cohomology controls, exact/coexact orthogonality, finite differences, covariance-spectrum identities, null-bank idempotence, safe-file leakage rejection, corrupted-seal rejection, complete-grid enforcement, generated-asset hashes, and fail-closed manuscript activation.
+
+The scientific statement is finite size. It does not establish conventional energy-resolved ETH, thermalization, a real-time Lyapunov exponent, a spatially local SUSY universality class, or an asymptotic concentration theorem. Berry-curvature randomness in generic \(\mathcal N=2\) SYK is prior art \cite{chen2026berry,chen2024bps}. The new comparison is the common, prospective four-channel response test across one-sided Laughlin and two-sided cohomological protection mechanisms.
+
+\bibliography{references}
+
+\end{document}
diff --git a/tracks/mps/solutions/Wander-276/verify.sh b/tracks/mps/solutions/Wander-276/verify.sh
index f8c13f6fa..e90521c86 100755
--- a/tracks/mps/solutions/Wander-276/verify.sh
+++ b/tracks/mps/solutions/Wander-276/verify.sh
@@ -4,3 +4,13 @@ set -euo pipefail
 SOLUTION_DIR="$(cd "$(dirname "${BASH_SOURCE[0]}")" && pwd)"
 cd "${SOLUTION_DIR}/research/01_task_folder/task_05/script"
 PYTHONDONTWRITEBYTECODE=1 bash run_quick_verify_v1.sh
+
+V7_TESTS="$(find tests -type f -name '*v7.py' -print | sort)"
+if [[ -z "${V7_TESTS}" ]]; then
+  echo "No v7 tests found" >&2
+  exit 1
+fi
+# Test paths are repository-controlled and contain no whitespace.
+PYTHONDONTWRITEBYTECODE=1 PYTHONPATH=. pytest -q ${V7_TESTS}
+PYTHONDONTWRITEBYTECODE=1 PYTHONPATH=. python verify_susy_hodge_delivery_v7.py
+PYTHONDONTWRITEBYTECODE=1 PYTHONPATH=. python verify_susy_hodge_manuscript_v7.py

From b6a040bcb94ab17967cdf0c309441ec8e72722ba Mon Sep 17 00:00:00 2001
From: JunkaiWang-TheoPhy <1181100960@qq.com>
Date: Tue, 4 Aug 2026 09:58:21 +0800
Subject: [PATCH 3/3] docs: finalize selected response branch wording

Result: replace the final conditional branch wording with the selected cohomological_non_gaussian_class verdict and repair the finite-size math notation.

Boundary: the complete-covariance and asymptotic nonclaims remain unchanged.

Tested: bash tracks/mps/solutions/Wander-276/verify.sh passes after the wording closeout.

Co-authored-by: OmX <omx@oh-my-codex.dev>
---
 tracks/mps/solutions/Wander-276/PR_BODY.md                      | 2 +-
 .../Wander-276/research/01_task_folder/task_05/README.md        | 2 +-
 .../task_05/script/output/susy_hodge_delivery_audit_v7.json     | 2 +-
 .../task_05/script/output/susy_hodge_manuscript_audit_v7.json   | 2 +-
 4 files changed, 4 insertions(+), 4 deletions(-)

diff --git a/tracks/mps/solutions/Wander-276/PR_BODY.md b/tracks/mps/solutions/Wander-276/PR_BODY.md
index d16d81267..e5bed1fba 100644
--- a/tracks/mps/solutions/Wander-276/PR_BODY.md
+++ b/tracks/mps/solutions/Wander-276/PR_BODY.md
@@ -49,7 +49,7 @@ Both primary physical intervals are disjoint from both sealed prediction interva
 
 - Established: an independent supersymmetric protection mechanism, exact Hodge-resolved response identity, analytic controls, and finite-size $N=8$--$14$ response memory beyond both frozen separable covariance-null families.
 - Not established: asymptotic Geometric ETH, thermalization, real-time chaos, or a thermodynamic-limit theorem.
-- Null rejection, if selected, means memory beyond the frozen separable Hodge/collapsed covariance models; it does not prove non-Gaussianity relative to every possible entrywise covariance model.
+- The selected null-rejection branch means memory beyond the frozen separable Hodge/collapsed covariance models; it does not prove non-Gaussianity relative to every possible entrywise covariance model.
 
 ## Deliverables
 
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/README.md b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/README.md
index 941fcd9cd..f786babf8 100644
--- a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/README.md
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/README.md
@@ -71,4 +71,4 @@ The script merges the pilot, generates the final result figure and report from f
 
 ## Interpretation Boundary
 
-The operational label `cohomological_non_gaussian_class`, if selected, means four-point response memory beyond the frozen separable collapsed and Hodge covariance nulls. It does not establish failure of every fully nonseparable Gaussian covariance model. No (N=8\)–(14) result is presented as asymptotic Geometric ETH.
+The selected label `cohomological_non_gaussian_class` means four-point response memory beyond the frozen separable collapsed and Hodge covariance nulls. It does not establish failure of every fully nonseparable Gaussian covariance model. No $N=8$--$14$ result is presented as asymptotic Geometric ETH.
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_delivery_audit_v7.json b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_delivery_audit_v7.json
index deb784bba..98dce0db2 100644
--- a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_delivery_audit_v7.json
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_delivery_audit_v7.json
@@ -42,7 +42,7 @@
     "unsealed_references_prediction": true,
     "valid_prediction_seal": true
   },
-  "generated_utc": "2026-08-04T01:54:03.863688+00:00",
+  "generated_utc": "2026-08-04T01:57:42.244273+00:00",
   "passed": true,
   "prediction_sha256": "fc300dc7e4bdc1be157919e458ac868d3468533cce31108f23c9fba4f7e9f102",
   "recomputed_branch": "cohomological_non_gaussian_class",
diff --git a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_manuscript_audit_v7.json b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_manuscript_audit_v7.json
index 792a9b34e..084fa1579 100644
--- a/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_manuscript_audit_v7.json
+++ b/tracks/mps/solutions/Wander-276/research/01_task_folder/task_05/script/output/susy_hodge_manuscript_audit_v7.json
@@ -27,7 +27,7 @@
     "selected_branch_in_source": true,
     "supplement_uses_generated_results": true
   },
-  "generated_utc": "2026-08-04T01:54:04.257681+00:00",
+  "generated_utc": "2026-08-04T01:57:42.639708+00:00",
   "passed": true,
   "prediction_sha256": "fc300dc7e4bdc1be157919e458ac868d3468533cce31108f23c9fba4f7e9f102",
   "selected_branch": "cohomological_non_gaussian_class",