[QMC] 🌠 Wander/漫步者: Issue #15 Neural Graviton Landscape in FQH Matter

tracks/qmc/solutions/Ranger/README.md

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+# Ranger — Neural Graviton Landscape
+
+## Team and challenge
+
+| Field | Value |
+|---|---|
+| Team | Ranger |
+| Members | Chenxi Wan, Yedi Shen, Junkai Wang |
+| Challenge | `Addresses #15` — [Symmetric neural-network ansatz for the chiral graviton at nu = 1/3](https://github.com/QuantumBFS/quantum.harness/issues/15), released by Lei Wang (Institute of Physics, CAS) |
+| Track | `qmc` — Variational Monte Carlo / Neural Quantum States |
+| Public research repository | [`JunkaiWang-TheoPhy/symmetric-neural-network-ansatz-chiral-graviton`](https://github.com/JunkaiWang-TheoPhy/symmetric-neural-network-ansatz-chiral-graviton/tree/codex/neural-graviton-paper) |
+| Manuscript | [Neural Graviton Landscape (PDF)](https://github.com/JunkaiWang-TheoPhy/symmetric-neural-network-ansatz-chiral-graviton/blob/codex/neural-graviton-paper/paper/neural-graviton-microscope/neural-graviton-landscape.pdf) |
+| License | AGPL-3.0-only |
+
+Ranger turns chiral many-body response into a coordinate-space,
+symmetry-native neural Monte Carlo workflow with an auditable path from
+configuration to **state → probe → interaction → scaling**. The implementation
+certifies the full spin-two multiplet, learns a sharper microscopic stress
+probe, discovers its leading two-graviton output, and carries the response
+calculation beyond dense exact diagonalization.
+
+![Neural Graviton Microscope](https://raw.githubusercontent.com/JunkaiWang-TheoPhy/symmetric-neural-network-ansatz-chiral-graviton/codex/competition-showcase/results/competition_showcase/final/showcase.svg)
+
+## Headline certificates
+
+| Result | Certificate |
+|---|---:|
+| `N=4` strict-LLL graviton gap | `0.13185675492702376` |
+| maximum dense-oracle difference | `2.66e-15` |
+| five-state multiplet dimension | `5` |
+| maximum `L^2` error | `6.22e-15` |
+| maximum multiplet energy spread | `4.44e-16` |
+| `N=8` direct coordinate tangent | `0.1396847 +/- 0.0005706` |
+| `N=8` stochastic one-mode frequency | `0.1399489 +/- 0.0008219` |
+| independent-estimator agreement | `0.264` combined standard errors |
+| neural closure leakage | `0.499178073 -> 1.9864e-7` |
+| finite-size nonlinear coupling | `g_224=-0.419946827` |
+
+The `N=4` strict-LLL neural irrep gives
+
+```text
+E(L=0) = 1.8711384121456025
+E(L=2) = 2.0029951670726263
+Delta   = 0.13185675492702376
+```
+
+Fermionic antisymmetry and rotational covariance are exact architectural
+invariants.  The components `M=2,1,0,-1,-2` provide a symmetry-complete
+finite-size graviton certificate.
+
+## Five linked algorithmic advances
+
+### 1. Symmetry-native shared neural state
+
+One shared ground/tangent parameterization preserves exchange antisymmetry and
+rotational covariance by construction. The complete `M=2,1,0,-1,-2`
+multiplet therefore follows from the architecture rather than symmetry repair
+after optimization.
+
+### 2. Projector-free strict-LLL tangent VMC
+
+The coordinate backend applies the holomorphic quadrupole directly to the
+many-electron wave function with an `O(N^2)` generator.  At `N=8`, it reaches
+a 319,770-state Fock space while evaluating the response entirely in particle
+coordinates.  This replaces combinatorial vector storage with Monte Carlo
+chains that parallelize over walkers and seeds.
+
+### 3. Covariance-preserving common-bridge geometry estimator
+
+Ground and tangent states share the mixture
+
+```text
+q(R) proportional to |Psi_0(R)|^2 + alpha |Psi_T(R)|^2.
+```
+
+One configuration stream estimates overlap, Hamiltonian, quantum metric,
+Berry curvature, stiffness, and pole frequency.  Bridge ESS, bridge balance,
+tangent-overlap autocorrelation, block error, and adjusted ESS make sampling
+quality a measurable part of the physics result.
+
+### 4. Target-free microscopic operator discovery
+
+A permutation-shared neural Casimir filter trains exclusively on overlap and
+first/second Hamiltonian moments.  It removes `54.76%` of non-dominant weight
+at `N=4` and `37.32%` at `N=5`, with metric fidelities `0.998389` and
+`0.994852`.  Held-out pole measurements certify that the learned operator is
+a sharper chiral-graviton probe.
+
+Rotation-resolved closure then identifies the first additional channel as
+`L=4`.  Direct spin-four sources and symmetrized two-graviton composites span
+the same resolved spaces at `N=4,5`; the learned tower extracts the finite-size
+`g_224` interaction.
+
+### 5. Outcome-complete higher-dimensional scaling
+
+Direct complex-wave-function VMC encodes exchange and magnetic phase in
+`Psi_theta` while sampling the positive density
+
+```text
+p_theta(R) = |Psi_theta(R)|^2 / Z_theta.
+```
+
+This removes path-integral average-sign reweighting from the variational
+estimator.  A multi-size protocol then measures completion, variance,
+autocorrelation, adjusted ESS, bridge ESS, memory, and wall time.
+
+The production campaign preregisters 80 `N=10,12` chains. Every seed and
+scheduler status is retained, every record is SHA-bound to a readable
+configuration, and an automatic finalizer captures Slurm accounting and
+validates the complete manifest.  Independent `N=4,8` anchors use the same
+record contract.
+
+## Why the new stack reaches farther
+
+1. **Architectural symmetry:** exchange antisymmetry and spherical covariance
+   hold throughout optimization and evaluation.
+2. **Coordinate response:** the `O(N^2)` tangent removes the dense-vector
+   storage bottleneck and reaches `N=8` directly.
+3. **Moment-supervised discovery:** the microscopic stress emerges from
+   low-order response information and receives held-out pole certification.
+4. **Closure-driven field content:** the rotational irrep missing from the
+   graviton code determines the leading nonlinear output.
+5. **Record-level reproducibility:** hashes, seed retention, scheduler
+   accounting, and statistical gates make every scaling statement auditable.
+
+## Evidence and reproduction
+
+The [PR-local evidence pack](evidence/) contains the technical report,
+higher-dimensional analysis, chain schema, and machine-readable scaling
+summary.  The public research branch contains the complete paper, code,
+configs, records, and reproducible XH5 workflow.
+
+```bash
+git clone --recurse-submodules \
+  --branch codex/neural-graviton-paper \
+  https://github.com/JunkaiWang-TheoPhy/symmetric-neural-network-ansatz-chiral-graviton.git
+cd symmetric-neural-network-ansatz-chiral-graviton
+uv sync --frozen
+
+uv run pytest -q \
+  tests/test_fermion_scaling_schema.py \
+  tests/test_build_fermion_scaling_report.py \
+  tests/test_render_pr262_sign_response.py
+uv run python scripts/audit_neural_graviton_citations.py
+uv run python scripts/build_neural_graviton_paper.py
+```
+
+## Promising research trajectory
+
+The verified contribution links a symmetry-exact finite-size graviton state,
+a target-free neural probe, a two-graviton composite channel, an on-shell
+operator equivalence class, and a direct-wave-function multi-size sampling
+study. The same architecture now provides explicit programs for
+thermodynamic extrapolation, linewidth spectroscopy, and microscopic field
+identification, with each next claim inheriting an executable certificate.
+
+## Reviewer checklist
+
+- [ ] Reproduce the strict-LLL `N=4` energy and five-state multiplet.
+- [ ] Inspect the `O(N^2)` coordinate tangent and independent `N=8` agreement.
+- [ ] Confirm that the neural-probe training inputs are overlap and moments.
+- [ ] Inspect the spin-two/spin-four closure and `g_224` extraction.
+- [ ] Validate the chain/config SHA bindings and seed-preserving report.
+- [ ] Read the APS-style manuscript and PR-local technical evidence.

tracks/qmc/solutions/Ranger/evidence/README.md

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+# Ranger evidence pack
+
+This directory is the review-facing map from each headline claim to its
+public evidence. The research repository is the source of record for the
+complete code, configurations, individual chain records, manuscript, and XH5
+workflow.
+
+## Claim-to-evidence map
+
+| Capability | PR-local evidence | Public source of record |
+|---|---|---|
+| integrated state → probe → interaction → scaling result | `technical-report.md` | [technical delivery report](https://github.com/JunkaiWang-TheoPhy/symmetric-neural-network-ansatz-chiral-graviton/blob/codex/neural-graviton-paper/docs/final-technical-report.md) |
+| direct complex-wave-function VMC and higher-dimensional scope | `higher-dimensional-fermions.md` | [scientific analysis](https://github.com/JunkaiWang-TheoPhy/symmetric-neural-network-ansatz-chiral-graviton/blob/codex/neural-graviton-paper/docs/higher-dimensional-fermion-vmc.md) |
+| per-chain outcome-complete contract | `fermion-scaling-chain-v1.schema.json` | [JSON Schema](https://github.com/JunkaiWang-TheoPhy/symmetric-neural-network-ansatz-chiral-graviton/blob/codex/neural-graviton-paper/schemas/fermion-scaling-chain-v1.schema.json) |
+| hash-verified multi-size aggregation | `fermion-scaling-summary.json` | [machine-readable summary](https://github.com/JunkaiWang-TheoPhy/symmetric-neural-network-ansatz-chiral-graviton/blob/codex/neural-graviton-paper/results/fermion_scaling/summary.json) |
+| one-row-per-chain review table | `chains.tsv` | [human-readable table](https://github.com/JunkaiWang-TheoPhy/symmetric-neural-network-ansatz-chiral-graviton/blob/codex/neural-graviton-paper/results/fermion_scaling/chains.tsv) |
+| readable inputs and individual records | — | [records and configurations](https://github.com/JunkaiWang-TheoPhy/symmetric-neural-network-ansatz-chiral-graviton/tree/codex/neural-graviton-paper/results/fermion_scaling) |
+| full scientific narrative and figures | — | [16-page APS-style manuscript](https://github.com/JunkaiWang-TheoPhy/symmetric-neural-network-ansatz-chiral-graviton/blob/codex/neural-graviton-paper/paper/neural-graviton-microscope/neural-graviton-landscape.pdf) |
+| scheduler submission and automatic aggregation | — | [XH5 protocol](https://github.com/JunkaiWang-TheoPhy/symmetric-neural-network-ansatz-chiral-graviton/tree/codex/neural-graviton-paper/hpc/xh5) |
+
+## Terminal quantitative certificate
+
+The final package contains all 84 preregistered chains across
+`N=4,8,10,12`: 71 completed estimator paths and 13 recorded eight-hour
+scheduler boundaries. Completion is 35/40 at `N=10` and 32/40 at `N=12`.
+Median bridge fractions remain `0.718676` and `0.694447`, while median
+tangent-overlap IATs remain `1.64475` and `1.84971` at the two XH5 sizes.
+
+Every predeclared completion, ESS, variance, bridge, and autocorrelation gate
+passes. The machine-readable classification is
+`controlled_over_tested_sizes`, expressed positively as: **Sampling remains
+controlled across tested sizes N=4, N=8, N=10, N=12.**
+
+## Public entry points
+
+- [research repository](https://github.com/JunkaiWang-TheoPhy/symmetric-neural-network-ansatz-chiral-graviton/tree/codex/neural-graviton-paper)
+- [Neural Graviton Landscape manuscript](https://github.com/JunkaiWang-TheoPhy/symmetric-neural-network-ansatz-chiral-graviton/blob/codex/neural-graviton-paper/paper/neural-graviton-microscope/neural-graviton-landscape.pdf)
+- [technical delivery report](https://github.com/JunkaiWang-TheoPhy/symmetric-neural-network-ansatz-chiral-graviton/blob/codex/neural-graviton-paper/docs/final-technical-report.md)
+- [machine-readable scaling summary](https://github.com/JunkaiWang-TheoPhy/symmetric-neural-network-ansatz-chiral-graviton/blob/codex/neural-graviton-paper/results/fermion_scaling/summary.json)
+
+Together these artifacts bind the algorithmic advances, numerical
+certificates, and reproducibility record into one self-contained public
+delivery.