diff --git a/tracks/mps/solutions/Ranger-123/.gitignore b/tracks/mps/solutions/Ranger-123/.gitignore
new file mode 100644
index 000000000..94ec4eaa6
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/.gitignore
@@ -0,0 +1,15 @@
+.venv*/
+__pycache__/
+*.py[cod]
+.pytest_cache/
+.mypy_cache/
+.ruff_cache/
+.omx/
+work/
+build/
+dist/
+*.egg-info/
+/results/
+/docs/plans/
+/docs/superpowers/
+/julia/Manifest.toml
diff --git a/tracks/mps/solutions/Ranger-123/CITATION.cff b/tracks/mps/solutions/Ranger-123/CITATION.cff
new file mode 100644
index 000000000..7786cfbfb
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/CITATION.cff
@@ -0,0 +1,29 @@
+cff-version: 1.2.0
+title: "Floquet-IF Many-body: N=2,3"
+message: "If you use this research implementation, cite this software and the upstream methods."
+type: software
+authors:
+  - family-names: "Wang"
+    given-names: "Thomas"
+version: 0.1.0
+date-released: 2026-07-29
+license: AGPL-3.0-or-later
+references:
+  - type: article
+    title: "Exact Floquet Dynamics of Strongly Damped Driven Quantum Systems"
+    authors:
+      - family-names: Mickiewicz
+        given-names: Konrad
+      - family-names: Link
+        given-names: Valentin
+      - family-names: Strunz
+        given-names: Walter T.
+    year: 2026
+    doi: 10.1103/5z1m-122d
+  - type: software
+    title: "UniformTEMPO.jl"
+    url: "https://github.com/uniformTEMPO/UniformTEMPO.jl"
+    version: "b76a018c32e5415989761d902b1b0e95f1a337da"
+  - type: software
+    title: "OQuPy"
+    url: "https://github.com/tempoCollaboration/OQuPy"
diff --git a/tracks/mps/solutions/Ranger-123/LICENSE b/tracks/mps/solutions/Ranger-123/LICENSE
new file mode 100644
index 000000000..0ad25db4b
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/LICENSE
@@ -0,0 +1,661 @@
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diff --git a/tracks/mps/solutions/Ranger-123/README.md b/tracks/mps/solutions/Ranger-123/README.md
new file mode 100644
index 000000000..458ebf1e2
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/README.md
@@ -0,0 +1,146 @@
+# Floquet-IF Many-body: N=1--4 validation and N=2,3 production
+
+## Submission
+
+- Team: Ranger
+- Members: Chenxi Wan, Yedi Shen, Junkai Wang
+- Challenge: #123
+- Track: MPS
+- Completed scope: published single-spin validation, reproducible collective
+  common-bath calculations for \(N=2,3\), a convergence-gated \(N=4\) point,
+  and quantitative non-Markovian--Floquet-Markov benchmarks.
+
+This repository is a reproducible implementation of the two- and three-spin
+part of [QuantumBFS/quantum.harness issue #123](https://github.com/QuantumBFS/quantum.harness/issues/123).
+It combines exact symmetry reduction, a public uniform influence-functional
+solver, frequency-resolved bath heat currents, and a Floquet-Markov benchmark.
+
+The production backend is
+[UniformTEMPO.jl](https://github.com/uniformTEMPO/UniformTEMPO.jl), pinned to
+revision `b76a018c32e5415989761d902b1b0e95f1a337da`. The Python layer projects
+the physical model into its symmetry sectors, runs Julia, caches the uniform
+process tensor atomically, inserts operators into the extended process-tensor
+state, separates coherent delta peaks from the decaying correlation, and
+records every convergence comparison in JSON.
+
+## Completed results
+
+- Exact \(N=2\) singlet/triplet reduction, dark singlet, bright gaps, and
+  transition weights.
+- Exact \(N=3\) reflection \(6\oplus2\) reduction and the
+  \(J\)-independent embedded single-spin odd sector.
+- A converged six-point \(N=3\) heat-spectrum grid for
+  \(J/\Omega=0.25,0.5,1\) in both reflection sectors.
+- A converged \(3\times3\) \(N=2\) calibration grid comparing uniform TEMPO
+  with Floquet-Markov/QRT using state, correlation, and heat-spectrum errors.
+- A converged 6/6 same-model \(N=3\) benchmark comparing each existing
+  reflection-sector UniformTEMPO point directly to Floquet-Markov/QRT.
+- Floquet matrix-element, collective-variance, counterterm, and normalization
+  diagnostics.
+- Full convergence of the two bounded-normalization model variants.
+- Compression convergence of both Kac-normalized variants, with their
+  remaining timestep/phase refinement explicitly marked as cluster work.
+- An independent 3/3 reproduction of the published transversal-drive Fig. 3
+  bottom panel, plus a coarse UniformTEMPO--OQuPy cross-check.
+- A converged reflection-odd \(N=4\) pilot with a same-model
+  Floquet-Markov/QRT heat-spectrum error of 3.405 and resolved collective
+  spectral peaks.
+- A converged reflection-even \(N=4\) pilot using an automatically extended
+  six-period correlation window; its same-model heat-spectrum error is 5.494.
+- A pole-resolved, fixed-frequency \(N=1,2,3\) heat-valve pre-scan and
+  three-point \(N=3\) UniformTEMPO go/no-go pilot. The pilot rejects—not
+  confirms—the dark-channel hypothesis: the quasienergy gap collapses while
+  the observable transfer-pole residue increases.
+
+The main \(N=2\) and \(N=3\) results do **not** require a cluster. The failed
+heat-valve pilot does not justify a cluster-scale nine-point continuation.
+Only the optional full Kac refinement does. Reflection-resolved \(N=4\)
+support is implemented and both sector pilots pass all declared gates; the
+even sector records the required six-period tail-window extension explicitly.
+The project makes no thermodynamic-limit, continuum, or critical-exponent
+claim.
+
+## Reproduce
+
+Python 3.12 and Julia 1.12 are the recorded production versions.
+
+```bash
+python3.12 -m venv .venv
+.venv/bin/python -m pip install -e '.[dev,nonmarkov]'
+julia --project=julia -e 'using Pkg; Pkg.instantiate()'
+
+# Exact and legacy validation baselines
+PYTHON_BIN=.venv/bin/python scripts/run_baselines.sh
+PYTHON_BIN=.venv/bin/python scripts/run_pt_baselines.sh
+
+# Resumable production calculation and strict audit
+PYTHON_BIN=.venv/bin/python scripts/run_paper_extension.sh all
+
+# Independent backend checks
+.venv/bin/python scripts/run_uniform_validation.py
+.venv/bin/python scripts/run_fig3_validation.py --drive-frequency 1
+.venv/bin/python scripts/run_fig3_validation.py --drive-frequency 1.5
+.venv/bin/python scripts/run_fig3_validation.py --drive-frequency 2
+.venv/bin/python scripts/run_fig3_validation.py --plot-summary
+
+# Convergence-gated N=4 sector points
+.venv/bin/python -m floquet_if_manybody.cli n4-pilot --sector odd --j 0.25
+.venv/bin/python -m floquet_if_manybody.cli n4-pilot --sector even --j 0.25
+
+# Software and result verification
+.venv/bin/python -m pytest -q
+.venv/bin/python -m ruff check src tests scripts/run_uniform_validation.py scripts/run_fig3_validation.py
+.venv/bin/python -m mypy src scripts/run_fig3_validation.py
+.venv/bin/python -m floquet_if_manybody.cli audit results
+.venv/bin/python -m floquet_if_manybody.cli paper-audit results/paper
+
+# Pole-resolved heat-valve pilot. The audit intentionally exits nonzero
+# because the dark-channel claim gates are not met.
+.venv/bin/python -m floquet_if_manybody.cli heat-valve --pilot
+.venv/bin/python -m floquet_if_manybody.cli \
+  heat-valve-audit results/heat-valve
+```
+
+The production command is resumable. Its cache is content-addressed by the
+physical model, numerical controls, projected operators, solver revision, and
+source revision. Cache files are excluded from the research archive.
+
+The upstream harness excludes machine-generated `results/` data from Git.
+The commands above reproduce those local files. This submission commits the
+publication figures, reports, test suite, and compact validation snapshots;
+`validation/ARTIFACT_PROVENANCE.json` records hashes for the audited local
+artifact set.
+
+To continue the Kac variants on a cluster:
+
+```bash
+FULL_KAC=1 PYTHON_BIN=.venv/bin/python \
+  scripts/run_paper_extension.sh models
+```
+
+## Result guide
+
+| Artifact | Meaning | Status |
+|---|---|---|
+| `figures/n2_exact.*` | Interacting-triplet gaps and bright weights | Exact |
+| `figures/n3_exact.*` | Collective cat gap and weight | Exact |
+| `figures/paper/n3_sector_heat.*` | \(N=3\) even/odd heat spectra | 6/6 converged |
+| `figures/paper/n3_odd_difference.*` | Odd-sector \(J\)-invariance residual | Exact zero on the projected grid |
+| `figures/paper/error_maps.*` | Uniform TEMPO vs Floquet-Markov/QRT | 9/9 converged |
+| `figures/paper/n3_error_maps.*` | Same-parameter \(N=3\) UniformTEMPO vs Floquet-Markov/QRT | 6/6 converged |
+| `figures/validation/fig3_transversal_summary.*` | Published Fig. 3 bottom data vs independent calculation | 3/3 physical gates passed |
+| `figures/paper/n4_odd_j0p25_comparison.*` | Same-model \(N=4\) odd-sector comparison | Converged; heat error 3.405 |
+| `figures/paper/n4_even_j0p25_comparison.*` | Same-model \(N=4\) even-sector comparison | Converged; heat error 5.494 |
+| `figures/paper/dark_diagnostics.*` | Floquet matrix elements, heat, and \(\mathrm{Var}(S)\) | Converged heat plus exact Floquet diagnostic |
+| `figures/paper/model_variants.*` | Bounded/Kac and counterterm comparison | Bounded converged; Kac compression-audited |
+| `figures/heat-valve/heat_valve_hero.*` | Quasienergy collapse tested against exact transfer-pole residues | Pilot complete; dark-channel claim rejected |
+| `docs/heat-valve-result-zh.md` | Fixed-frequency go/no-go evidence and independent claim audit | 3/3 \(N=3\) pilot points; full grid intentionally not run |
+| `validation/*.json` | Artifact provenance and independent backend checks | Diagnostic validation |
+
+See [the Chinese report](docs/report-zh.md),
+[the heat-valve pilot result](docs/heat-valve-result-zh.md),
+[theory conventions](docs/theory.md), [numerical methods](docs/methods.md), and
+the [completion matrix](docs/completion-matrix.md).
+
+This integrated project is distributed under the repository's
+AGPL-3.0-or-later license. Third-party solvers retain their own licenses.
diff --git a/tracks/mps/solutions/Ranger-123/configs/n2_baseline.yaml b/tracks/mps/solutions/Ranger-123/configs/n2_baseline.yaml
new file mode 100644
index 000000000..bd55efec0
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/configs/n2_baseline.yaml
@@ -0,0 +1,13 @@
+model:
+  n: 2
+  j: 0.5
+  omega: 1.0
+  drive_amplitude: 0.2
+  drive_frequency: 0.6180339887498949
+  normalization: bounded
+bath:
+  alpha: 0.05
+  cutoff: 2.5
+  temperature: 0.0
+sector: triplet
+method: finite_memory_if
diff --git a/tracks/mps/solutions/Ranger-123/configs/n3_even_baseline.yaml b/tracks/mps/solutions/Ranger-123/configs/n3_even_baseline.yaml
new file mode 100644
index 000000000..c6aadd299
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/configs/n3_even_baseline.yaml
@@ -0,0 +1,13 @@
+model:
+  n: 3
+  j: 0.5
+  omega: 1.0
+  drive_amplitude: 0.2
+  drive_frequency: 0.4450418679126287
+  normalization: bounded
+bath:
+  alpha: 0.05
+  cutoff: 2.5
+  temperature: 0.0
+sector: even
+method: floquet_markov
diff --git a/tracks/mps/solutions/Ranger-123/configs/n3_odd_check.yaml b/tracks/mps/solutions/Ranger-123/configs/n3_odd_check.yaml
new file mode 100644
index 000000000..bf9cbefb1
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/configs/n3_odd_check.yaml
@@ -0,0 +1,9 @@
+model:
+  n: 3
+  j: 1.0
+  omega: 1.0
+  drive_amplitude: 0.2
+  drive_frequency: 1.0
+  normalization: bounded
+sector: odd
+method: closed
diff --git a/tracks/mps/solutions/Ranger-123/docs/completion-matrix.md b/tracks/mps/solutions/Ranger-123/docs/completion-matrix.md
new file mode 100644
index 000000000..e94fc7dee
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/docs/completion-matrix.md
@@ -0,0 +1,70 @@
+# Completion matrix
+
+| Requirement | Evidence | Status |
+|---|---|---|
+| Reproducible Python/Julia package | `pyproject.toml`, `uv.lock`, pinned source in `julia/Project.toml` | Complete |
+| \(N=2\) singlet dark sector | `tests/test_symmetry_n2.py` | Complete |
+| \(N=2\) exact gaps and weights | `tests/test_spectra_n2.py`, `figures/n2_exact.*` | Complete |
+| \(N=3\) \(6\oplus2\) reflection split | `tests/test_symmetry_n3.py` | Complete |
+| \(N=3\) odd-sector \(J\)-independence | projected operator hashes and zero curve difference | Complete |
+| \(N=3\) cat-gap coefficient | `tests/test_spectra_n3.py` | Complete |
+| Closed Floquet solver | `tests/test_floquet.py` | Complete |
+| Public uniform process-tensor backend | pinned UniformTEMPO revision, Julia runner | Complete |
+| Extended-state multi-time insertions | Julia runner and backend tests | Complete |
+| Delta/continuum separation | correlation and heat-current tests | Complete |
+| Atomic, content-addressed cache | convergence/backend tests | Complete |
+| Nested compression/timestep/phase controller | adaptive tests and per-point evidence | Complete |
+| \(N=3\) even/odd heat grid | `figures/paper/n3_sector_heat.*`, audited local manifest | 6/6 converged |
+| Odd-sector spectral invariance | relative maximum difference 0 | Complete |
+| \(N=2\) exact-vs-Markov grid | `error_map_manifest.json` | 9/9 converged |
+| Three Markov-error metrics | all nine cells | Complete |
+| \(N=3\) same-model exact-vs-Markov grid | `validation/n3_same_model_error_map.json`, `figures/paper/n3_error_maps.*` | 6/6 converged |
+| Floquet dark-channel diagnostics | \(|m|\le40\), Parseval tests | Complete diagnostic |
+| Independent drive/bath normalization | model and projected-sector regression tests | Complete |
+| Floquet transfer eigenvalues and residuals | Julia Krylov extraction plus real \(N=1\) smoke | Complete |
+| Observable pole-residue fit and mode tracking | synthetic exact-recovery and matching tests | Complete |
+| Fixed-frequency \(N=1,2,3\) coherent-destruction scan | `docs/heat-valve-result-zh.md`, hero figure | Complete |
+| \(N=3\) pole-resolved heat-valve pilot | report, hero figure, and audited local manifest | 3/3 executed; claim gates rejected |
+| Nine-point \(N=1,2,3\) heat-valve grid | go/no-go required threefold heat and residue suppression | Intentionally not run: pilot failed |
+| Bounded normalization/counterterm variants | full adaptive evidence | 2/2 converged |
+| Kac normalization/counterterm variants | passed compression evidence | Local endpoint complete; full timestep/phase requires cluster |
+| Independent single-spin validation | `validation/uniform_tempo_single_spin.json` | Passed |
+| Published Fig. 3 bottom-panel reproduction | `validation/fig3_transversal_summary.json`, `figures/validation/fig3_transversal_summary.*` | 3/3 physical gates passed |
+| Independent OQuPy cross-check | `validation/uniform_tempo_oqupy_crosscheck.json` | Diagnostic, not convergence |
+| Publication PNG/PDF figures | `figures/paper` | Visually checked |
+| Pole-resolved hero figure | `figures/heat-valve/heat_valve_hero.{png,pdf}` | Visually checked; labeled candidate/rejected |
+| Chinese report | `docs/report-zh.md` | Complete |
+| Heat-valve negative-result report | `docs/heat-valve-result-zh.md` | Complete |
+| \(N=4\) reflection implementation | `tests/test_symmetry_n4.py`, convergence-gated `n4-pilot` command | Complete, \(10\oplus6\) blocks |
+| \(N=4\) reflection-odd pilot and same-model benchmark | `figures/paper/n4_odd_j0p25_comparison.*` | Converged; \(\epsilon_j=3.405\) |
+| \(N=4\) reflection-even pilot and same-model benchmark | six-period tail-window evidence, comparison figure | Converged; \(\epsilon_j=5.494\) |
+| Continuum and critical exponent | Outside finite-system scope | Not claimed |
+
+## Final gates
+
+```bash
+.venv/bin/python -m pytest -q
+.venv/bin/ruff check src tests scripts/run_uniform_validation.py
+.venv/bin/mypy src
+.venv/bin/python -m floquet_if_manybody.cli audit results
+.venv/bin/python -m floquet_if_manybody.cli paper-audit results/paper
+```
+
+`paper-audit` requires all six \(N=3\) points and all nine error-grid points to
+be converged. It also requires both bounded model variants to be fully
+converged. The two Kac variants are accepted only as an explicitly declared
+timestep resource ceiling after a passed compression comparison; they are
+never re-labeled as converged.
+
+The additional command
+
+```bash
+.venv/bin/python -m floquet_if_manybody.cli \
+  heat-valve-audit results/heat-valve
+```
+
+is expected to return nonzero for the archived pilot. This is a scientific
+result, not a software failure: heat is not suppressed against both flanks,
+the visible pole residue increases, the full nine-point grid was therefore
+not authorized by the predeclared resource gate, and the figure is labeled
+`candidate; claim gates not met`.
diff --git a/tracks/mps/solutions/Ranger-123/docs/heat-valve-result-zh.md b/tracks/mps/solutions/Ranger-123/docs/heat-valve-result-zh.md
new file mode 100644
index 000000000..1580a332d
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/docs/heat-valve-result-zh.md
@@ -0,0 +1,207 @@
+# Floquet pole heat-valve pilot：准能隙塌缩不等于暗通道
+
+## 结论
+
+本轮新增实验完成了一个固定频率、固定浴、可由 transfer poles 独立审计的
+\(N=1,2,3\) Floquet heat-valve 搜索。结果是否定性的：
+
+\[
+\boxed{
+\text{闭系统 quasienergy/cat gap 的深极小}
+\;\not\Rightarrow\;
+\text{开放系统 heat 或 observable residue 变暗}
+}
+\]
+
+在 \(N=3\) 的闭系统扫描中，
+
+\[
+\omega_d=3\Omega,\qquad J=\Omega,\qquad
+\xi=\frac{2A}{\omega_d},
+\]
+
+于 \(\xi=3.05\) 得到
+
+\[
+\Delta_{\rm cat}=5.85\times10^{-5}\Omega.
+\]
+
+但是同一点的 UniformTEMPO 结果显示：
+
+- integrated absolute continuous heat 只从左侧的 0.009806 降到
+  0.008976，之后在右侧继续降到 0.008747；
+- visible transfer-pole residue weight 从 0.4547 增至 0.9812，并继续
+  增至 1.5278；
+- dominant residue 同样从 0.2411 增至 0.5370，再增至 0.8276。
+
+所以 \(\xi=3.05\) 既不是双侧 heat minimum，也不是 residue minimum。
+独立审计器正确拒绝 `dark channel` 文字。根据预先规定的 go/no-go gate，
+没有扩展到九个 \(N=1,2,3\) UniformTEMPO 点，也没有提交集群。
+
+![Pole-resolved heat-valve pilot](../figures/heat-valve/heat_valve_hero.png)
+
+## 1. 为什么要把 drive 和 bath normalization 分开
+
+旧基准使用同一算符同时表示纵向驱动和共同浴耦合：
+
+\[
+S_N=\frac1N M_z.
+\]
+
+这会让“相同 drive amplitude”实际对应不同的每自旋驱动力。新实验明确
+使用
+
+\[
+H_{\rm drive}(t)=A\cos(\omega_dt)M_z,
+\qquad
+H_{SB}=\frac{M_z}{N}\otimes B.
+\]
+
+因此不同 \(N\) 之间保持物理驱动 \(A\) 相同，同时继续使用 bounded bath
+coupling。代码默认仍为旧的 `drive_normalization="coupling"`，只有本实验
+选择 `per_spin`，所以历史结果语义没有改变。
+
+## 2. 预先规定的判据
+
+只有同时满足以下条件，结果才允许称为 dark channel：
+
+1. \(\omega_d,J,\alpha,\omega_c,T_B\) 和 bath normalization 在扫描中固定；
+2. minimum 相对左右两个 flank 的 continuous heat 均至少降低十倍；
+3. 相应 observable transfer-pole residue 相对两个 flank 均至少降低十倍；
+4. transfer eigenpair residual 不超过 \(10^{-8}\)；
+5. 所有物理 poles 满足 \(|\lambda|\le1+10^{-6}\)；
+6. pole reconstruction 的 normalized \(L^1\) residual 不超过 5%；
+7. trace、Hermiticity、fixed point 和 connected tail 通过物理门槛。
+
+在 pilot 阶段，只有 heat 和 residue 都至少降低三倍，才值得分配资源给完整
+九点网格。这个 pilot gate 远未满足。
+
+## 3. 闭系统预扫描
+
+预扫描固定
+
+\[
+\Omega=1,\quad J=1,\quad\omega_d=3,\quad
+\xi\in[1.8,4.0],
+\]
+
+采用步长 0.05。每个点用 240 个 midpoint Floquet steps。\(N=2\) 投影到
+triplet，\(N=3\) 投影到 reflection-even 六维 sector。
+
+| \(N\) | fitted \(\xi_\ast\) | cat gap | cat-subspace overlap | \(M_z/N\) brightness |
+|---:|---:|---:|---:|---:|
+| 1 | 2.35 | \(1.1402\times10^{-2}\) | 1.0000 | 1.8813 |
+| 2 | 3.65 | \(6.5304\times10^{-2}\) | 0.9378 | 1.8800 |
+| 3 | 3.05 | \(5.8516\times10^{-5}\) | 0.8638 | 1.7279 |
+
+\(N=1\) minimum 靠近第一 Bessel 零点 \(x_1=2.4048256\)。相互作用把
+\(N=2,3\) 的 minima 明显推移。尤其 \(N=3\) gap 很深，但 bath operator 的
+闭系统 brightness 仍为 \(O(1)\)，已经预示它可能不是 selection-rule dark
+channel。
+
+## 4. UniformTEMPO transfer-pole pilot
+
+只运行 \(N=3\) 的三点：
+
+\[
+\xi=2.85,\quad3.05,\quad3.20.
+\]
+
+统一数值控制为：
+
+\[
+M=60,\quad \epsilon=10^{-6},\quad N_\phi=3,\quad
+\tau_{\max}=12T,\quad K=8.
+\]
+
+共同浴参数为
+
+\[
+\alpha=0.05,\qquad\omega_c=2.5,\qquad T_B=0.
+\]
+
+UniformTEMPO 固定在 revision
+`b76a018c32e5415989761d902b1b0e95f1a337da`，生产代码 snapshot 为
+`b42725363a01e2ca88b951c3d28026df8104aa40`。
+
+| \(\xi\) | \(\int d\omega\,|\bar j|\) | visible residue | dominant residue | pole fit residual | connected tail |
+|---:|---:|---:|---:|---:|---:|
+| 2.85 | 0.0098063 | 0.45465 | 0.24109 | 0.04171 | 0.12827 |
+| 3.05 | 0.0089765 | 0.98121 | 0.53697 | 0.04452 | 0.19073 |
+| 3.20 | 0.0087470 | 1.52779 | 0.82761 | 0.06341 | 0.20993 |
+
+三点 bond dimension 均为 13。trace error 约 \(8\times10^{-5}\)，
+Hermiticity error 约 \(10^{-10}\)，fixed-point residual 约
+\(1.2\times10^{-4}\)。最大 eigenpair residual 为
+\(7.04\times10^{-11}\)，最大 pole modulus 为 0.99087；因此 Krylov
+eigenpairs 和单位圆检查通过。
+
+三点的 connected tail 均未降到 0.05 以下，右侧点的 pole reconstruction
+也略高于 5%。所以这些数据被诚实标为 pilot / unconverged，而不是最终
+精确热谱。
+
+## 5. 为什么当前证据足以停止扩展
+
+长时间窗可能改变有限窗口 Fourier 积分的精确数值，因此本项目不把三点热谱
+称为完全收敛的负结果。但停止九点扩展不依赖这种细节：
+
+1. \(\xi=3.05\) 相对右侧的 heat ratio 为 1.026，不存在 minimum；
+2. \(\xi=3.05\) 相对较弱 residue flank 的 ratio 为 2.158，方向与
+   suppression 相反；
+3. dominant residue 也单调增大，不是多个小 residues 求和造成的假象；
+4. 前两个点的 pole reconstruction 已低于 5%，但 residue 增强已经超过
+   两倍。
+
+要从这些数据得到十倍 residue suppression，需要的不是数值微调，而是改变
+物理机制。因此继续延长三点的 correlation window，或把相同假设扩到
+\(N=1,2\) 的六个昂贵点，不能通过 go/no-go 的资源合理性门槛。
+
+## 6. 物理解读
+
+高频纵向驱动给出近似
+
+\[
+\Omega_{\rm eff}\simeq \Omega J_0(2A/\omega_d).
+\]
+
+在铁磁 cluster 中，cat tunneling gap 可以比单自旋 gap 更快塌缩。但共同浴
+同样通过 \(M_z\) 耦合；在 cat basis 中，\(M_z\) 并不会因 tunneling gap
+变小而自动失去矩阵元。这个 pilot 直接展示了两件事必须分开：
+
+\[
+\text{quasienergy collapse}
+\quad\text{与}\quad
+\text{bath-dark observable residue}.
+\]
+
+本例中前者极强，后者反而增强。这是比单纯画一条低热流曲线更有价值的
+诊断：它排除了“看到小 gap 就宣称 many-body dark channel”的常见误判。
+
+## 7. 当前最合理的后续方向
+
+不建议为同一 heat-valve 假设提交集群。若继续 Issue #123，优先级应改为：
+
+1. 把 transfer-pole/residue decomposition 用于已经收敛的 \(N=3\)
+   even/odd 热谱，建立 peak–pole 对应；
+2. 搜索真正满足
+   \(S_{\alpha\beta}^{(m)}=0\) 的 symmetry-protected operator/drive
+   组合，而不是只搜索 quasienergy crossing；
+3. 只有新的闭系统预扫描同时显示 bright matrix element suppression，才运行
+   新的 UniformTEMPO pilot；
+4. 不扩展 \(N=4\)，也不做 thermodynamic 或 critical claim。
+
+## 8. 可复现命令
+
+```bash
+.venv/bin/python -m floquet_if_manybody.cli heat-valve \
+  --pilot \
+  --output results/heat-valve \
+  --cache results/cache/uniform_tempo \
+  --figures figures/heat-valve
+
+.venv/bin/python -m floquet_if_manybody.cli \
+  heat-valve-audit results/heat-valve
+```
+
+第二条命令预期返回非零，因为 scientific claim gates 被正确拒绝。完整输入、
+三点结果、manifest、PNG/PDF 和审计失败原因均已保留。
diff --git a/tracks/mps/solutions/Ranger-123/docs/methods.md b/tracks/mps/solutions/Ranger-123/docs/methods.md
new file mode 100644
index 000000000..eb2df3a0a
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/docs/methods.md
@@ -0,0 +1,203 @@
+# Numerical methods and evidence labels
+
+## Exact finite-system layer
+
+`exact_diagonalization` constructs the operators in the full computational
+basis and projects them with orthonormal isometries obtained from the exact
+swap/reflection operators. Tests require sector leakage below \(10^{-13}\).
+The resulting physical dimensions are \(d=3\) for the \(N=2\) triplet,
+\(d=6\) for the \(N=3\) reflection-even sector, and \(d=2\) for the
+reflection-odd sector.
+
+`closed_unitary` uses midpoint time ordering,
+
+\[
+U(T)\approx\prod_n\exp[-iH(t_{n+1/2})\delta t],
+\]
+
+and supplies Floquet modes and Fourier matrix elements. Tests cover unitarity,
+the static limit, quasienergy-zone placement, and second-order timestep
+convergence.
+
+## Uniform influence-functional backend
+
+The production method label is `uniform_tempo_floquet_multitime`.
+[UniformTEMPO.jl](https://github.com/uniformTEMPO/UniformTEMPO.jl) is pinned in
+`julia/Project.toml` pins the package source to revision
+`b76a018c32e5415989761d902b1b0e95f1a337da`.
+
+For the zero-temperature Ohmic bath,
+
+\[
+J_B(\omega)=\alpha\omega e^{-\omega/\omega_c},\qquad
+C_B(t)=\frac{\alpha\omega_c^2}{(1+i\omega_ct)^2}.
+\]
+
+The Julia runner builds or reloads a serialized uniform process tensor, forms
+the periodic influence-functional transfer sequence, solves its extended
+Floquet fixed point, and evaluates two-time correlations by inserting
+left-acting system operators into the extended state. It does not apply the
+quantum regression theorem to a reduced density matrix.
+
+The period average uses phase samples across one drive cycle. The correlation
+is decomposed as
+
+\[
+\bar C(\tau)=C_{\rm dec}(\tau)+C_{\rm coh}(\tau).
+\]
+
+Only \(C_{\rm dec}\) is numerically Fourier integrated. Fourier coefficients
+of \(\langle S(t)\rangle\) are stored separately as analytic coherent delta
+weights, preventing finite-window broadening.
+
+## Nested convergence controller
+
+The publication schedule is:
+
+| control | ladder |
+|---|---|
+| steps per period | \(60,90,120\) |
+| uniform compression tolerance | \(3\times10^{-7},10^{-7},3\times10^{-8}\) |
+| phase samples | \(3,15\) |
+
+The inexpensive \(N=2\) error grid may continue the tolerance ladder through
+\(10^{-8}\) and \(3\times10^{-9}\).
+
+At each timestep grid the controller first establishes compression
+convergence. A timestep comparison is accepted only if compression passed on
+both participating grids. Phase refinement is performed only after a
+timestep comparison passes. The residual limits are
+
+\[
+r_\rho\le0.05,\qquad r_C\le0.08,\qquad r_j\le0.08.
+\]
+
+Final physical gates require:
+
+- fixed-point residual \(\le10^{-3}\);
+- trace and Hermiticity errors \(\le5\times10^{-3}\);
+- connected-correlation tail \(\le0.05\);
+- minimum density eigenvalue \(\ge-5\times10^{-3}\).
+
+Every comparison records the coarse/refined fingerprints, steps, tolerance,
+phase count, bond dimensions, three residuals, and pass/fail status. The cache
+uses atomic replacement so interrupted calculations can be resumed safely.
+
+## Production outcomes
+
+### \(N=3\) sector grid
+
+All six points pass the nested controller and physical gates:
+
+| sector | \(J/\Omega\) | final steps | bond | timestep \(r_j\) | tail |
+|---|---:|---:|---:|---:|---:|
+| even | 0.25 | 90 | 40 | 0.00844 | 0.02792 |
+| even | 0.50 | 90 | 43 | 0.02799 | 0.00562 |
+| even | 1.00 | 120 | 46 | 0.04890 | 0.01077 |
+| odd | 0.25, 0.50, 1.00 | 90 | 16 | 0.00151 | 0.03986 |
+
+The projected odd-sector Hamiltonian and coupling are exactly \(J\)
+independent; the three production spectra have relative maximum difference
+zero.
+
+### \(N=2\) exact-vs-Markov grid
+
+The calibration grid contains all nine combinations of
+\(\alpha=0.025,0.05,0.1\) and
+\(\omega_d/\Delta_g=0.75,1,1.25\). All nine exact points pass the production
+gates. The weak-coupling delay window grows as
+\(\max(4,\lceil0.3/\alpha\rceil)\) periods.
+
+The three reported errors are:
+
+\[
+D_\rho=\tfrac12\|\rho_{\rm IF}-\rho_{\rm ME}\|_1,
+\]
+
+\[
+\epsilon_C=\frac{\int d\tau\,|C_{\rm IF}-C_{\rm ME}|}
+{\int d\tau\,|C_{\rm IF}|},\qquad
+\epsilon_j=\frac{\int d\omega\,|\bar j_{\rm IF}-\bar j_{\rm ME}|}
+{\int d\omega\,|\bar j_{\rm IF}|}.
+\]
+
+Across the grid, \(D_\rho=0.9968\)–\(0.9997\),
+\(\epsilon_C=1.10\)–\(1.86\), and
+\(\epsilon_j=5.03\)–\(68.84\). These large values are a result, not a
+convergence failure: the uniform-TEMPO reference points themselves are
+converged.
+
+### \(N=3\) same-model exact-vs-Markov grid
+
+The six converged \(N=3\) sector points are also compared to
+Floquet-Markov/QRT without changing the Hamiltonian, drive, bath, sector, or
+frequency and delay grids. In the even sector, the heat-spectrum error is
+9.02–11.72 and the trace distance is 0.992–1.000. In the exactly
+\(J\)-independent odd sector, all three rows reproduce the same errors:
+\(D_\rho=0.4753\), \(\epsilon_C=0.5666\), and \(\epsilon_j=0.3920\).
+This closes the same-model comparison required by Tier 3 rather than using the
+\(N=2\) calibration as a proxy.
+
+### Model-definition variants
+
+At \(N=3,J/\Omega=0.5,\alpha=0.1\), the bounded variants
+\(S=M_z/3\), with and without \(+\alpha\omega_cS^2\), pass compression,
+timestep, phase, and physical gates (final bond dimension 45).
+
+The Kac variants \(S=M_z/\sqrt3\) pass the compression comparison:
+
+| variant | refined bond | compression \(r_j\) |
+|---|---:|---:|
+| Kac, no counterterm | 82 | 0.02373 |
+| Kac, counterterm | 81 | 0.00502 |
+
+Their next timestep and phase layers are intentionally not run by the local
+default because the larger coupling raises the process-tensor cost sharply.
+They are labeled `local_resource_ceiling`, not converged. `--full-kac`
+continues the same auditable ladder on a cluster.
+
+## Independent validation
+
+`scripts/run_fig3_validation.py` downloads the immutable author archive from
+Zenodo, verifies MD5 `0f3f9d9d8538aa96aee089973df7d9c2`, and independently
+recomputes all three transversal-drive curves in Fig. 3 (bottom) at
+\(\omega_d/\Omega=1,1.5,2\). All three points pass the same density, fixed-point,
+Hermiticity, trace, and correlation-tail gates. The normalized shape
+\(L^1\) discrepancies are 0.0562, 0.2736, and 0.3718 respectively; these are
+reported as quantitative structural reproduction, not bitwise identity.
+
+`scripts/run_uniform_validation.py` performs:
+
+- a single-spin UniformTEMPO smoke calculation that passes its declared
+  physical gates (bond 19, fixed-point residual \(1.40\times10^{-4}\));
+- a coarse reflection-odd UniformTEMPO–OQuPy comparison.
+
+The latter has heat \(L^1\) difference 0.517 and is retained as an independent
+implementation diagnostic, not as a convergence claim. It also verifies the
+projected odd-sector \(J\)-invariance exactly.
+
+## Benchmark and legacy backends
+
+`floquet_markov` / `floquet_markov_qr` implement a Born-Markov, fully secular
+periodic Lindblad benchmark with QRT correlations. They are never labeled
+non-Markovian.
+
+The in-repository finite-memory QUAPI code exposes the exponential
+\(O[(d^2)^{K+1}]\) wall and is used for regression tests. OQuPy 0.5.0 remains
+available as an independent PT-TEMPO validation backend. Neither supplies the
+production values in `results/paper`.
+
+## N=4 convergence-gated extension
+
+The generic reflection projector produces \(10\oplus6\) blocks for \(N=4\).
+At \(J/\Omega=0.25\), the odd-sector point passes nested compression,
+timestep, phase, and physical gates at 60 steps per period, tolerance
+\(3\times10^{-6}\), and 15 phases (bond 8, connected tail 0.0368). Its same-model
+Floquet-Markov/QRT heat-spectrum error is 3.405. The exact continuous spectrum
+has its three largest peaks at 0.4725, 0.9600, and 1.4400 \(\Omega\), whereas
+the selected drive frequency is 0.9256 \(\Omega\).
+
+The even-sector three-period endpoint missed only the connected-tail gate
+(0.0552 against 0.05). Without weakening the gate, the production point was
+rerun with six delay periods. It then passed every layer at bond 13 with tail
+0.0213; its same-model heat-spectrum error is 5.494.
diff --git a/tracks/mps/solutions/Ranger-123/docs/report-zh.md b/tracks/mps/solutions/Ranger-123/docs/report-zh.md
new file mode 100644
index 000000000..898fb2775
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/docs/report-zh.md
@@ -0,0 +1,295 @@
+# Issue #123：\(N=2,3\) 完整实施与数值结果
+
+## 1. 最终结论
+
+本项目已经把 Issue #123 的 \(N=2,3\) 部分做成可运行、可恢复、可审计的
+研究实现。生产计算使用公开的
+[UniformTEMPO.jl](https://github.com/uniformTEMPO/UniformTEMPO.jl)，固定在
+revision `b76a018c32e5415989761d902b1b0e95f1a337da`；OQuPy 只作为独立粗粒度
+交叉检查。
+
+完成状态如下：
+
+1. \(N=2,3\) 的解析对称性、暗 sector、能隙和谱权重已由精确对角化与单元
+   测试验证。
+2. \(N=3\) 的 reflection-even/odd 六个热谱点全部通过 compression、
+   timestep、15 相位以及 density-matrix 物理性门槛。
+3. \(N=2\) 的 \(3\times3\) exact-vs-Floquet-Markov 网格九个点全部收敛，
+   同时给出稳态、两时间关联和热谱三种误差。
+4. bounded normalization 的有/无 counterterm 两个模型全部收敛。
+5. Kac normalization 的两个模型已通过压缩收敛，但完整 timestep/phase
+   认证需要集群；结果明确标成 `local_resource_ceiling`。
+6. 论文 Fig. 3 底图的三个横向驱动频率全部由独立 UniformTEMPO 计算通过
+   物理门槛，并与作者公开数据做了定量谱形和面积比较。
+7. \(N=4\) reflection-odd 点通过完整收敛阶梯，并完成同模型
+   Floquet-Markov/QRT 对照；heat error 为 3.405。
+8. \(N=4\) reflection-even 点在不放宽尾门槛的情况下将关联窗从三周期
+   扩展到六周期并收敛；heat error 为 5.494。
+
+所以，对“需要提交集群吗”的答案是：
+
+- 核心 \(N=2,N=3\) 结论不需要，已经在本地完成；
+- 只有可选的 Kac 全收敛扩展需要集群；
+- \(N=4\) odd-sector 的有限尺寸试算已经完成；热力学连续谱和临界幂律
+  不属于这次完成范围，也没有被暗示为已解决。
+
+## 2. 模型与数值方法
+
+系统 Hamiltonian 为
+
+\[
+H_0=-J\sum_{i=1}^{N-1}Z_iZ_{i+1}
+  +\frac{\Omega}{2}\sum_iX_i,
+\]
+
+驱动和共同浴通过
+
+\[
+S_N=\eta_N\sum_i Z_i
+\]
+
+耦合。基准采用 \(\Omega=1\)、零温 Ohmic bath
+
+\[
+J_B(\omega)=\alpha\omega e^{-\omega/\omega_c},\qquad \omega_c=2.5.
+\]
+
+生产 backend 构造 uniform influence tensor，并在扩展的
+system-Liouville × environment-memory 空间中求 Floquet fixed point。两时间
+关联通过在扩展态中插入左作用算符得到，不使用 reduced-state quantum
+regression theorem。
+
+周期平均关联拆成
+
+\[
+\bar C(\tau)=C_{\rm dec}(\tau)+C_{\rm coh}(\tau).
+\]
+
+\(C_{\rm dec}\) 数值 Fourier 积分得到连续热谱；\(\langle S(t)\rangle\) 的
+Fourier 系数单独转成解析 delta 权重，避免有限时间窗制造假展宽。
+
+### 收敛规则
+
+uniform 计算采用嵌套阶梯：
+
+\[
+M=60,90,120,\qquad
+\epsilon=3\times10^{-7},10^{-7},3\times10^{-8},\qquad
+N_\phi=3,15.
+\]
+
+每个 timestep 网格必须先通过 compression 收敛，之后才能参与 timestep
+比较；最后再做相位细化。门槛为
+
+\[
+r_\rho\le0.05,\qquad r_C\le0.08,\qquad r_j\le0.08.
+\]
+
+最终还要求 fixed-point residual \(\le10^{-3}\)、迹与厄米误差
+\(\le5\times10^{-3}\)、关联尾 \(\le0.05\)、最小 density eigenvalue
+\(\ge-5\times10^{-3}\)。
+
+## 3. \(N=2\)：解析结构
+
+交换对称性将四维 Hilbert space 分成三维 triplet 与一维 singlet。
+
+\[
+S_2|s\rangle=0
+\]
+
+且 Hamiltonian 不泄漏 singlet，因此 singlet 是 collective drive 和 common
+bath 下的严格暗态。生产热谱直接投影到 triplet，避免完整空间中 steady
+state 非唯一。
+
+triplet 的两条 collective gaps 为
+
+\[
+\Delta_{\rm low/high}=\sqrt{J^2+\Omega^2}\mp J,
+\]
+
+权重为
+
+\[
+W_{\rm low/high}=2\eta_2^2
+\left(1\pm\frac{J}{\sqrt{J^2+\Omega^2}}\right).
+\]
+
+数值与解析式的最大偏差为 \(1.55\times10^{-15}\)。强铁磁区出现强的低频
+collective-cat transition 和逐渐变暗的高频支路。
+
+![N=2 exact spectrum](../figures/n2_exact.png)
+
+## 4. \(N=3\)：最小 many-body onset
+
+open chain 的 edge reflection 给出
+
+\[
+\mathcal H=\mathcal H_{R=+}^{(6)}\oplus\mathcal H_{R=-}^{(2)}.
+\]
+
+odd sector 是 edge singlet 与中央自旋组成的嵌入单自旋模型，投影后的
+Hamiltonian 和耦合算符严格独立于 \(J\)。even sector 则等价于一个
+spin-1 edge 与中央 spin-\(\tfrac12\) 的六维模型。
+
+在强铁磁区，even sector 的主 gap 满足
+
+\[
+\Delta_{\rm cat}^{(3)}\simeq\frac{\Omega^3}{4J^2}.
+\]
+
+在 \(J=16\Omega\) 时，
+
+\[
+\frac{4J^2\Delta_g}{\Omega^3}=0.999023,
+\]
+
+bright weight 为 0.999267。
+
+![N=3 exact collective gap](../figures/n3_exact.png)
+
+### 六点热谱
+
+\(J/\Omega=0.25,0.5,1\) 的 even/odd 六点全部收敛：
+
+| sector | \(J/\Omega\) | 最终 \(M\) | bond | timestep \(r_j\) | 关联尾 |
+|---|---:|---:|---:|---:|---:|
+| even | 0.25 | 90 | 40 | 0.00844 | 0.02792 |
+| even | 0.50 | 90 | 43 | 0.02799 | 0.00562 |
+| even | 1.00 | 120 | 46 | 0.04890 | 0.01077 |
+| odd | 0.25, 0.50, 1.00 | 90 | 16 | 0.00151 | 0.03986 |
+
+even 主峰随 \(J\) 增大向低频移动并出现更多结构；odd 三条曲线完全重合，
+相对最大差为 0。这同时验证了 sector 推导和数值实现。
+
+![N=3 converged sector heat](../figures/paper/n3_sector_heat.png)
+
+## 5. Floquet-Markov 在哪里失败
+
+\(N=2\) interacting triplet 的校准网格为
+
+\[
+\alpha=0.025,0.05,0.1,\qquad
+\omega_d/\Delta_g=0.75,1,1.25.
+\]
+
+弱耦合时相关时间窗按
+
+\[
+N_{\rm delay}=\max(4,\lceil0.3/\alpha\rceil)
+\]
+
+增长；必要时 compression tolerance 深化到 \(10^{-8}\) 或
+\(3\times10^{-9}\)。九个 UniformTEMPO 点全部通过最终审计。
+
+三种误差范围为：
+
+\[
+D_\rho=0.9968\text{--}0.9997,
+\]
+
+\[
+\epsilon_C=1.10\text{--}1.86,
+\qquad
+\epsilon_j=5.03\text{--}68.84.
+\]
+
+这些值说明在所选参数层中 Floquet-Markov/QRT 与非马尔可夫参考严重不符。
+特别是热谱误差远大于 reduced-state 指标能够直观表达的差异，因此仅比较
+单时 observables 不能验证 calorimetry。
+
+![Converged exact-vs-Markov error map](../figures/paper/error_maps.png)
+
+为消除“Tier 2 是 \(N=3\)，但误差图只在 \(N=2\)”的尺寸错位，现进一步
+对六个已经收敛的 \(N=3\) sector 点逐一运行完全相同模型和参数的
+Floquet-Markov/QRT。六点全部完成：even sector 的
+\(D_\rho=0.9921\text{--}0.9999\)、\(\epsilon_C=1.024\text{--}1.153\)、
+\(\epsilon_j=9.02\text{--}11.72\)；odd sector 因投影模型严格
+\(J\)-不变，三点均给出 \(D_\rho=0.4753\)、\(\epsilon_C=0.5666\)、
+\(\epsilon_j=0.3920\)。这构成 Tier 3 所要求的 same-model 定量闭环。
+
+![N=3 same-model exact-vs-Markov map](../figures/paper/n3_error_maps.png)
+
+## 6. 暗通道与模型定义
+
+Floquet matrix elements 计算到 \(|m|\le40\)，Parseval 残差保持在机器精度。
+结合 \(\bar j(\omega)\) 与 \(\overline{\mathrm{Var}(S)}\) 可以区分小矩阵元
+候选、collective fluctuation 与真正的 heat suppression；不能简单以“纠缠
+较强”等价于“暗”。
+
+![Floquet diagnostics](../figures/paper/dark_diagnostics.png)
+
+对 \(N=3,J/\Omega=0.5,\alpha=0.1\)，比较
+
+\[
+S=M_z/3,\qquad S=M_z/\sqrt3
+\]
+
+以及有/无
+
+\[
+H_{\rm ct}=+\alpha\omega_c S^2.
+\]
+
+bounded 两点完整收敛，最终 bond 均为 45。Kac 两点的压缩比较通过：
+
+- no counterterm：bond 63→82，热残差 0.02373；
+- counterterm：bond 63→81，热残差 0.00502。
+
+Kac 曲线仍以虚线显示，表示 timestep/phase 未完成，而不是表示压缩失败。
+这已经证明 normalization 和 counterterm 会改变数值难度与谱形，不能只在
+画图阶段重标度。
+
+![Model variants](../figures/paper/model_variants.png)
+
+## 7. 独立验证
+
+对于原论文 Fig. 3 底图，脚本先校验 Zenodo 归档 MD5，再在
+\(\omega_d/\Omega=1,1.5,2\) 上独立运行。三个点的归一化谱形 \(L^1\) 误差
+分别为 0.0562、0.2736、0.3718，积分强度比分别为 1.0268、1.1622、
+1.3119；全部通过 fixed-point、迹、厄米性、正定性和关联尾门槛。这是
+定量结构复现，而不是逐点完全相同的声明。
+
+![Fig. 3 bottom independent reproduction](../figures/validation/fig3_transversal_summary.png)
+
+单自旋 UniformTEMPO smoke test 的 bond 为 19，fixed-point residual 为
+\(1.40\times10^{-4}\)，关联尾为 0.00555，全部通过物理门槛。
+
+粗粒度 UniformTEMPO–OQuPy 对照得到 phase-state Frobenius difference
+0.374、correlation \(L^1\) difference 0.282、heat \(L^1\) difference
+0.517。由于两边离散化和压缩设置都很粗，该结果只作为独立实现诊断，不作为
+两种 backend 已收敛一致的声明。投影后的 odd-sector \(J\) 不变性在该检查中
+仍精确成立。
+
+## 8. \(N=4\) 收敛门控结果
+
+通用 reflection projector 将 \(N=4\) 分成 even 10 维和 odd 6 维子空间。
+在 \(J/\Omega=0.25\) 上，odd sector 通过 compression、30→60 步时间网格、
+3→15 相位和全部物理门槛；最终 bond 为 8，关联尾为 0.0368。同模型
+Floquet-Markov/QRT 的 \(\epsilon_j=3.405\)。连续谱三个最强峰位于
+0.4725、0.9600、1.4400 \(\Omega\)，相对于 0.9256 \(\Omega\) 驱动呈现
+多峰 collective structure。
+
+even sector 的三周期计算仅关联尾 0.0552 未过 0.05 门槛。保持原门槛并将
+关联窗扩展到六周期后，最终 bond 为 13、尾幅为 0.0213，全部自适应证据
+通过；同模型 \(\epsilon_j=5.494\)。
+
+![N=4 odd same-model comparison](../figures/paper/n4_odd_j0p25_comparison.png)
+
+![N=4 even same-model comparison](../figures/paper/n4_even_j0p25_comparison.png)
+
+## 9. 如何彻底续跑
+
+本地默认命令已经完成论文主网格。若有集群，只需继续 Kac 阶梯：
+
+```bash
+FULL_KAC=1 PYTHON_BIN=.venv/bin/python \
+  scripts/run_paper_extension.sh models
+```
+
+cache key 包含全部物理/数值参数与 solver revision，已有点会被安全复用。
+下一阶段若扩大研究范围，推荐顺序为：
+
+1. 完成 Kac 的 \(M=90,120\) 与 15 相位认证；
+2. 再考虑 \(N=4\) 的 matrix-free / Krylov 实现；
+3. 只有具备多个尺寸的 finite-size scaling 后，才讨论 continuum 或临界
+   power law。
diff --git a/tracks/mps/solutions/Ranger-123/docs/theory.md b/tracks/mps/solutions/Ranger-123/docs/theory.md
new file mode 100644
index 000000000..e63883886
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/docs/theory.md
@@ -0,0 +1,115 @@
+# Theory and conventions
+
+## Model
+
+All baselines use an open chain and \(\hbar=k_B=1\):
+
+\[
+H_0=-J\sum_{i=1}^{N-1}Z_iZ_{i+1}
+    +\frac{\Omega}{2}\sum_{i=1}^N X_i ,
+\qquad
+H(t)=H_0+\epsilon_d\cos(\omega_dt)S_N .
+\]
+
+The bath couples through
+
+\[
+S_N=\eta_N\sum_iZ_i.
+\]
+
+The default `bounded` normalization is \(\eta_N=1/N\). `kac` means
+\(\eta_N=1/\sqrt N\), and `collective` means \(\eta_N=1\).
+An optional counterterm is specified by its explicit coefficient
+`counterterm_strength`; setting it to \(\Lambda\) adds \(+\Lambda S_N^2\).
+
+The zero-temperature Ohmic convention is
+
+\[
+J_B(\omega)=\alpha\omega e^{-\omega/\omega_c},\qquad
+C_B(t)=\frac{\alpha\omega_c^2}{(1+i\omega_ct)^2}.
+\]
+
+OQuPy defines its power-law spectral density with a factor of two. The wrapper
+therefore passes `alpha/2`; this is tested and recorded in every PT-TEMPO result.
+
+## N=2
+
+Exchange symmetry decomposes the Hilbert space as
+
+\[
+\mathcal H=\mathcal H_{\rm triplet}\oplus\mathcal H_{\rm singlet}.
+\]
+
+The singlet is dark:
+
+\[
+S_2|s\rangle=0,\qquad H(t)|s\rangle=J|s\rangle.
+\]
+
+In the triplet, define \(E=\sqrt{J^2+\Omega^2}\). The three energies are
+\(-E,-J,+E\), so the two allowed gaps and weights are
+
+\[
+\Delta_{\rm low/high}=E\mp J,
+\]
+
+\[
+W_{\rm low/high}=2\eta_2^2(1\pm J/E).
+\]
+
+All four formulas are compared with numerical diagonalization for multiple
+values of \(J\) at machine precision.
+
+## N=3
+
+Reflection \(1\leftrightarrow3\) gives
+
+\[
+\mathcal H=\mathcal H_{R=+}\oplus\mathcal H_{R=-},\qquad 8=6+2.
+\]
+
+The odd sector is the edge singlet times the central spin. The Ising term
+vanishes in this sector, so its gap is exactly \(\Omega\) for every \(J\). The
+even sector contains the collective physics. At strong ferromagnetic coupling,
+the lowest bright transition obeys
+
+\[
+\Delta_{\rm cat}=\frac{\Omega^3}{4J^2}+O(J^{-4}),
+\]
+
+and its normalized bright weight tends to one.
+
+## Heat-current convention
+
+For the period-averaged collective correlation
+
+\[
+\bar C(\tau)=T^{-1}\int_0^Tdt\,
+\langle S(t+\tau)S(t)\rangle ,
+\]
+
+the continuous heat-current density is
+
+\[
+\bar j_{\rm con}(\omega)=2J_B(\omega)\omega
+\int_0^\infty d\tau\left[
+\cos(\omega\tau)\operatorname{Re}C_{\rm con}(\tau)
++(1+2n_B)\sin(\omega\tau)\operatorname{Im}C_{\rm con}(\tau)
+\right].
+\]
+
+The factorized asymptotic part is never windowed into fake finite-width peaks.
+If
+
+\[
+\langle S(t)\rangle=\sum_nm_ne^{-in\omega_dt},
+\]
+
+its positive-frequency coherent correlation weight is \(2|m_n|^2\), and the
+heat delta weight is
+
+\[
+\pi J_B(n\omega_d)n\omega_d\,2|m_n|^2.
+\]
+
+The JSON schema stores these peaks separately under `delta_peaks`.
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diff --git a/tracks/mps/solutions/Ranger-123/julia/Project.toml b/tracks/mps/solutions/Ranger-123/julia/Project.toml
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index 000000000..41450d12f
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/julia/Project.toml
@@ -0,0 +1,14 @@
+[deps]
+JSON3 = "0f8b85d8-7281-11e9-16c2-39a750bddbf1"
+KrylovKit = "0b1a1467-8014-51b9-945f-bf0ae24f4b77"
+OrdinaryDiffEq = "1dea7af3-3e70-54e6-95c3-0bf5283fa5ed"
+UniformTEMPO = "df6cb18e-c722-4276-9e4b-1aef7d428362"
+
+[sources]
+UniformTEMPO = {url = "https://github.com/uniformTEMPO/UniformTEMPO.jl.git", rev = "b76a018c32e5415989761d902b1b0e95f1a337da"}
+
+[compat]
+JSON3 = "1"
+KrylovKit = "0.10"
+OrdinaryDiffEq = "6"
+julia = "1.12"
diff --git a/tracks/mps/solutions/Ranger-123/julia/run_uniform_tempo.jl b/tracks/mps/solutions/Ranger-123/julia/run_uniform_tempo.jl
new file mode 100644
index 000000000..d8f1163b3
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/julia/run_uniform_tempo.jl
@@ -0,0 +1,359 @@
+#!/usr/bin/env julia
+
+if length(ARGS) != 2
+    println(stderr, "UniformTEMPO input error: expected input JSON path and output JSON path")
+    exit(2)
+end
+if !isfile(ARGS[1])
+    println(stderr, "UniformTEMPO input error: input JSON does not exist: $(ARGS[1])")
+    exit(2)
+end
+
+using JSON3
+using KrylovKit
+using LinearAlgebra
+using OrdinaryDiffEq
+using SHA
+using Serialization
+using UniformTEMPO
+
+const METHOD = "uniform_tempo_floquet_multitime"
+const UNIFORM_TEMPO_REVISION = "b76a018c32e5415989761d902b1b0e95f1a337da"
+
+function fail(message::AbstractString)
+    println(stderr, "UniformTEMPO input error: " * message)
+    exit(2)
+end
+
+function required(object, key::Symbol)
+    haskey(object, key) || fail("missing input field: $(key)")
+    return object[key]
+end
+
+function decode_real_matrix(raw, label::AbstractString)
+    rows = [Float64.(collect(row)) for row in raw]
+    isempty(rows) && fail("$(label) must not be empty")
+    width = length(first(rows))
+    width > 0 || fail("$(label) must not have empty rows")
+    all(length(row) == width for row in rows) ||
+        fail("$(label) rows have inconsistent lengths")
+    return reduce(vcat, permutedims.(rows))
+end
+
+function decode_complex_matrix(raw, label::AbstractString)
+    real_part = decode_real_matrix(required(raw, :real), "$(label).real")
+    imag_part = decode_real_matrix(required(raw, :imag), "$(label).imag")
+    size(real_part) == size(imag_part) ||
+        fail("$(label) real and imaginary shapes differ")
+    return ComplexF64.(real_part, imag_part)
+end
+
+encode_complex(values) = Dict(
+    "real" => real.(values),
+    "imag" => imag.(values),
+    "shape" => collect(size(values)),
+)
+
+function finite_complex(values)
+    return all(isfinite, real.(values)) && all(isfinite, imag.(values))
+end
+
+function validate_hermitian(matrix, label::AbstractString)
+    size(matrix, 1) == size(matrix, 2) || fail("$(label) must be square")
+    norm(matrix - matrix') <= 1e-10 || fail("$(label) must be Hermitian")
+end
+
+function atomic_json_write(path::AbstractString, payload)
+    directory = dirname(path)
+    mkpath(directory)
+    temporary = path * ".tmp-" * string(getpid())
+    open(temporary, "w") do io
+        JSON3.pretty(io, payload)
+        write(io, '\n')
+    end
+    mv(temporary, path; force=true)
+end
+
+function load_or_build_process_tensor(
+    coupling,
+    dt,
+    bcf,
+    tolerance;
+    auto_nc,
+    memory_cutoff,
+    truncation,
+    cap_rank,
+    low_rank_svd,
+    max_rank,
+    cache_path,
+    cache_key,
+)
+    if cache_path !== nothing && isfile(cache_path)
+        record = deserialize(cache_path)
+        record isa AbstractDict ||
+            fail("process tensor cache record is invalid")
+        get(record, :key, nothing) == cache_key ||
+            fail("process tensor cache key does not match")
+        get(record, :uniform_tempo_revision, nothing) == UNIFORM_TEMPO_REVISION ||
+            fail("process tensor cache revision does not match")
+        get(record, :system_dimension, nothing) == size(coupling, 1) ||
+            fail("process tensor cache dimension does not match")
+        cached_dt = get(record, :dt, nothing)
+        cached_dt isa Real && isapprox(cached_dt, dt; rtol=1e-13, atol=1e-15) ||
+            fail("process tensor cache timestep does not match")
+        haskey(record, :process_tensor) ||
+            fail("process tensor cache has no tensor")
+        return record[:process_tensor], true
+    end
+
+    pt = uniTEMPO(
+        coupling,
+        dt,
+        bcf,
+        tolerance;
+        auto_nc=auto_nc,
+        n_c=memory_cutoff,
+        truncation=truncation,
+        cap_rank=cap_rank,
+        low_rank_svd=low_rank_svd,
+        max_rank=max_rank,
+    )
+    if cache_path !== nothing
+        mkpath(dirname(cache_path))
+        temporary = cache_path * ".tmp-" * string(getpid())
+        record = Dict(
+            :key => cache_key,
+            :uniform_tempo_revision => UNIFORM_TEMPO_REVISION,
+            :system_dimension => size(coupling, 1),
+            :dt => dt,
+            :process_tensor => pt,
+        )
+        open(temporary, "w") do io
+            serialize(io, record)
+        end
+        mv(temporary, cache_path; force=true)
+    end
+    return pt, false
+end
+
+function main()
+    input_path, output_path = ARGS
+
+    input = JSON3.read(read(input_path, String))
+    h0 = decode_complex_matrix(required(input, :h0), "h0")
+    coupling = decode_complex_matrix(required(input, :coupling), "coupling")
+    drive = decode_complex_matrix(required(input, :drive), "drive")
+    validate_hermitian(h0, "h0")
+    validate_hermitian(coupling, "coupling")
+    validate_hermitian(drive, "drive")
+    size(h0) == size(coupling) ||
+        fail("h0 and coupling dimensions differ")
+    size(h0) == size(drive) ||
+        fail("h0 and drive dimensions differ")
+
+    model = required(input, :model)
+    drive_amplitude = Float64(required(model, :drive_amplitude))
+    drive_frequency = Float64(required(model, :drive_frequency))
+    drive_frequency > 0 || fail("drive_frequency must be positive")
+
+    bath = required(input, :bath)
+    alpha = Float64(required(bath, :alpha))
+    cutoff = Float64(required(bath, :cutoff))
+    temperature = Float64(required(bath, :temperature))
+    alpha >= 0 || fail("alpha must be nonnegative")
+    cutoff > 0 || fail("cutoff must be positive")
+    temperature == 0 ||
+        fail("the current analytic bath correlation supports temperature=0 only")
+
+    controls = required(input, :controls)
+    period_steps = Int(required(controls, :steps_per_period))
+    tolerance = Float64(required(controls, :tolerance))
+    phase_offsets = Int.(collect(required(controls, :phase_offsets)))
+    delay_steps = Int(required(controls, :delay_steps))
+    auto_nc = Bool(required(controls, :auto_nc))
+    memory_cutoff = Int(required(controls, :memory_cutoff))
+    low_rank_svd = Bool(required(controls, :low_rank_svd))
+    truncation = Symbol(String(required(controls, :truncation)))
+    cap_rank = Int(required(controls, :cap_rank))
+    max_rank = Int(required(controls, :max_rank))
+    pole_count = Int(required(controls, :pole_count))
+    pole_tolerance = Float64(required(controls, :pole_tolerance))
+    pole_maxiter = Int(required(controls, :pole_maxiter))
+    process_tensor_cache_path = if haskey(controls, :process_tensor_cache_path)
+        String(controls[:process_tensor_cache_path])
+    else
+        nothing
+    end
+    process_tensor_cache_key = if haskey(controls, :process_tensor_cache_key)
+        String(controls[:process_tensor_cache_key])
+    else
+        nothing
+    end
+
+    period_steps >= 2 || fail("steps_per_period must be at least two")
+    0 < tolerance < 1 || fail("tolerance must lie between zero and one")
+    delay_steps >= 1 || fail("delay_steps must be positive")
+    memory_cutoff >= 1 || fail("memory_cutoff must be positive")
+    cap_rank >= 1 || fail("cap_rank must be positive")
+    max_rank >= cap_rank || fail("max_rank must be at least cap_rank")
+    pole_count >= 0 || fail("pole_count must be nonnegative")
+    pole_tolerance > 0 || fail("pole_tolerance must be positive")
+    pole_maxiter >= 1 || fail("pole_maxiter must be positive")
+    truncation in (:rel, :abs) || fail("truncation must be rel or abs")
+    length(phase_offsets) >= 2 ||
+        fail("at least two phase offsets are required")
+    length(unique(phase_offsets)) == length(phase_offsets) ||
+        fail("phase offsets must be unique")
+    all(0 .<= phase_offsets .< period_steps) ||
+        fail("phase offsets must lie within one period")
+    (process_tensor_cache_path === nothing) ==
+        (process_tensor_cache_key === nothing) ||
+        fail("process tensor cache path and key must be supplied together")
+    process_tensor_cache_key === nothing ||
+        occursin(r"^[0-9a-f]{64}$", process_tensor_cache_key) ||
+        fail("process tensor cache key must be a SHA-256 digest")
+
+    period = 2π / drive_frequency
+    dt = period / period_steps
+    h_s(time) = h0 + drive_amplitude * cos(drive_frequency * time) * drive
+    bcf(time) = alpha * (cutoff / (1 + im * cutoff * time))^2
+
+    pt, process_tensor_cache_hit = load_or_build_process_tensor(
+        coupling,
+        dt,
+        bcf,
+        tolerance;
+        auto_nc=auto_nc,
+        memory_cutoff=memory_cutoff,
+        truncation=truncation,
+        cap_rank=cap_rank,
+        low_rank_svd=low_rank_svd,
+        max_rank=max_rank,
+        cache_path=process_tensor_cache_path,
+        cache_key=process_tensor_cache_key,
+    )
+    ptf = floquet_process_tensor(pt, h_s, period)
+    extended_floquet_state = steadystate(ptf; return_full=true)
+    floquet_state = reshape(
+        ptf.v_l * extended_floquet_state,
+        size(h0),
+    )
+    floquet_state ./= tr(floquet_state)
+    floquet_transfer = reshape(
+        ptf.q,
+        size(ptf.q, 1) * size(ptf.q, 2),
+        size(ptf.q, 1) * size(ptf.q, 2),
+    )
+    floquet_transfer_residual = norm(
+        floquet_transfer * extended_floquet_state[:] -
+        extended_floquet_state[:]
+    ) / max(norm(extended_floquet_state), eps())
+    transfer_eigenvalues = ComplexF64[]
+    transfer_eigenpair_residuals = Float64[]
+    if pole_count > 0
+        requested = min(pole_count, size(floquet_transfer, 1) - 1)
+        values_raw, vectors, _ = eigsolve(
+            floquet_transfer,
+            requested,
+            :LM;
+            tol=pole_tolerance,
+            maxiter=pole_maxiter,
+        )
+        order = sortperm(abs.(values_raw); rev=true)
+        length(order) >= requested ||
+            error("KrylovKit returned fewer transfer poles than requested")
+        selected = order[1:requested]
+        transfer_eigenvalues = ComplexF64.(values_raw[selected])
+        transfer_eigenpair_residuals = [
+            norm(
+                floquet_transfer * vectors[index] -
+                values_raw[index] * vectors[index]
+            ) / max(norm(vectors[index]), eps())
+            for index in selected
+        ]
+    end
+
+    micromotion = evolve(pt, extended_floquet_state, period_steps; h_s=h_s)
+    extended_after_period = evolve(
+        pt,
+        extended_floquet_state,
+        period_steps;
+        h_s=h_s,
+        return_full=true,
+    )
+    fixed_point_residual = norm(
+        extended_after_period - extended_floquet_state
+    ) / max(norm(extended_floquet_state), eps())
+
+    selected_states = [micromotion[offset + 1] for offset in phase_offsets]
+    one_point = [real(tr(coupling * state)) for state in selected_states]
+    correlation_records = Vector{Vector{ComplexF64}}()
+    for offset in phase_offsets
+        extended_phase_state = if offset == 0
+            extended_floquet_state
+        else
+            evolve(
+                pt,
+                extended_floquet_state,
+                offset;
+                h_s=h_s,
+                return_full=true,
+            )
+        end
+        h_shifted(time) = h_s(time + offset * dt)
+        record = two_point_correlations(
+            pt,
+            extended_phase_state,
+            0,
+            delay_steps,
+            coupling,
+            coupling;
+            h_s=h_shifted,
+        )
+        push!(correlation_records, ComplexF64.(record))
+    end
+    total_correlation = reduce(+, correlation_records) / length(correlation_records)
+
+    trace_error = maximum(abs(tr(state) - 1) for state in selected_states)
+    hermiticity_error = maximum(norm(state - state') for state in selected_states)
+    minimum_density_eigenvalue = minimum(
+        minimum(eigvals(Hermitian((state + state') / 2)))
+        for state in selected_states
+    )
+    finite_complex(floquet_state) || error("non-finite Floquet state")
+    finite_complex(total_correlation) || error("non-finite correlation")
+    finite_complex(transfer_eigenvalues) || error("non-finite transfer eigenvalue")
+    all(isfinite, transfer_eigenpair_residuals) ||
+        error("non-finite transfer eigenpair residual")
+
+    manifest_path = joinpath(dirname(Base.active_project()), "Manifest.toml")
+    payload = Dict(
+        "method" => METHOD,
+        "dt" => dt,
+        "period_steps" => period_steps,
+        "bond_dimension" => bond_dim(pt),
+        "floquet_state" => encode_complex(floquet_state),
+        "phase_states" => encode_complex(cat(selected_states...; dims=3)),
+        "one_point" => one_point,
+        "phase_offsets" => phase_offsets,
+        "delay" => collect(0:delay_steps) .* dt,
+        "correlation" => encode_complex(total_correlation),
+        "diagnostics" => Dict(
+            "trace_error" => trace_error,
+            "hermiticity_error" => hermiticity_error,
+            "minimum_density_eigenvalue" => minimum_density_eigenvalue,
+            "fixed_point_residual" => fixed_point_residual,
+            "floquet_transfer_residual" => floquet_transfer_residual,
+        ),
+        "julia_version" => string(VERSION),
+        "uniform_tempo_revision" => UNIFORM_TEMPO_REVISION,
+        "manifest_sha256" => bytes2hex(sha256(read(manifest_path))),
+        "process_tensor_cache_hit" => process_tensor_cache_hit,
+        "transfer_eigenvalues" => encode_complex(transfer_eigenvalues),
+        "transfer_eigenpair_residuals" => transfer_eigenpair_residuals,
+        "transfer_dimension" => size(floquet_transfer, 1),
+    )
+    atomic_json_write(output_path, payload)
+end
+
+main()
diff --git a/tracks/mps/solutions/Ranger-123/julia/smoke_input.json b/tracks/mps/solutions/Ranger-123/julia/smoke_input.json
new file mode 100644
index 000000000..e6984ab15
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/julia/smoke_input.json
@@ -0,0 +1,31 @@
+{
+  "h0": {
+    "real": [[0.0, 0.5], [0.5, 0.0]],
+    "imag": [[0.0, 0.0], [0.0, 0.0]]
+  },
+  "coupling": {
+    "real": [[1.0, 0.0], [0.0, -1.0]],
+    "imag": [[0.0, 0.0], [0.0, 0.0]]
+  },
+  "model": {
+    "drive_amplitude": 0.2,
+    "drive_frequency": 1.0
+  },
+  "bath": {
+    "alpha": 0.01,
+    "cutoff": 2.5,
+    "temperature": 0.0
+  },
+  "controls": {
+    "steps_per_period": 8,
+    "tolerance": 0.001,
+    "phase_offsets": [0, 4],
+    "delay_steps": 4,
+    "auto_nc": false,
+    "memory_cutoff": 6,
+    "low_rank_svd": false,
+    "truncation": "rel",
+    "cap_rank": 100,
+    "max_rank": 1000
+  }
+}
diff --git a/tracks/mps/solutions/Ranger-123/output/pdf/Ranger-123-technical-report.pdf b/tracks/mps/solutions/Ranger-123/output/pdf/Ranger-123-technical-report.pdf
new file mode 100644
index 000000000..4941a2c86
Binary files /dev/null and b/tracks/mps/solutions/Ranger-123/output/pdf/Ranger-123-technical-report.pdf differ
diff --git a/tracks/mps/solutions/Ranger-123/pyproject.toml b/tracks/mps/solutions/Ranger-123/pyproject.toml
new file mode 100644
index 000000000..b2658d6b5
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/pyproject.toml
@@ -0,0 +1,51 @@
+[build-system]
+requires = ["hatchling>=1.27"]
+build-backend = "hatchling.build"
+
+[project]
+name = "floquet-if-manybody"
+version = "0.1.0"
+description = "Reproducible N=2,3 study for quantum.harness issue 123"
+readme = "README.md"
+requires-python = ">=3.11"
+license = {text = "AGPL-3.0-or-later"}
+dependencies = [
+  "numpy>=1.26,<2.0",
+  "scipy>=1.14",
+  "matplotlib>=3.9",
+  "PyYAML>=6.0",
+]
+
+[project.optional-dependencies]
+dev = [
+  "pytest>=8.3",
+  "ruff>=0.9",
+  "mypy>=1.14",
+]
+nonmarkov = [
+  "oqupy==0.5.0",
+]
+
+[project.scripts]
+floquet-if = "floquet_if_manybody.cli:main"
+
+[tool.hatch.build.targets.wheel]
+packages = ["src/floquet_if_manybody"]
+
+[tool.pytest.ini_options]
+testpaths = ["tests"]
+addopts = "-ra"
+
+[tool.ruff]
+line-length = 100
+target-version = "py311"
+
+[tool.ruff.lint]
+select = ["E", "F", "I", "UP", "B"]
+
+[tool.mypy]
+python_version = "3.12"
+strict = true
+ignore_missing_imports = true
+disallow_any_generics = false
+packages = ["floquet_if_manybody"]
diff --git a/tracks/mps/solutions/Ranger-123/report/data-summary.txt b/tracks/mps/solutions/Ranger-123/report/data-summary.txt
new file mode 100644
index 000000000..bc3258ea0
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/report/data-summary.txt
@@ -0,0 +1,47 @@
+Quantum Harness Issue #123 - Ranger machine-readable summary companion
+Generated: 2026-07-30 Asia/Shanghai
+UniformTEMPO revision: b76a018c32e5415989761d902b1b0e95f1a337da
+
+TIER 1 - PUBLISHED FIG. 3 BOTTOM REPRODUCTION
+Reference: https://zenodo.org/records/19593671
+Archive MD5: 0f3f9d9d8538aa96aee089973df7d9c2
+All points use dt = pi/60 and delay_periods = 12.
+
+wd/Omega  converged  bond  tolerance  phases  tail_amplitude  fixed_point_residual  hermiticity_error  shape_L1  area_ratio
+1.0       true       26    1e-7       15      0.0016272564    0.0000808715          0.0036099263       0.0562435 1.0267712
+1.5       true       14    1e-6       4       0.0023604904    0.0005313577          0.0042726147       0.2735650 1.1622298
+2.0       true       14    1e-6       4       0.0156057456    0.0003084472          0.0032007799       0.3718315 1.3118951
+
+TIER 2 - N=3 COLLECTIVE HEAT GRID
+Six of six reflection-sector points converged for J/Omega = 0.25, 0.5, 1.0.
+The reflection-odd projected model and heat curve are exactly J-independent.
+
+TIER 3 - N=3 SAME-MODEL UNIFORMTEMPO VS FLOQUET-MARKOV/QRT
+sector  J/Omega  trace_distance  correlation_error  heat_error
+even    0.25     0.9996997       1.1529658          9.0167068
+even    0.50     0.9999011       1.0341251          11.7157802
+even    1.00     0.9920892       1.0243259          9.0772348
+odd     0.25     0.4752510       0.5666192          0.3920114
+odd     0.50     0.4752510       0.5666192          0.3920114
+odd     1.00     0.4752510       0.5666192          0.3920114
+
+N=4 CONVERGENCE-GATED EXTENSION AT J/OMEGA=0.25
+sector  dimension  status       bond  tail_amplitude  markov_heat_error
+odd     6          converged    8     0.0367791       3.4047954
+even    10         converged    13    0.0213318       5.4937769
+
+N=4 odd largest continuous-spectrum peaks (omega/Omega, jbar):
+(0.4725, 0.00176277), (0.9600, 0.01938817), (1.4400, 0.00510966)
+Selected drive frequency: 0.9256058858 Omega
+
+Verification at this snapshot:
+pytest: 110 passed
+ruff: passed
+mypy: passed
+root result audit: passed (6 files)
+paper audit: passed
+
+Compact JSON evidence:
+validation/fig3_transversal_summary.json
+validation/n3_same_model_error_map.json
+validation/ARTIFACT_PROVENANCE.json
diff --git a/tracks/mps/solutions/Ranger-123/report/generated-results.tex b/tracks/mps/solutions/Ranger-123/report/generated-results.tex
new file mode 100644
index 000000000..e7d40f4ce
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/report/generated-results.tex
@@ -0,0 +1,12 @@
+\newcommand{\TierOneStatus}{3/3 通过物理门槛}
+\newcommand{\TierTwoStatus}{$N=3$ 六点、$N=4$ 两 sector 均收敛}
+\newcommand{\FigThreeRows}{%
+1.0 & 26 & $1.63\times10^{-3}$ & 0.056 & 1.027 \\
+1.5 & 14 & $2.36\times10^{-3}$ & 0.274 & 1.162 \\
+2.0 & 14 & $1.56\times10^{-2}$ & 0.372 & 1.312 \\
+}
+\newcommand{\NFourRows}{%
+even & 10 & 收敛 & 13 & 0.0213 & 5.494 \\
+odd & 6 & 收敛 & 8 & 0.0368 & 3.405 \\
+}
+\newcommand{\NFourConclusion}{两个 sector 的 compression、时间步、相位和物理性门槛全部通过。odd sector 使用三周期关联窗；even sector 的三周期尾幅为 0.0552，因此按门槛扩展到六周期并降至 0.0213。两点均完成同模型 Markov 对照。}
diff --git a/tracks/mps/solutions/Ranger-123/report/technical-report.tex b/tracks/mps/solutions/Ranger-123/report/technical-report.tex
new file mode 100644
index 000000000..b0c1eaace
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/report/technical-report.tex
@@ -0,0 +1,184 @@
+\documentclass[11pt,a4paper]{ctexart}
+\usepackage[margin=2.15cm]{geometry}
+\usepackage{amsmath,amssymb,booktabs,graphicx,hyperref,longtable,microtype,xcolor}
+\usepackage{fancyhdr}
+\hypersetup{colorlinks=true,linkcolor=blue!45!black,urlcolor=blue!55!black,citecolor=blue!45!black}
+\graphicspath{{../figures/paper/}{../figures/validation/}{../figures/heat-valve/}}
+\setlength{\parindent}{2em}
+\setlength{\parskip}{0.25em}
+\setlength{\headheight}{14pt}
+\pagestyle{fancy}
+\fancyhf{}
+\lhead{Quantum Harness Issue \#123}
+\rhead{Team Ranger}
+\cfoot{\thepage}
+\newcommand{\code}[1]{\texttt{#1}}
+\InputIfFileExists{generated-results.tex}{}{\errmessage{generated-results.tex is required}}
+
+\title{\textbf{共同非马尔可夫浴中的多体 Floquet 热输运}\\
+\large Quantum Harness Issue \#123 技术报告}
+\author{Team Ranger\\Chenxi Wan \quad Yedi Shen \quad Junkai Wang}
+\date{2026 年 7 月 30 日}
+
+\begin{document}
+\maketitle
+
+\begin{abstract}
+本项目将单自旋 Floquet influence functional 方法扩展到共同浴耦合的相互作用自旋链，给出可恢复、可审计的 uniform TEMPO 数值流程。我们完成原题 Tier 1 的三频率单自旋 Fig.~3 底图独立复现、Tier 2 的 $N=3$ 六点生产网格与 $N=4$ 收敛门控试算，并在完全相同的 Hamiltonian、驱动、浴、对称 sector 和频率网格上完成 Tier 3 的 Floquet-Markov/QRT 定量对照。核心结果是：$N=3$ even sector 的热谱相对误差达到 $9.02$--$11.72$，而 odd sector 为 $0.3920$；这表明弱耦合、无记忆近似的失效具有显著 sector 依赖性。项目同时记录一个预注册的暗通道负结果，避免把能隙塌缩误判为热抑制。所有声明均绑定到机器可读 JSON、图件哈希和自动化门槛。
+\end{abstract}
+
+\section{赛题要求与完成边界}
+Issue \#123 的三级路线分别要求：(i) 复现 Mickiewicz 等人单自旋横向驱动 Fig.~3 的热流密度；(ii) 研究 $N=3,4$ 小链中 collective modes 的出现；(iii) 对同一多体模型和同一参数实施 Floquet-Lindblad 或等价 master-equation benchmark。表~\ref{tab:tier} 按原题而非提交者自定义口径列出证据。
+
+\begin{table}[htbp]
+\centering
+\caption{原题三级路线与本项目证据。}
+\label{tab:tier}
+\begin{tabular}{p{0.10\linewidth}p{0.54\linewidth}p{0.25\linewidth}}
+\toprule
+级别 & 交付证据 & 状态 \\
+\midrule
+Tier 1 & 公开 Zenodo 曲线的校验下载；$\omega_d/\Omega=1,1.5,2$ 三个独立 UniformTEMPO 点；连续谱和解析 $\delta$ 峰分离 & \TierOneStatus \\
+Tier 2 & $N=3$ even/odd 六点收敛热谱；$N=4$ reflection 分块、回归测试及收敛门控点 & \TierTwoStatus \\
+Tier 3 & $N=3$ 六点在同模型、同参数下与 Floquet-Markov/QRT 比较 $D_\rho,\epsilon_C,\epsilon_j$ & 6/6 收敛 \\
+\bottomrule
+\end{tabular}
+\end{table}
+
+本报告不声称热力学极限、连续相变或临界指数。可选 Kac normalization 的完整时间步和相位细化也不被重新标记为已收敛。
+
+\section{模型与算法}
+系统 Hamiltonian 为
+\begin{equation}
+H_0=-J\sum_{i=1}^{N-1}Z_iZ_{i+1}+\frac{\Omega}{2}\sum_{i=1}^{N}X_i,
+\qquad
+H_{\mathrm d}(t)=\epsilon_{\mathrm d}\cos(\omega_{\mathrm d}t)S_N,
+\end{equation}
+共同零温 Ohmic 浴经 $S_N=\eta_N\sum_i Z_i$ 耦合，谱密度为
+\begin{equation}
+J_B(\omega)=\alpha\omega\exp(-\omega/\omega_c),\qquad \omega_c=2.5\Omega.
+\end{equation}
+生产后端固定到 UniformTEMPO.jl revision \code{b76a018c32e5}（完整哈希见机器数据）。Python 层完成对称投影、内容寻址缓存、自适应收敛阶梯、扩展 process-tensor state 中的多时间算符插入，以及连续谱与相干 $\delta$ 峰的分离。
+
+本实现包含三项面向本题的算法性改进：
+\begin{enumerate}
+\item 在 system-Liouville 与环境记忆的扩展态中直接插入算符，避免用 reduced-state QRT 冒充非马尔可夫两时间关联；
+\item 对 reflection symmetry 做精确分块，$N=3$ 化为 $6\oplus2$，$N=4$ 化为 $10\oplus6$，并把投影算符哈希写入缓存键；
+\item 用 compression、时间步、相位和物理性四层门槛控制计算，只有全部通过的点才进入定量图和误差图。
+\end{enumerate}
+
+\section{Tier 1：单自旋 Fig.~3 独立复现}
+公开作者数据来自 Zenodo record \href{https://zenodo.org/records/19593671}{19593671}，下载归档 MD5 为 {\scriptsize\texttt{0f3f9d9d8538aa96aee089973df7d9c2}}。独立计算采用论文参数 $\Omega=\epsilon_d=1$、$\alpha=0.05$、$\omega_c=2.5$、$\Delta t=\pi/60$，并将 connected correlation 的 Fourier 连续部分与驱动谐波的解析 $\delta$ 权重分别处理。
+
+\begin{table}[htbp]
+\centering
+\caption{Fig.~3 底图三频率独立计算。$L^1_{\rm shape}$ 比较归一化谱形，$R_{\rm area}$ 为积分强度比。}
+\label{tab:fig3}
+\begin{tabular}{ccccc}
+\toprule
+$\omega_d/\Omega$ & bond & 尾幅 & $L^1_{\rm shape}$ & $R_{\rm area}$ \\
+\midrule
+\FigThreeRows
+\bottomrule
+\end{tabular}
+\end{table}
+
+\begin{figure}[htbp]
+\centering
+\includegraphics[width=\linewidth]{fig3_transversal_summary.png}
+\caption{论文 Fig.~3 底图公开数据与独立 UniformTEMPO 连续谱。竖线标出独立计算得到的相干峰位置；比较不把 $\delta$ 峰伪装成有限宽峰。}
+\label{fig:fig3}
+\end{figure}
+
+这些曲线是定量的结构复现而非逐点相同。差异主要来自独立实现使用的压缩阶数、有限关联窗和相位采样；因此报告同时给出直接幅度误差、归一化谱形误差和面积比，不以肉眼相似替代数值指标。
+
+\section{Tier 2：\texorpdfstring{$N=3$}{N=3} collective heat spectrum}
+$N=3$ reflection-even/odd 两个 sector 在 $J/\Omega=0.25,0.5,1$ 上共六点全部通过收敛门槛。odd sector 的投影 Hamiltonian 与耦合算符对 $J$ 严格不变，因此三条曲线在机器精度内重合；even sector 则显示随 $J$ 移动的 collective features。
+
+\begin{figure}[htbp]
+\centering
+\includegraphics[width=0.88\linewidth]{n3_sector_heat.png}
+\caption{$N=3$ reflection sector 分辨的频率热流密度。}
+\label{fig:n3heat}
+\end{figure}
+
+\section{Tier 3：同模型非马尔可夫与 Markov 对照}
+误差定义为
+\begin{align}
+D_\rho&=\frac12\lVert\rho_{\rm IF}-\rho_{\rm ME}\rVert_1,\\
+\epsilon_C&=\frac{\int d\tau\,|C_{\rm IF}(\tau)-C_{\rm ME}(\tau)|}{\int d\tau\,|C_{\rm IF}(\tau)|},\\
+\epsilon_j&=\frac{\int d\omega\,|\bar j_{\rm IF}(\omega)-\bar j_{\rm ME}(\omega)|}{\int d\omega\,|\bar j_{\rm IF}(\omega)|}.
+\end{align}
+even sector 上 $D_\rho=0.9921$--$0.9999$、$\epsilon_C=1.024$--$1.153$、$\epsilon_j=9.02$--$11.72$；odd sector 三点均为 $D_\rho=0.4753$、$\epsilon_C=0.5666$、$\epsilon_j=0.3920$。大误差不是精确端未收敛，而是同参数 Markov benchmark 的真实偏差。
+
+\begin{figure}[htbp]
+\centering
+\includegraphics[width=0.92\linewidth]{n3_error_maps.png}
+\caption{$N=3$ 同模型 UniformTEMPO 与 Floquet-Markov/QRT 的三种误差。}
+\label{fig:n3error}
+\end{figure}
+
+\section{\texorpdfstring{$N=4$}{N=4} 收敛门控结果}
+$N=4$ 采用 reflection-even $10$ 维和 reflection-odd $6$ 维子空间。试算预先固定两级阶梯：每周期步数 $30\rightarrow60$，压缩 tolerance $10^{-5}\rightarrow3\times10^{-6}$，相位数 $3\rightarrow15$。结果只在 state、correlation、heat、trace、Hermiticity 和 density positivity 门槛全部通过后，才运行同模型 Markov 对照。
+
+\begin{table}[htbp]
+\centering
+\caption{$N=4,J/\Omega=0.25$ 的门控试算。}
+\label{tab:n4}
+\begin{tabular}{cccccc}
+\toprule
+sector & dim & 状态 & bond & 尾幅 & $\epsilon_j$ \\
+\midrule
+\NFourRows
+\bottomrule
+\end{tabular}
+\end{table}
+
+\NFourConclusion
+
+\begin{figure}[htbp]
+\centering
+\begin{minipage}{0.49\linewidth}
+\includegraphics[width=\linewidth]{n4_even_j0p25_comparison.png}
+\end{minipage}\hfill
+\begin{minipage}{0.49\linewidth}
+\includegraphics[width=\linewidth]{n4_odd_j0p25_comparison.png}
+\end{minipage}
+\caption{$N=4$ even（左）和 odd（右）sector 的收敛 UniformTEMPO 热谱及同模型 Floquet-Markov/QRT 对照。odd 连续谱主要峰位于 $0.4725,0.9600,1.4400\,\Omega$，显示相对于驱动频率 $0.9256\,\Omega$ 的多峰 collective structure。}
+\label{fig:n4}
+\end{figure}
+
+\section{预注册负结果与创新点}
+我们在计算前定义了暗通道继续条件：中心点热流相对两侧至少降低三倍，且可观测 transfer-pole residue 也至少降低三倍。$N=3$ 三点 pilot 中，准能隙虽塌缩，residue 却上升，热流门槛也未通过，因此九点扩展被按规则停止。这是可复现的负结果：它说明仅观察 quasienergy gap 或小 Floquet matrix element 不足以声称 entanglement-assisted heat suppression。
+
+相较于直接扫描，本项目的主要创新价值是：(i) 把对称性化简、非马尔可夫多时间关联和热谱计算整合为可恢复管线；(ii) 给出同一 $N=3$ 模型上的 sector-resolved master-equation breakdown map；(iii) 把假设检验写成机器门槛，从而把失败结论也保存为研究输出；(iv) 为 $N=4$ 建立不依赖全 Hilbert 空间的 reflection-resolved 入口。
+
+\section{可重复性与数据交付}
+仓库提交源代码、测试、PNG/PDF 图、紧凑 JSON 和本报告源文件。体积较大的 \code{results/} 按上游仓库规则不纳入 Git；\code{validation/ARTIFACT\_PROVENANCE.json} 保存本地审计产物的 SHA-256。推荐验证命令为：
+\begin{verbatim}
+.venv/bin/python -m pytest -q
+.venv/bin/python -m ruff check src tests scripts
+.venv/bin/python -m mypy src scripts/run_fig3_validation.py
+.venv/bin/python -m floquet_if_manybody.cli audit results
+.venv/bin/python -m floquet_if_manybody.cli paper-audit results/paper
+\end{verbatim}
+
+\section{结论}
+本项目已经从单自旋代码验证推进到 $N=3$ 多体生产计算，并用同模型误差图直接回答了原题最具方法学价值的问题：Floquet-Markov/QRT 的失效不仅显著，而且依赖多体对称 sector。$N=4$ 结果按预先声明的收敛门槛分类，不以“程序跑完”替代“数值可信”。所有正结果和负结果都可以从固定版本后端、缓存键、JSON 指标与图件哈希重新审计。
+
+\begin{thebibliography}{9}
+\bibitem{mickiewicz2026}
+K. Mickiewicz, V. Link, and W. T. Strunz,
+``Exact Floquet Dynamics of Strongly Damped Driven Quantum Systems,''
+\emph{Physical Review Letters} \textbf{136}, 200201 (2026).
+\bibitem{link2024}
+V. Link, H.-H. Tu, and W. T. Strunz,
+``Open Quantum System Dynamics from Infinite Tensor Network Contraction,''
+\emph{Physical Review Letters} \textbf{132}, 200403 (2024).
+\bibitem{garbellini2026}
+M. Garbellini, K. Mickiewicz, V. Link, A. Eisfeld, and W. T. Strunz,
+``Uniform process tensor approach for the calculation of multi-time correlation functions of non-Markovian open systems,''
+\emph{Journal of Chemical Physics} (2026), doi:10.1063/5.0331783.
+\end{thebibliography}
+
+\end{document}
diff --git a/tracks/mps/solutions/Ranger-123/scripts/instantiate_julia.sh b/tracks/mps/solutions/Ranger-123/scripts/instantiate_julia.sh
new file mode 100755
index 000000000..3aa2e7fd1
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/scripts/instantiate_julia.sh
@@ -0,0 +1,8 @@
+#!/usr/bin/env bash
+set -euo pipefail
+
+project_root="$(cd "$(dirname "${BASH_SOURCE[0]}")/.." && pwd)"
+julia --project="${project_root}/julia" -e \
+  'using Pkg; Pkg.resolve(); Pkg.instantiate(); Pkg.precompile()'
+julia --project="${project_root}/julia" -e \
+  'using UniformTEMPO, OrdinaryDiffEq, JSON3; println("UniformTEMPO environment ready")'
diff --git a/tracks/mps/solutions/Ranger-123/scripts/run_baselines.sh b/tracks/mps/solutions/Ranger-123/scripts/run_baselines.sh
new file mode 100755
index 000000000..21ac784ce
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/scripts/run_baselines.sh
@@ -0,0 +1,9 @@
+#!/bin/sh
+set -eu
+
+project_dir=$(CDPATH= cd -- "$(dirname -- "$0")/.." && pwd)
+cd "$project_dir"
+
+python_bin="${PYTHON_BIN:-$project_dir/.venv/bin/python}"
+"$python_bin" -m floquet_if_manybody.cli baselines --output results --figures figures
+"$python_bin" -m floquet_if_manybody.cli audit results
diff --git a/tracks/mps/solutions/Ranger-123/scripts/run_fig3_validation.py b/tracks/mps/solutions/Ranger-123/scripts/run_fig3_validation.py
new file mode 100644
index 000000000..bbbe5bfdf
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/scripts/run_fig3_validation.py
@@ -0,0 +1,277 @@
+#!/usr/bin/env python3
+"""Reproduce and compare the transversal single-spin data from PRL Fig. 3."""
+
+from __future__ import annotations
+
+import argparse
+import hashlib
+import json
+from dataclasses import asdict
+from io import BytesIO
+from pathlib import Path
+from typing import Any
+from urllib.request import urlopen
+from zipfile import ZipFile
+
+import numpy as np
+from matplotlib import pyplot as plt
+from scipy.integrate import trapezoid
+
+from floquet_if_manybody.backends.uniform_tempo import (
+    UNIFORM_TEMPO_REVISION,
+    UniformTempoBackend,
+    UniformTempoControls,
+)
+from floquet_if_manybody.config import BathConfig, ModelConfig
+from floquet_if_manybody.convergence import atomic_write_result, curve_residual
+from floquet_if_manybody.heat_current import heat_current_spectrum
+from floquet_if_manybody.operators import pauli
+
+ZENODO_RECORD = "https://zenodo.org/records/19593671"
+ZENODO_ARCHIVE = (
+    "https://zenodo.org/api/records/19593671/files/"
+    "exact_floquet_dynamics_of_strongly_damped_driven_quantum_systems.zip/content"
+)
+ZENODO_MD5 = "0f3f9d9d8538aa96aee089973df7d9c2"
+REFERENCE_FREQUENCY = np.arange(0.005, 15.0001, 0.005)
+
+
+def _reference_name(drive_frequency: float) -> str:
+    label = f"{drive_frequency:g}"
+    return (
+        "fig_3/heat_current_transversal_Ω_1_ϵ_d_1_"
+        f"ω_d_{label}_α_0.05_ω_c_2.5_bond_dim_235_dt_0.052.csv"
+    )
+
+
+def download_reference() -> dict[float, np.ndarray]:
+    """Download the immutable author archive and extract the three bottom-panel curves."""
+    with urlopen(ZENODO_ARCHIVE, timeout=30) as response:  # noqa: S310
+        archive = response.read()
+    digest = hashlib.md5(archive, usedforsecurity=False).hexdigest()
+    if digest != ZENODO_MD5:
+        raise ValueError(f"Zenodo archive checksum mismatch: {digest}")
+    curves: dict[float, np.ndarray] = {}
+    with ZipFile(BytesIO(archive)) as bundle:
+        for drive_frequency in (1.0, 1.5, 2.0):
+            values = np.loadtxt(BytesIO(bundle.read(_reference_name(drive_frequency))))
+            if values.shape != REFERENCE_FREQUENCY.shape or not np.all(np.isfinite(values)):
+                raise ValueError(f"invalid Fig. 3 reference curve for wd={drive_frequency:g}")
+            curves[drive_frequency] = np.asarray(values, dtype=float)
+    return curves
+
+
+def comparison_metrics(reference: np.ndarray, candidate: np.ndarray) -> dict[str, float]:
+    """Return direct-amplitude and normalized-shape discrepancies."""
+    direct = curve_residual(
+        REFERENCE_FREQUENCY,
+        reference,
+        REFERENCE_FREQUENCY,
+        candidate,
+    )
+    reference_area = float(trapezoid(abs(reference), REFERENCE_FREQUENCY))
+    candidate_area = float(trapezoid(abs(candidate), REFERENCE_FREQUENCY))
+    if reference_area <= 0 or candidate_area <= 0:
+        raise ValueError("Fig. 3 curves must have positive integrated magnitude")
+    shape = curve_residual(
+        REFERENCE_FREQUENCY,
+        reference / reference_area,
+        REFERENCE_FREQUENCY,
+        candidate / candidate_area,
+    )
+    return {
+        "continuous_relative_l1": direct,
+        "normalized_shape_relative_l1": shape,
+        "integrated_magnitude_ratio": candidate_area / reference_area,
+    }
+
+
+def run_point(
+    drive_frequency: float,
+    reference: np.ndarray,
+    cache_directory: Path,
+    *,
+    tolerance: float = 1e-6,
+    phase_samples: int = 4,
+) -> dict[str, Any]:
+    """Run one independent UniformTEMPO point at the published Fig. 3 controls."""
+    steps_per_period = int(round(120 / drive_frequency))
+    model = ModelConfig(
+        n=1,
+        j=0.0,
+        omega=1.0,
+        drive_amplitude=1.0,
+        drive_frequency=drive_frequency,
+    )
+    bath = BathConfig(alpha=0.05, cutoff=2.5, temperature=0.0)
+    controls = UniformTempoControls(
+        steps_per_period=steps_per_period,
+        tolerance=tolerance,
+        phase_samples=phase_samples,
+        delay_periods=12,
+        low_rank_svd=True,
+        truncation="abs",
+        cap_rank=5_000,
+        max_rank=10_000,
+    )
+    run = UniformTempoBackend(
+        tensor_cache_directory=cache_directory / "process_tensors"
+    ).run_periodic(
+        0.5 * pauli("x"),
+        pauli("z"),
+        model,
+        bath,
+        controls,
+        drive_operator=pauli("z"),
+    )
+    heat = heat_current_spectrum(run.correlation, bath, REFERENCE_FREQUENCY)
+    diagnostics = {
+        **run.diagnostics,
+        **run.metadata,
+        "connected_tail_amplitude": float(abs(run.correlation.connected[-1])),
+    }
+    physical_gates_passed = bool(
+        float(diagnostics["fixed_point_residual"]) <= 1e-3
+        and float(diagnostics["trace_error"]) <= 5e-3
+        and float(diagnostics["hermiticity_error"]) <= 5e-3
+        and float(diagnostics["minimum_density_eigenvalue"]) >= -5e-3
+        and float(diagnostics["connected_tail_amplitude"]) <= 5e-2
+    )
+    return {
+        "method": "uniform_tempo_fig3_transversal_reproduction",
+        "converged": physical_gates_passed,
+        "reference": {
+            "record": ZENODO_RECORD,
+            "archive_md5": ZENODO_MD5,
+            "panel": "Fig. 3 bottom",
+        },
+        "uniform_tempo_revision": UNIFORM_TEMPO_REVISION,
+        "model": asdict(model),
+        "bath": asdict(bath),
+        "controls": asdict(controls),
+        "diagnostics": diagnostics,
+        "metrics": comparison_metrics(reference, heat.continuous),
+        "frequency": heat.frequencies.tolist(),
+        "reference_continuous": reference.tolist(),
+        "continuous": heat.continuous.tolist(),
+        "delta_peaks": [asdict(item) for item in heat.delta_peaks],
+    }
+
+
+def plot_result(result: dict[str, Any], stem: Path) -> None:
+    frequency = np.asarray(result["frequency"], dtype=float)
+    reference = np.asarray(result["reference_continuous"], dtype=float)
+    candidate = np.asarray(result["continuous"], dtype=float)
+    figure, axis = plt.subplots(figsize=(7.2, 4.2))
+    axis.plot(frequency, reference, label="Mickiewicz et al. Fig. 3 data", lw=1.5)
+    axis.plot(frequency, candidate, "--", label="independent UniformTEMPO", lw=1.2)
+    for peak in result["delta_peaks"]:
+        axis.axvline(float(peak["frequency"]), color="black", alpha=0.35, lw=0.8)
+    model = result["model"]
+    axis.set(
+        xlim=(0, 4),
+        xlabel=r"bath frequency $\omega/\Omega$",
+        ylabel=r"continuous $\bar j(\omega)/\Omega$",
+        title=rf"Fig. 3 bottom validation, $\omega_d={float(model['drive_frequency']):g}\Omega$",
+    )
+    axis.grid(alpha=0.2)
+    axis.legend(frameon=False)
+    figure.tight_layout()
+    stem.parent.mkdir(parents=True, exist_ok=True)
+    figure.savefig(stem.with_suffix(".png"), dpi=220)
+    figure.savefig(stem.with_suffix(".pdf"))
+    plt.close(figure)
+
+
+def plot_summary(results: list[dict[str, Any]], stem: Path) -> None:
+    """Plot the complete three-curve bottom-panel validation in one artifact."""
+    ordered = sorted(results, key=lambda item: float(item["model"]["drive_frequency"]))
+    figure, axes = plt.subplots(1, 3, figsize=(12.0, 3.55), sharex=True)
+    for axis, result in zip(axes, ordered, strict=True):
+        frequency = np.asarray(result["frequency"], dtype=float)
+        reference = np.asarray(result["reference_continuous"], dtype=float)
+        candidate = np.asarray(result["continuous"], dtype=float)
+        model = result["model"]
+        metrics = result["metrics"]
+        axis.plot(frequency, reference, label="published data", lw=1.35)
+        axis.plot(frequency, candidate, "--", label="independent run", lw=1.15)
+        for peak in result["delta_peaks"]:
+            if float(peak["frequency"]) <= 4:
+                axis.axvline(float(peak["frequency"]), color="black", alpha=0.3, lw=0.7)
+        axis.set(
+            xlim=(0, 4),
+            xlabel=r"$\omega/\Omega$",
+            title=(
+                rf"$\omega_d={float(model['drive_frequency']):g}\Omega$"
+                "\n"
+                rf"shape $L^1={float(metrics['normalized_shape_relative_l1']):.3f}$"
+            ),
+        )
+        axis.grid(alpha=0.2)
+    axes[0].set_ylabel(r"continuous $\bar j(\omega)/\Omega$")
+    axes[0].legend(frameon=False, fontsize=8)
+    figure.suptitle("Independent reproduction of Mickiewicz et al., Fig. 3 bottom")
+    figure.tight_layout()
+    stem.parent.mkdir(parents=True, exist_ok=True)
+    figure.savefig(stem.with_suffix(".png"), dpi=220)
+    figure.savefig(stem.with_suffix(".pdf"))
+    plt.close(figure)
+
+
+def main() -> int:
+    parser = argparse.ArgumentParser()
+    parser.add_argument(
+        "--drive-frequency",
+        type=float,
+        choices=(1.0, 1.5, 2.0),
+        default=2.0,
+    )
+    parser.add_argument("--plot-only", type=Path)
+    parser.add_argument("--plot-summary", action="store_true")
+    parser.add_argument("--tolerance", type=float, default=1e-6)
+    parser.add_argument("--phase-samples", type=int, default=4)
+    parser.add_argument(
+        "--figures",
+        type=Path,
+        default=Path("figures/validation"),
+    )
+    parser.add_argument("--output", type=Path, default=Path("results/validation"))
+    parser.add_argument(
+        "--cache",
+        type=Path,
+        default=Path("results/cache/fig3_uniform_tempo"),
+    )
+    arguments = parser.parse_args()
+    if arguments.plot_summary:
+        result_paths = [
+            arguments.output / "fig3_transversal_wd1.json",
+            arguments.output / "fig3_transversal_wd1p5.json",
+            arguments.output / "fig3_transversal_wd2.json",
+        ]
+        results = [json.loads(path.read_text(encoding="utf-8")) for path in result_paths]
+        if not all(bool(result["converged"]) for result in results):
+            raise ValueError("all three Fig. 3 points must pass physical gates")
+        plot_summary(results, arguments.figures / "fig3_transversal_summary")
+        return 0
+    if arguments.plot_only is not None:
+        result = json.loads(arguments.plot_only.read_text(encoding="utf-8"))
+        label = f"{float(result['model']['drive_frequency']):g}".replace(".", "p")
+        plot_result(result, arguments.figures / f"fig3_transversal_wd{label}")
+        return 0
+    references = download_reference()
+    result = run_point(
+        arguments.drive_frequency,
+        references[arguments.drive_frequency],
+        arguments.cache,
+        tolerance=arguments.tolerance,
+        phase_samples=arguments.phase_samples,
+    )
+    arguments.output.mkdir(parents=True, exist_ok=True)
+    label = f"{arguments.drive_frequency:g}".replace(".", "p")
+    atomic_write_result(arguments.output / f"fig3_transversal_wd{label}.json", result)
+    plot_result(result, arguments.figures / f"fig3_transversal_wd{label}")
+    return 0 if result["converged"] else 1
+
+
+if __name__ == "__main__":
+    raise SystemExit(main())
diff --git a/tracks/mps/solutions/Ranger-123/scripts/run_paper_extension.sh b/tracks/mps/solutions/Ranger-123/scripts/run_paper_extension.sh
new file mode 100755
index 000000000..1d61c51ac
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/scripts/run_paper_extension.sh
@@ -0,0 +1,45 @@
+#!/usr/bin/env bash
+set -euo pipefail
+
+PYTHON_BIN="${PYTHON_BIN:-.venv-py312/bin/python}"
+TARGET="${1:-all}"
+OUTPUT_DIR="${OUTPUT_DIR:-results/paper}"
+CACHE_DIR="${CACHE_DIR:-results/cache/uniform_tempo}"
+FIGURE_DIR="${FIGURE_DIR:-figures/paper}"
+FULL_KAC="${FULL_KAC:-0}"
+
+run_n3() {
+  "$PYTHON_BIN" -m floquet_if_manybody.cli n3-heat-grid \
+    --output "$OUTPUT_DIR" --cache "$CACHE_DIR" --figures "$FIGURE_DIR"
+}
+
+run_errors() {
+  "$PYTHON_BIN" -m floquet_if_manybody.cli error-map \
+    --output "$OUTPUT_DIR" --cache "$CACHE_DIR" --figures "$FIGURE_DIR"
+}
+
+run_models() {
+  local extra=()
+  if [[ "$FULL_KAC" == "1" ]]; then
+    extra+=(--full-kac)
+  fi
+  "$PYTHON_BIN" -m floquet_if_manybody.cli model-comparison \
+    --output "$OUTPUT_DIR" --cache "$CACHE_DIR" --figures "$FIGURE_DIR" \
+    "${extra[@]}"
+}
+
+case "$TARGET" in
+  n3) run_n3 ;;
+  errors) run_errors ;;
+  models) run_models ;;
+  all)
+    run_n3
+    run_errors
+    run_models
+    "$PYTHON_BIN" -m floquet_if_manybody.cli paper-audit "$OUTPUT_DIR"
+    ;;
+  *)
+    echo "usage: $0 {n3|errors|models|all}" >&2
+    exit 2
+    ;;
+esac
diff --git a/tracks/mps/solutions/Ranger-123/scripts/run_pt_baselines.sh b/tracks/mps/solutions/Ranger-123/scripts/run_pt_baselines.sh
new file mode 100755
index 000000000..7a3511864
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/scripts/run_pt_baselines.sh
@@ -0,0 +1,9 @@
+#!/bin/sh
+set -eu
+
+project_dir=$(CDPATH= cd -- "$(dirname -- "$0")/.." && pwd)
+cd "$project_dir"
+
+python_bin="${PYTHON_BIN:-$project_dir/.venv-py312/bin/python}"
+"$python_bin" -m floquet_if_manybody.cli pt-baselines --output results --figures figures
+"$python_bin" -m floquet_if_manybody.cli audit results
diff --git a/tracks/mps/solutions/Ranger-123/scripts/run_uniform_validation.py b/tracks/mps/solutions/Ranger-123/scripts/run_uniform_validation.py
new file mode 100644
index 000000000..127e1727c
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/scripts/run_uniform_validation.py
@@ -0,0 +1,193 @@
+#!/usr/bin/env python3
+"""Generate runtime validation records for the pinned UniformTEMPO backend."""
+
+from __future__ import annotations
+
+import argparse
+from dataclasses import asdict
+from pathlib import Path
+from typing import Any, cast
+
+import numpy as np
+from numpy.typing import NDArray
+
+from floquet_if_manybody.backends.uniform_tempo import (
+    UNIFORM_TEMPO_REVISION,
+    UniformTempoBackend,
+    UniformTempoControls,
+)
+from floquet_if_manybody.config import BathConfig, ModelConfig
+from floquet_if_manybody.convergence import (
+    ConvergenceCache,
+    atomic_write_result,
+    curve_residual,
+    state_residual,
+)
+from floquet_if_manybody.heat_current import heat_current_spectrum
+from floquet_if_manybody.n3_heat import N3HeatPoint, prepare_n3_sector, run_n3_heat_point
+from floquet_if_manybody.operators import pauli
+
+
+def _complex_values(values: NDArray[np.complex128]) -> dict[str, Any]:
+    return {
+        "real": np.real(values).astype(float).tolist(),
+        "imag": np.imag(values).astype(float).tolist(),
+    }
+
+
+def _complex_array(value: dict[str, Any]) -> NDArray[np.complex128]:
+    return cast(
+        NDArray[np.complex128],
+        np.asarray(value["real"], dtype=float) + 1j * np.asarray(value["imag"], dtype=float),
+    )
+
+
+def single_spin_record(cache_directory: Path) -> dict[str, Any]:
+    model = ModelConfig(
+        n=1,
+        j=0.0,
+        omega=1.0,
+        drive_amplitude=0.2,
+        drive_frequency=1.0,
+    )
+    bath = BathConfig(alpha=0.05, cutoff=2.5, temperature=0.0)
+    controls = UniformTempoControls(
+        steps_per_period=60,
+        tolerance=1e-6,
+        phase_samples=3,
+        delay_periods=6,
+        low_rank_svd=True,
+        truncation="abs",
+        cap_rank=5_000,
+        max_rank=10_000,
+    )
+    run = UniformTempoBackend(
+        tensor_cache_directory=cache_directory / "process_tensors"
+    ).run_periodic(0.5 * pauli("x"), pauli("z"), model, bath, controls)
+    frequency = np.linspace(0.0, 3.0, 401)
+    heat = heat_current_spectrum(run.correlation, bath, frequency)
+    diagnostics = {
+        **run.diagnostics,
+        **run.metadata,
+        "connected_tail_amplitude": float(abs(run.correlation.connected[-1])),
+    }
+    accepted = bool(
+        diagnostics["fixed_point_residual"] <= 1e-3
+        and diagnostics["trace_error"] <= 5e-3
+        and diagnostics["hermiticity_error"] <= 5e-3
+        and diagnostics["minimum_density_eigenvalue"] >= -5e-3
+        and diagnostics["connected_tail_amplitude"] <= 5e-2
+    )
+    return {
+        "method": "uniform_tempo_single_spin_runtime_validation",
+        "converged": accepted,
+        "uniform_tempo_revision": UNIFORM_TEMPO_REVISION,
+        "model": asdict(model),
+        "bath": asdict(bath),
+        "controls": asdict(controls),
+        "diagnostics": diagnostics,
+        "phase_state": _complex_values(run.floquet_state),
+        "frequency": heat.frequencies.tolist(),
+        "continuous": heat.continuous.tolist(),
+        "delta_peaks": [asdict(item) for item in heat.delta_peaks],
+    }
+
+
+def cross_backend_record(cache_directory: Path) -> dict[str, Any]:
+    common = dict(
+        j=0.25,
+        sector="odd",
+        steps_per_period=60,
+        phase_samples=3,
+        delay_periods=1,
+        frequency_points=401,
+    )
+    uniform_point = N3HeatPoint(
+        **common,
+        backend="uniform_tempo",
+        epsrel=1e-6,
+        uniform_low_rank_svd=True,
+        uniform_truncation="abs",
+        uniform_cap_rank=5_000,
+        uniform_max_rank=10_000,
+    )
+    oqupy_point = N3HeatPoint(
+        **common,
+        backend="oqupy",
+        memory_steps=3,
+        epsrel=1e-5,
+        steady_periods=20,
+    )
+    cache = ConvergenceCache(cache_directory)
+    uniform = run_n3_heat_point(uniform_point, cache)
+    oqupy = run_n3_heat_point(oqupy_point, cache, commit="oqupy-cross-validation-v1")
+    uniform_grid = np.asarray(uniform["frequency"], dtype=float)
+    oqupy_grid = np.asarray(oqupy["frequency"], dtype=float)
+    uniform_delay = np.asarray(uniform["correlation"]["delay"], dtype=float)
+    oqupy_delay = np.asarray(oqupy["correlation"]["delay"], dtype=float)
+    metrics = {
+        "phase_state_frobenius": state_residual(
+            _complex_array(oqupy["phase_state"]),
+            _complex_array(uniform["phase_state"]),
+        ),
+        "connected_correlation_relative_l1": curve_residual(
+            oqupy_delay,
+            _complex_array(oqupy["correlation"]["connected"]),
+            uniform_delay,
+            _complex_array(uniform["correlation"]["connected"]),
+        ),
+        "continuous_heat_relative_l1": curve_residual(
+            oqupy_grid,
+            np.asarray(oqupy["continuous"], dtype=float),
+            uniform_grid,
+            np.asarray(uniform["continuous"], dtype=float),
+        ),
+    }
+    reference = prepare_n3_sector(uniform_point)
+    target = prepare_n3_sector(N3HeatPoint(**{**asdict(uniform_point), "j": 1.0}))
+    return {
+        "method": "coarse_uniform_tempo_vs_oqupy_cross_validation",
+        "complete": True,
+        "converged": bool(
+            uniform.get("complete")
+            and oqupy.get("complete")
+            and all(np.isfinite(value) for value in metrics.values())
+        ),
+        "interpretation": ("independent coarse-backend diagnostic; not a convergence refinement"),
+        "uniform_fingerprint": uniform["fingerprint"],
+        "oqupy_fingerprint": oqupy["fingerprint"],
+        "projected_odd_j_invariance": {
+            "h0_frobenius_residual": float(np.linalg.norm(reference.h0 - target.h0)),
+            "coupling_frobenius_residual": float(
+                np.linalg.norm(reference.coupling - target.coupling)
+            ),
+        },
+        "metrics": metrics,
+    }
+
+
+def main() -> int:
+    parser = argparse.ArgumentParser()
+    parser.add_argument("--output", type=Path, default=Path("results/validation"))
+    parser.add_argument(
+        "--cache",
+        type=Path,
+        default=Path("results/cache/uniform_tempo"),
+    )
+    arguments = parser.parse_args()
+    arguments.output.mkdir(parents=True, exist_ok=True)
+    single = single_spin_record(arguments.cache)
+    atomic_write_result(
+        arguments.output / "uniform_tempo_single_spin.json",
+        single,
+    )
+    cross = cross_backend_record(arguments.cache)
+    atomic_write_result(
+        arguments.output / "uniform_tempo_oqupy_crosscheck.json",
+        cross,
+    )
+    return 0 if single["converged"] and cross["converged"] else 1
+
+
+if __name__ == "__main__":
+    raise SystemExit(main())
diff --git a/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/__init__.py b/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/__init__.py
new file mode 100644
index 000000000..04a1f16ea
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/__init__.py
@@ -0,0 +1,6 @@
+"""Few-body Floquet heat-spectroscopy research tools."""
+
+from .config import BathConfig, ModelConfig, NumericsConfig, RunConfig
+
+__all__ = ["BathConfig", "ModelConfig", "NumericsConfig", "RunConfig"]
+__version__ = "0.1.0"
diff --git a/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/adaptive.py b/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/adaptive.py
new file mode 100644
index 000000000..a9d034784
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/adaptive.py
@@ -0,0 +1,702 @@
+"""Ordered, resumable refinement of PT-TEMPO numerical controls."""
+
+from __future__ import annotations
+
+from collections.abc import Callable
+from dataclasses import dataclass, replace
+from typing import Any, Literal, cast
+
+import numpy as np
+from numpy.typing import NDArray
+from scipy.integrate import trapezoid
+
+from .convergence import ConvergenceCache, state_residual
+from .n3_heat import N3HeatPoint
+
+Parameter = Literal[
+    "memory_steps",
+    "steps_per_period",
+    "epsrel",
+    "phase_samples",
+]
+Runner = Callable[[N3HeatPoint, ConvergenceCache | None], dict[str, Any]]
+
+
+@dataclass(frozen=True)
+class AdaptiveSchedule:
+    memory_steps: tuple[int, ...] = (3, 4, 5)
+    steps_per_period: tuple[int, ...] = (12, 16, 20)
+    epsrel: tuple[float, ...] = (1e-5, 3e-6)
+    state_threshold: float = 5e-2
+    correlation_threshold: float = 5e-2
+    heat_threshold: float = 5e-2
+    phase_threshold: float = 1e-3
+    trace_threshold: float = 5e-3
+
+    def __post_init__(self) -> None:
+        if any(value <= 0 for value in self.memory_steps + self.steps_per_period):
+            raise ValueError("integer refinement controls must be positive")
+        if any(not 0 < value < 1 for value in self.epsrel):
+            raise ValueError("epsrel refinements must lie between zero and one")
+        if tuple(sorted(self.memory_steps)) != self.memory_steps:
+            raise ValueError("memory_steps must increase")
+        if tuple(sorted(self.steps_per_period)) != self.steps_per_period:
+            raise ValueError("steps_per_period must increase")
+        if tuple(sorted(self.epsrel, reverse=True)) != self.epsrel:
+            raise ValueError("epsrel must decrease")
+
+
+@dataclass(frozen=True)
+class UniformAdaptiveSchedule:
+    """Refinement controls for a uniform infinite process tensor."""
+
+    steps_per_period: tuple[int, ...] = (60, 90, 120)
+    tolerances: tuple[float, ...] = (3e-7, 1e-7, 3e-8)
+    phase_samples: tuple[int, ...] = (3, 15)
+    state_threshold: float = 5e-2
+    correlation_threshold: float = 8e-2
+    heat_threshold: float = 8e-2
+    phase_threshold: float = 1e-3
+    trace_threshold: float = 5e-3
+    hermiticity_threshold: float = 5e-3
+
+    def __post_init__(self) -> None:
+        if any(value < 2 for value in self.steps_per_period):
+            raise ValueError("steps_per_period values must be at least two")
+        if any(not 0 < value < 1 for value in self.tolerances):
+            raise ValueError("tolerances must lie between zero and one")
+        if any(value < 2 for value in self.phase_samples):
+            raise ValueError("phase_samples values must be at least two")
+        if tuple(sorted(self.steps_per_period)) != self.steps_per_period:
+            raise ValueError("steps_per_period must increase")
+        if tuple(sorted(self.tolerances, reverse=True)) != self.tolerances:
+            raise ValueError("tolerances must decrease")
+        if tuple(sorted(self.phase_samples)) != self.phase_samples:
+            raise ValueError("phase_samples must increase")
+        if any(
+            steps % samples != 0
+            for steps in self.steps_per_period
+            for samples in self.phase_samples
+        ):
+            raise ValueError(
+                "every phase_samples value must divide every timestep refinement"
+            )
+
+
+@dataclass(frozen=True)
+class RefinementEvidence:
+    parameter: Parameter
+    coarse_fingerprint: str
+    refined_fingerprint: str
+    coarse_value: float
+    refined_value: float
+    state_residual: float
+    correlation_residual: float
+    heat_residual: float
+    passed: bool
+    coarse_bond_dimension: int | None = None
+    refined_bond_dimension: int | None = None
+    coarse_steps_per_period: int | None = None
+    refined_steps_per_period: int | None = None
+    coarse_tolerance: float | None = None
+    refined_tolerance: float | None = None
+    coarse_phase_samples: int | None = None
+    refined_phase_samples: int | None = None
+
+
+@dataclass(frozen=True)
+class AdaptiveResult:
+    converged: bool
+    status: Literal["converged", "resource_ceiling", "backend_failure"]
+    final_point: N3HeatPoint
+    final_result: dict[str, Any]
+    evidence: tuple[RefinementEvidence, ...]
+    failed_parameter: Parameter | None = None
+
+
+def _complex_array(value: dict[str, Any]) -> NDArray[np.complex128]:
+    return cast(
+        NDArray[np.complex128],
+        np.asarray(value["real"], dtype=float)
+        + 1j * np.asarray(value["imag"], dtype=float),
+    )
+
+
+def _aligned_residual(
+    candidate_grid: NDArray[np.float64],
+    candidate: NDArray[np.complex128] | NDArray[np.float64],
+    reference_grid: NDArray[np.float64],
+    reference: NDArray[np.complex128] | NDArray[np.float64],
+) -> float:
+    """Compare curves on the coarser grid over their common domain."""
+    lower = max(float(candidate_grid[0]), float(reference_grid[0]))
+    upper = min(float(candidate_grid[-1]), float(reference_grid[-1]))
+    common = candidate_grid[
+        (candidate_grid >= lower - 1e-14) & (candidate_grid <= upper + 1e-14)
+    ]
+    if len(common) < 2:
+        raise ValueError("curve grids do not share a usable interval")
+    candidate_common = np.interp(common, candidate_grid, np.real(candidate)) + 1j * np.interp(
+        common, candidate_grid, np.imag(candidate)
+    )
+    reference_common = np.interp(common, reference_grid, np.real(reference)) + 1j * np.interp(
+        common, reference_grid, np.imag(reference)
+    )
+    numerator = float(trapezoid(abs(candidate_common - reference_common), common))
+    denominator = float(trapezoid(abs(reference_common), common)) + 1e-15
+    return numerator / denominator
+
+
+def _residuals(
+    coarse: dict[str, Any], refined: dict[str, Any]
+) -> tuple[float, float, float]:
+    state = state_residual(
+        _complex_array(coarse["phase_state"]),
+        _complex_array(refined["phase_state"]),
+    )
+    coarse_correlation = _complex_array(coarse["correlation"]["connected"])
+    refined_correlation = _complex_array(refined["correlation"]["connected"])
+    correlation = _aligned_residual(
+        np.asarray(coarse["correlation"]["delay"], dtype=float),
+        coarse_correlation,
+        np.asarray(refined["correlation"]["delay"], dtype=float),
+        refined_correlation,
+    )
+    heat = _aligned_residual(
+        np.asarray(coarse["frequency"], dtype=float),
+        np.asarray(coarse["continuous"], dtype=float),
+        np.asarray(refined["frequency"], dtype=float),
+        np.asarray(refined["continuous"], dtype=float),
+    )
+    return state, correlation, heat
+
+
+def _refinement_values(
+    point: N3HeatPoint, schedule: AdaptiveSchedule, parameter: Parameter
+) -> tuple[int | float, ...]:
+    if parameter == "memory_steps":
+        values: tuple[int | float, ...] = schedule.memory_steps
+        current: int | float = point.memory_steps
+    elif parameter == "steps_per_period":
+        values = schedule.steps_per_period
+        current = point.steps_per_period
+    else:
+        values = schedule.epsrel
+        current = point.epsrel
+    if current in values:
+        return values[values.index(current) :]
+    if parameter != "epsrel":
+        return current, *tuple(value for value in values if value > current)
+    return current, *tuple(value for value in values if value < current)
+
+
+def _replace_parameter(
+    point: N3HeatPoint, parameter: Parameter, value: int | float
+) -> N3HeatPoint:
+    if parameter == "memory_steps":
+        return replace(point, memory_steps=int(value))
+    if parameter == "steps_per_period":
+        steps = int(value)
+        memory = max(
+            point.memory_steps,
+            int(round(point.memory_steps * steps / point.steps_per_period)),
+        )
+        return replace(point, steps_per_period=steps, memory_steps=memory)
+    return replace(point, epsrel=float(value))
+
+
+def run_adaptive(
+    point: N3HeatPoint,
+    schedule: AdaptiveSchedule,
+    runner: Runner,
+    cache: ConvergenceCache | None,
+) -> AdaptiveResult:
+    """Refine memory, timestep, and SVD tolerance in that order."""
+    current_point = point
+    current_result = runner(current_point, cache)
+    evidence: list[RefinementEvidence] = []
+    if not bool(current_result.get("converged", False)):
+        return AdaptiveResult(
+            False, "backend_failure", current_point, current_result, tuple(evidence)
+        )
+
+    for parameter in ("memory_steps", "steps_per_period", "epsrel"):
+        typed_parameter: Parameter = parameter
+        values = _refinement_values(current_point, schedule, typed_parameter)
+        if len(values) < 2:
+            return AdaptiveResult(
+                False,
+                "resource_ceiling",
+                current_point,
+                current_result,
+                tuple(evidence),
+                typed_parameter,
+            )
+        parameter_passed = False
+        for value in values[1:]:
+            refined_point = _replace_parameter(current_point, typed_parameter, value)
+            refined_result = runner(refined_point, cache)
+            if not bool(refined_result.get("converged", False)):
+                return AdaptiveResult(
+                    False,
+                    "backend_failure",
+                    refined_point,
+                    refined_result,
+                    tuple(evidence),
+                    typed_parameter,
+                )
+            state, correlation, heat = _residuals(current_result, refined_result)
+            passed = (
+                state <= schedule.state_threshold
+                and correlation <= schedule.correlation_threshold
+                and heat <= schedule.heat_threshold
+            )
+            evidence.append(
+                RefinementEvidence(
+                    typed_parameter,
+                    str(current_result["fingerprint"]),
+                    str(refined_result["fingerprint"]),
+                    float(getattr(current_point, typed_parameter)),
+                    float(value),
+                    state,
+                    correlation,
+                    heat,
+                    passed,
+                )
+            )
+            current_point = refined_point
+            current_result = refined_result
+            if passed:
+                parameter_passed = True
+                break
+        if not parameter_passed:
+            return AdaptiveResult(
+                False,
+                "resource_ceiling",
+                current_point,
+                current_result,
+                tuple(evidence),
+                typed_parameter,
+            )
+
+    diagnostics = current_result.get("diagnostics", {})
+    final_checks = (
+        float(diagnostics.get("phase_residual", np.inf))
+        <= schedule.phase_threshold
+        and float(diagnostics.get("trace_error", np.inf))
+        <= schedule.trace_threshold
+        and float(diagnostics.get("minimum_density_eigenvalue", -np.inf)) >= -5e-3
+        and float(diagnostics.get("connected_tail_amplitude", np.inf)) <= 5e-2
+    )
+    return AdaptiveResult(
+        final_checks,
+        "converged" if final_checks else "backend_failure",
+        current_point,
+        current_result,
+        tuple(evidence),
+    )
+
+
+def _schedule_tail(
+    current: int | float,
+    values: tuple[int, ...] | tuple[float, ...],
+    *,
+    increasing: bool,
+) -> tuple[int | float, ...]:
+    if current in values:
+        return values[values.index(current) :]
+    if increasing:
+        return current, *tuple(value for value in values if value > current)
+    return current, *tuple(value for value in values if value < current)
+
+
+def _uniform_refined_point(
+    point: N3HeatPoint,
+    parameter: Parameter,
+    value: int | float,
+) -> N3HeatPoint:
+    if parameter == "steps_per_period":
+        return replace(point, steps_per_period=int(value))
+    if parameter == "phase_samples":
+        return replace(point, phase_samples=int(value))
+    if parameter == "epsrel":
+        return replace(point, epsrel=float(value))
+    raise ValueError(f"unsupported uniform refinement parameter {parameter}")
+
+
+def _bond_dimension(result: dict[str, Any]) -> int | None:
+    value = result.get("diagnostics", {}).get("bond_dimension")
+    if value is None:
+        return None
+    return int(value)
+
+
+def _uniform_physical_checks(
+    result: dict[str, Any],
+    schedule: UniformAdaptiveSchedule,
+) -> bool:
+    diagnostics = result.get("diagnostics", {})
+    return bool(
+        float(diagnostics.get("phase_residual", np.inf))
+        <= schedule.phase_threshold
+        and float(diagnostics.get("trace_error", np.inf))
+        <= schedule.trace_threshold
+        and float(diagnostics.get("hermiticity_error", np.inf))
+        <= schedule.hermiticity_threshold
+        and float(diagnostics.get("minimum_density_eigenvalue", -np.inf)) >= -5e-3
+        and float(diagnostics.get("connected_tail_amplitude", np.inf)) <= 5e-2
+    )
+
+
+def run_uniform_adaptive(
+    point: N3HeatPoint,
+    schedule: UniformAdaptiveSchedule,
+    runner: Runner,
+    cache: ConvergenceCache | None,
+) -> AdaptiveResult:
+    """Converge compression at every timestep, then refine phase quadrature.
+
+    Compression and Trotter errors are coupled: a tolerance that is adequate on
+    one time grid need not be adequate on the next.  Each timestep candidate is
+    therefore converged across the tolerance ladder before two adjacent
+    timestep candidates are compared.
+    """
+    if point.backend != "uniform_tempo":
+        raise ValueError("uniform adaptive runner requires backend='uniform_tempo'")
+    current_phase_samples = point.phase_samples
+    if current_phase_samples is None:
+        raise ValueError("uniform adaptive runner requires explicit phase_samples")
+
+    evidence: list[RefinementEvidence] = []
+    timestep_values = _schedule_tail(
+        point.steps_per_period,
+        schedule.steps_per_period,
+        increasing=True,
+    )
+    tolerance_values = _schedule_tail(
+        point.epsrel,
+        schedule.tolerances,
+        increasing=False,
+    )
+    if len(timestep_values) < 2 or len(tolerance_values) < 2:
+        failed: Parameter = (
+            "steps_per_period" if len(timestep_values) < 2 else "epsrel"
+        )
+        initial_result = runner(point, cache)
+        return AdaptiveResult(
+            False,
+            "resource_ceiling",
+            point,
+            initial_result,
+            tuple(evidence),
+            failed,
+        )
+
+    previous_timestep_point: N3HeatPoint | None = None
+    previous_timestep_result: dict[str, Any] | None = None
+    previous_compression_passed = False
+    current_point = point
+    current_result: dict[str, Any] | None = None
+    timestep_passed = False
+
+    for step_index, step_value in enumerate(timestep_values):
+        compression_point = replace(
+            point,
+            steps_per_period=int(step_value),
+            epsrel=float(tolerance_values[0]),
+        )
+        compression_result = runner(compression_point, cache)
+        if not bool(compression_result.get("complete", False)):
+            return AdaptiveResult(
+                False,
+                "backend_failure",
+                compression_point,
+                compression_result,
+                tuple(evidence),
+                "epsrel",
+            )
+
+        compression_passed = False
+        for tolerance in tolerance_values[1:]:
+            refined_point = replace(
+                compression_point,
+                epsrel=float(tolerance),
+            )
+            refined_result = runner(refined_point, cache)
+            if not bool(refined_result.get("complete", False)):
+                return AdaptiveResult(
+                    False,
+                    "backend_failure",
+                    refined_point,
+                    refined_result,
+                    tuple(evidence),
+                    "epsrel",
+                )
+            state, correlation, heat = _residuals(
+                compression_result,
+                refined_result,
+            )
+            passed = (
+                state <= schedule.state_threshold
+                and correlation <= schedule.correlation_threshold
+                and heat <= schedule.heat_threshold
+            )
+            evidence.append(
+                RefinementEvidence(
+                    "epsrel",
+                    str(compression_result["fingerprint"]),
+                    str(refined_result["fingerprint"]),
+                    float(compression_point.epsrel),
+                    float(tolerance),
+                    state,
+                    correlation,
+                    heat,
+                    passed,
+                    _bond_dimension(compression_result),
+                    _bond_dimension(refined_result),
+                    compression_point.steps_per_period,
+                    refined_point.steps_per_period,
+                    compression_point.epsrel,
+                    refined_point.epsrel,
+                    compression_point.phase_samples,
+                    refined_point.phase_samples,
+                )
+            )
+            compression_point = refined_point
+            compression_result = refined_result
+            if passed:
+                compression_passed = True
+                break
+        current_point = compression_point
+        current_result = compression_result
+        if not compression_passed and step_index == len(timestep_values) - 1:
+            return AdaptiveResult(
+                False,
+                "resource_ceiling",
+                current_point,
+                current_result,
+                tuple(evidence),
+                "epsrel",
+            )
+
+        if previous_timestep_point is not None and previous_timestep_result is not None:
+            state, correlation, heat = _residuals(
+                previous_timestep_result,
+                current_result,
+            )
+            passed = (
+                previous_compression_passed
+                and compression_passed
+                and state <= schedule.state_threshold
+                and correlation <= schedule.correlation_threshold
+                and heat <= schedule.heat_threshold
+                and _uniform_physical_checks(current_result, schedule)
+            )
+            evidence.append(
+                RefinementEvidence(
+                    "steps_per_period",
+                    str(previous_timestep_result["fingerprint"]),
+                    str(current_result["fingerprint"]),
+                    float(previous_timestep_point.steps_per_period),
+                    float(current_point.steps_per_period),
+                    state,
+                    correlation,
+                    heat,
+                    passed,
+                    _bond_dimension(previous_timestep_result),
+                    _bond_dimension(current_result),
+                    previous_timestep_point.steps_per_period,
+                    current_point.steps_per_period,
+                    previous_timestep_point.epsrel,
+                    current_point.epsrel,
+                    previous_timestep_point.phase_samples,
+                    current_point.phase_samples,
+                )
+            )
+            if passed:
+                timestep_passed = True
+                break
+        previous_timestep_point = current_point
+        previous_timestep_result = current_result
+        previous_compression_passed = compression_passed
+
+    if current_result is None:
+        raise RuntimeError("uniform adaptive refinement produced no result")
+    if not timestep_passed:
+        return AdaptiveResult(
+            False,
+            "resource_ceiling",
+            current_point,
+            current_result,
+            tuple(evidence),
+            "steps_per_period",
+        )
+
+    phase_values = _schedule_tail(
+        current_phase_samples,
+        schedule.phase_samples,
+        increasing=True,
+    )
+    if len(phase_values) < 2:
+        return AdaptiveResult(
+            False,
+            "resource_ceiling",
+            current_point,
+            current_result,
+            tuple(evidence),
+            "phase_samples",
+        )
+    phase_passed = False
+    for phase_value in phase_values[1:]:
+        refined_point = replace(current_point, phase_samples=int(phase_value))
+        refined_result = runner(refined_point, cache)
+        if not bool(refined_result.get("complete", False)):
+            return AdaptiveResult(
+                False,
+                "backend_failure",
+                refined_point,
+                refined_result,
+                tuple(evidence),
+                "phase_samples",
+            )
+        state, correlation, heat = _residuals(current_result, refined_result)
+        passed = (
+            state <= schedule.state_threshold
+            and correlation <= schedule.correlation_threshold
+            and heat <= schedule.heat_threshold
+            and _uniform_physical_checks(refined_result, schedule)
+        )
+        evidence.append(
+            RefinementEvidence(
+                "phase_samples",
+                str(current_result["fingerprint"]),
+                str(refined_result["fingerprint"]),
+                float(current_point.phase_samples or current_phase_samples),
+                float(phase_value),
+                state,
+                correlation,
+                heat,
+                passed,
+                _bond_dimension(current_result),
+                _bond_dimension(refined_result),
+                current_point.steps_per_period,
+                refined_point.steps_per_period,
+                current_point.epsrel,
+                refined_point.epsrel,
+                current_point.phase_samples,
+                refined_point.phase_samples,
+            )
+        )
+        current_point = refined_point
+        current_result = refined_result
+        if passed:
+            phase_passed = True
+            break
+    if not phase_passed:
+        return AdaptiveResult(
+            False,
+            "resource_ceiling",
+            current_point,
+            current_result,
+            tuple(evidence),
+            "phase_samples",
+        )
+
+    final_checks = _uniform_physical_checks(current_result, schedule)
+    return AdaptiveResult(
+        final_checks,
+        "converged" if final_checks else "backend_failure",
+        current_point,
+        current_result,
+        tuple(evidence),
+    )
+
+
+def run_uniform_compression_audit(
+    point: N3HeatPoint,
+    schedule: UniformAdaptiveSchedule,
+    runner: Runner,
+    cache: ConvergenceCache | None,
+) -> AdaptiveResult:
+    """Converge only MPO compression and record a timestep resource ceiling.
+
+    This is used for explicitly exploratory points whose next timestep grid is
+    outside the declared local budget.  It never returns ``converged``.
+    """
+    if point.backend != "uniform_tempo":
+        raise ValueError("uniform compression audit requires backend='uniform_tempo'")
+    tolerance_values = _schedule_tail(
+        point.epsrel,
+        schedule.tolerances,
+        increasing=False,
+    )
+    current_point = point
+    current_result = runner(current_point, cache)
+    evidence: list[RefinementEvidence] = []
+    if not bool(current_result.get("complete", False)):
+        return AdaptiveResult(
+            False,
+            "backend_failure",
+            current_point,
+            current_result,
+            tuple(evidence),
+            "epsrel",
+        )
+    for tolerance in tolerance_values[1:]:
+        refined_point = replace(current_point, epsrel=float(tolerance))
+        refined_result = runner(refined_point, cache)
+        if not bool(refined_result.get("complete", False)):
+            return AdaptiveResult(
+                False,
+                "backend_failure",
+                refined_point,
+                refined_result,
+                tuple(evidence),
+                "epsrel",
+            )
+        state, correlation, heat = _residuals(current_result, refined_result)
+        passed = (
+            state <= schedule.state_threshold
+            and correlation <= schedule.correlation_threshold
+            and heat <= schedule.heat_threshold
+        )
+        evidence.append(
+            RefinementEvidence(
+                "epsrel",
+                str(current_result["fingerprint"]),
+                str(refined_result["fingerprint"]),
+                current_point.epsrel,
+                refined_point.epsrel,
+                state,
+                correlation,
+                heat,
+                passed,
+                _bond_dimension(current_result),
+                _bond_dimension(refined_result),
+                current_point.steps_per_period,
+                refined_point.steps_per_period,
+                current_point.epsrel,
+                refined_point.epsrel,
+                current_point.phase_samples,
+                refined_point.phase_samples,
+            )
+        )
+        current_point = refined_point
+        current_result = refined_result
+        if passed:
+            return AdaptiveResult(
+                False,
+                "resource_ceiling",
+                current_point,
+                current_result,
+                tuple(evidence),
+                "steps_per_period",
+            )
+    return AdaptiveResult(
+        False,
+        "resource_ceiling",
+        current_point,
+        current_result,
+        tuple(evidence),
+        "epsrel",
+    )
diff --git a/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/backends/__init__.py b/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/backends/__init__.py
new file mode 100644
index 000000000..265614438
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/backends/__init__.py
@@ -0,0 +1,21 @@
+"""Open-system solver backends."""
+
+from .base import OpenSystemResult
+from .finite_memory import FiniteMemoryBackend
+from .floquet_markov import FloquetMarkovBackend
+from .pt_tempo import PtTempoBackend
+from .uniform_tempo import (
+    UniformTempoBackend,
+    UniformTempoControls,
+    UniformTempoResult,
+)
+
+__all__ = [
+    "FiniteMemoryBackend",
+    "FloquetMarkovBackend",
+    "OpenSystemResult",
+    "PtTempoBackend",
+    "UniformTempoBackend",
+    "UniformTempoControls",
+    "UniformTempoResult",
+]
diff --git a/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/backends/base.py b/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/backends/base.py
new file mode 100644
index 000000000..8deb6b83d
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/backends/base.py
@@ -0,0 +1,20 @@
+"""Common, provenance-rich open-system result types."""
+
+from __future__ import annotations
+
+from dataclasses import dataclass
+from typing import Any
+
+import numpy as np
+from numpy.typing import NDArray
+
+
+@dataclass(frozen=True)
+class OpenSystemResult:
+    method: str
+    density_matrices: NDArray[np.complex128]
+    times: NDArray[np.float64]
+    converged: bool
+    diagnostics: dict[str, float]
+    metadata: dict[str, Any]
+    step_maps: NDArray[np.complex128] | None = None
diff --git a/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/backends/finite_memory.py b/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/backends/finite_memory.py
new file mode 100644
index 000000000..d6cea3b1e
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/backends/finite_memory.py
@@ -0,0 +1,136 @@
+"""Brute-force augmented-density-tensor influence-functional backend.
+
+This is a transparent finite-memory QUAPI implementation for few-level
+validation. Its cost is O((d^2)^(K+1)); it intentionally refuses unsafe sizes.
+"""
+
+from __future__ import annotations
+
+from collections.abc import Callable
+from dataclasses import asdict
+
+import numpy as np
+from scipy.linalg import expm
+
+from ..config import BathConfig
+from ..influence import InfluenceCoefficients, discretize_influence
+from ..operators import ComplexMatrix
+from .base import OpenSystemResult
+
+
+def _trace_from_vector(vector: np.ndarray, dimension: int) -> complex:
+    return complex(sum(vector[index * dimension + index] for index in range(dimension)))
+
+
+class FiniteMemoryBackend:
+    """Finite-memory path sum in the coupling-operator eigenbasis."""
+
+    method = "finite_memory_if"
+
+    def __init__(self, max_augmented_elements: int = 2_000_000):
+        self.max_augmented_elements = max_augmented_elements
+
+    @staticmethod
+    def _influence_table(
+        eigenvalues: np.ndarray, coefficients: InfluenceCoefficients, depth: int
+    ) -> np.ndarray:
+        dimension = len(eigenvalues)
+        q = dimension**2
+        pairs = [(plus, minus) for plus in range(dimension) for minus in range(dimension)]
+        shape = (q,) * (depth + 1)
+        table = np.ones(shape, dtype=np.complex128)
+        for new_index, (new_plus, new_minus) in enumerate(pairs):
+            delta = eigenvalues[new_plus] - eigenvalues[new_minus]
+            for indices in np.ndindex(*(q,) * depth):
+                exponent = 0.0j
+                for lag, history_index in enumerate(indices, start=1):
+                    old_plus, old_minus = pairs[history_index]
+                    eta = coefficients.values[lag]
+                    exponent -= delta * (
+                        eta * eigenvalues[old_plus] - eta.conjugate() * eigenvalues[old_minus]
+                    )
+                eta0 = coefficients.values[0]
+                exponent -= delta * (
+                    eta0 * eigenvalues[new_plus]
+                    - eta0.conjugate() * eigenvalues[new_minus]
+                )
+                table[(new_index, *indices)] = np.exp(exponent)
+        return table
+
+    def run(
+        self,
+        hamiltonian: Callable[[float], ComplexMatrix],
+        coupling: ComplexMatrix,
+        initial_density: ComplexMatrix,
+        bath: BathConfig,
+        dt: float,
+        steps: int,
+        memory_steps: int,
+    ) -> OpenSystemResult:
+        if steps < 1:
+            raise ValueError("steps must be positive")
+        eigenvalues, basis = np.linalg.eigh(coupling)
+        dimension = coupling.shape[0]
+        q = dimension**2
+        augmented_size = q ** (memory_steps + 1)
+        if augmented_size > self.max_augmented_elements:
+            raise ValueError(
+                f"augmented tensor requires {augmented_size} elements; "
+                f"limit is {self.max_augmented_elements}"
+            )
+        coefficients = discretize_influence(bath, dt, memory_steps)
+        rho = basis.conj().T @ initial_density @ basis
+        augmented = rho.reshape(q).copy()
+        histories = 1
+        output = [initial_density.copy()]
+        maximum_trace_error = 0.0
+        minimum_eigenvalue = float(np.min(np.linalg.eigvalsh(initial_density)))
+
+        for step in range(steps):
+            midpoint = (step + 0.5) * dt
+            transformed_h = basis.conj().T @ hamiltonian(midpoint) @ basis
+            unitary = expm(-1j * transformed_h * dt)
+            propagator = np.einsum("ac,bd->abcd", unitary, unitary.conj()).reshape(q, q)
+            active_depth = min(histories, memory_steps)
+            table = self._influence_table(eigenvalues, coefficients, active_depth)
+            transition_shape = (q, q) + (1,) * (active_depth - 1)
+            expanded = propagator.reshape(transition_shape) * augmented[np.newaxis, ...] * table
+            if histories >= memory_steps:
+                augmented = expanded.sum(axis=-1)
+            else:
+                augmented = expanded
+                histories += 1
+            reduced = augmented
+            while reduced.ndim > 1:
+                reduced = reduced.sum(axis=-1)
+            trace = _trace_from_vector(reduced, dimension)
+            maximum_trace_error = max(maximum_trace_error, abs(trace - 1))
+            if abs(trace) > 1e-14:
+                augmented /= trace
+                reduced /= trace
+            rho_s = reduced.reshape(dimension, dimension)
+            rho_lab = basis @ rho_s @ basis.conj().T
+            rho_lab = (rho_lab + rho_lab.conj().T) / 2
+            minimum_eigenvalue = min(minimum_eigenvalue, float(np.min(np.linalg.eigvalsh(rho_lab))))
+            output.append(rho_lab)
+
+        diagnostics = {
+            "trace_error": maximum_trace_error,
+            "minimum_density_eigenvalue": minimum_eigenvalue,
+            "quadrature_error": coefficients.quadrature_error,
+            "correlation_tail_bound": coefficients.tail_bound,
+        }
+        converged = maximum_trace_error < 1e-8 and minimum_eigenvalue > -1e-6
+        return OpenSystemResult(
+            self.method,
+            np.asarray(output),
+            np.asarray(np.arange(steps + 1) * dt, dtype=np.float64),
+            converged,
+            diagnostics,
+            {
+                "bath": asdict(bath),
+                "dt": dt,
+                "memory_steps": memory_steps,
+                "approximation": "finite timestep and hard memory cutoff",
+            },
+        )
diff --git a/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/backends/floquet_markov.py b/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/backends/floquet_markov.py
new file mode 100644
index 000000000..1f3e75d39
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/backends/floquet_markov.py
@@ -0,0 +1,192 @@
+"""Secular Floquet-Markov population solver."""
+
+from __future__ import annotations
+
+from collections.abc import Callable
+from dataclasses import dataclass
+
+import numpy as np
+from scipy.linalg import expm
+
+from ..bath import bose_occupation, ohmic_spectral_density
+from ..config import BathConfig
+from ..floquet import FloquetSolution, micromotion, solve_floquet
+from ..operators import ComplexMatrix
+from .base import OpenSystemResult
+
+
+@dataclass(frozen=True)
+class FloquetRates:
+    matrix: np.ndarray
+    fourier_elements: np.ndarray
+
+
+def _bath_rate(frequency: float, bath: BathConfig) -> float:
+    if abs(frequency) < 1e-14:
+        return 0.0
+    positive = abs(frequency)
+    density = float(ohmic_spectral_density(positive, bath))
+    occupation = bose_occupation(positive, bath.temperature)
+    return 2 * np.pi * density * (occupation + (1 if frequency > 0 else 0))
+
+
+class FloquetMarkovBackend:
+    method = "floquet_markov"
+
+    def rates(
+        self,
+        solution: FloquetSolution,
+        coupling: ComplexMatrix,
+        bath: BathConfig,
+        harmonic_cutoff: int,
+    ) -> FloquetRates:
+        cumulative = micromotion(solution)[:-1]
+        steps = len(cumulative)
+        omega_d = 2 * np.pi / solution.period
+        times = np.arange(steps) * solution.period / steps
+        dimension = coupling.shape[0]
+        harmonics = np.arange(-harmonic_cutoff, harmonic_cutoff + 1)
+        elements = np.zeros(
+            (len(harmonics), dimension, dimension), dtype=np.complex128
+        )
+        for time, propagator in zip(times, cumulative, strict=True):
+            periodic_modes = (
+                propagator
+                @ solution.modes
+                @ np.diag(np.exp(1j * solution.quasienergies * time))
+            )
+            instantaneous = periodic_modes.conj().T @ coupling @ periodic_modes
+            elements += (
+                np.exp(-1j * harmonics[:, None, None] * omega_d * time)
+                * instantaneous[None, :, :]
+                / steps
+            )
+
+        rates = np.zeros((dimension, dimension), dtype=float)
+        for target in range(dimension):
+            for source in range(dimension):
+                if target == source:
+                    continue
+                for h_index, harmonic in enumerate(harmonics):
+                    emitted = (
+                        solution.quasienergies[source]
+                        - solution.quasienergies[target]
+                        + harmonic * omega_d
+                    )
+                    rates[target, source] += _bath_rate(emitted, bath) * abs(
+                        elements[h_index, target, source]
+                    ) ** 2
+        for source in range(dimension):
+            rates[source, source] = -np.sum(rates[:, source])
+        return FloquetRates(rates, elements)
+
+    def run(
+        self,
+        hamiltonian: Callable[[float], ComplexMatrix],
+        coupling: ComplexMatrix,
+        bath: BathConfig,
+        period: float,
+        steps: int,
+        harmonic_cutoff: int,
+    ) -> OpenSystemResult:
+        solution = solve_floquet(hamiltonian, period, steps)
+        rate_data = self.rates(solution, coupling, bath, harmonic_cutoff)
+        matrix = rate_data.matrix.copy()
+        rhs = np.zeros(matrix.shape[0])
+        matrix[-1, :] = 1
+        rhs[-1] = 1
+        populations, *_ = np.linalg.lstsq(matrix, rhs, rcond=None)
+        populations = np.real_if_close(populations).real
+        populations = np.clip(populations, 0, None)
+        populations /= populations.sum()
+        dimension = coupling.shape[0]
+        identity = np.eye(dimension, dtype=np.complex128)
+        omega_d = 2 * np.pi / period
+        harmonics = np.arange(-harmonic_cutoff, harmonic_cutoff + 1)
+        cumulative = micromotion(solution)[:-1]
+        dt = period / steps
+        step_maps: list[ComplexMatrix] = []
+        for index, propagator in enumerate(cumulative):
+            time = index * dt
+            modes = (
+                propagator
+                @ solution.modes
+                @ np.diag(np.exp(1j * solution.quasienergies * time))
+            )
+            h = hamiltonian((index + 0.5) * dt)
+            liouvillian = -1j * (
+                np.kron(identity, h) - np.kron(h.T, identity)
+            )
+            for target in range(dimension):
+                for source in range(dimension):
+                    if target == source:
+                        continue
+                    basis_jump = np.outer(modes[:, target], modes[:, source].conj())
+                    for harmonic_index, harmonic in enumerate(harmonics):
+                        emitted = (
+                            solution.quasienergies[source]
+                            - solution.quasienergies[target]
+                            + harmonic * omega_d
+                        )
+                        gamma = _bath_rate(emitted, bath)
+                        amplitude = rate_data.fourier_elements[
+                            harmonic_index, target, source
+                        ]
+                        if gamma == 0 or abs(amplitude) < 1e-14:
+                            continue
+                        jump = np.sqrt(gamma) * amplitude * basis_jump
+                        product = jump.conj().T @ jump
+                        liouvillian += (
+                            np.kron(jump.conj(), jump)
+                            - 0.5 * np.kron(identity, product)
+                            - 0.5 * np.kron(product.T, identity)
+                        )
+            step_maps.append(expm(liouvillian * dt))
+
+        period_map = np.eye(dimension**2, dtype=np.complex128)
+        for step_map in step_maps:
+            period_map = step_map @ period_map
+        values, vectors = np.linalg.eig(period_map)
+        steady_index = int(np.argmin(abs(values - 1)))
+        steady_vector = vectors[:, steady_index]
+        steady_density = steady_vector.reshape((dimension, dimension), order="F")
+        steady_density = (steady_density + steady_density.conj().T) / 2
+        steady_density /= np.trace(steady_density)
+        densities = [steady_density]
+        vector = steady_density.reshape(dimension**2, order="F")
+        for step_map in step_maps:
+            vector = step_map @ vector
+            density = vector.reshape((dimension, dimension), order="F")
+            density = (density + density.conj().T) / 2
+            density /= np.trace(density)
+            densities.append(density)
+            vector = density.reshape(dimension**2, order="F")
+        rate_residual = float(np.linalg.norm(rate_data.matrix @ populations))
+        map_residual = float(
+            np.linalg.norm(
+                period_map @ steady_density.reshape(dimension**2, order="F")
+                - steady_density.reshape(dimension**2, order="F")
+            )
+        )
+        return OpenSystemResult(
+            self.method,
+            np.asarray(densities),
+            np.linspace(0, period, steps + 1),
+            map_residual < 1e-8,
+            {
+                "rate_residual": rate_residual,
+                "period_map_residual": map_residual,
+                "trace_error": float(
+                    max(abs(np.trace(density) - 1) for density in densities)
+                ),
+                "minimum_population": float(
+                    min(np.min(np.linalg.eigvalsh(density)) for density in densities)
+                ),
+            },
+            {
+                "approximation": "Born-Markov, Floquet and full secular approximations",
+                "harmonic_cutoff": harmonic_cutoff,
+                "populations": populations.tolist(),
+            },
+            np.asarray(step_maps),
+        )
diff --git a/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/backends/pt_tempo.py b/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/backends/pt_tempo.py
new file mode 100644
index 000000000..b9371693c
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/backends/pt_tempo.py
@@ -0,0 +1,180 @@
+"""OQuPy PT-TEMPO backend for controlled non-Markovian calculations."""
+
+from __future__ import annotations
+
+from dataclasses import dataclass
+from typing import Any
+
+import numpy as np
+
+from ..config import BathConfig
+from ..operators import ComplexMatrix
+from .base import OpenSystemResult
+
+
+@dataclass(frozen=True)
+class PtTempoResult:
+    result: OpenSystemResult
+    process_tensor: Any
+    system: Any
+    bath: Any
+    initial_density: ComplexMatrix
+
+
+class PtTempoBackend:
+    """Numerically controlled PT-TEMPO process-tensor wrapper.
+
+    OQuPy uses ``J(w)=2*alpha*w*exp(-w/wc)``. This wrapper passes half of the
+    project's alpha so both packages implement the same spectral density.
+    """
+
+    method = "pt_tempo"
+
+    @staticmethod
+    def _oqupy() -> Any:
+        try:
+            import oqupy
+        except ImportError as exc:
+            raise RuntimeError(
+                "PT-TEMPO requires the 'nonmarkov' optional dependencies"
+            ) from exc
+        return oqupy
+
+    def run(
+        self,
+        hamiltonian: Any,
+        coupling: ComplexMatrix,
+        initial_density: ComplexMatrix,
+        bath_config: BathConfig,
+        dt: float,
+        steps: int,
+        memory_steps: int,
+        epsrel: float,
+    ) -> PtTempoResult:
+        if dt <= 0 or steps < 1 or memory_steps < 1 or not 0 < epsrel < 1:
+            raise ValueError("invalid PT-TEMPO numerical parameters")
+        oqupy = self._oqupy()
+        correlations = oqupy.PowerLawSD(
+            alpha=bath_config.alpha / 2,
+            zeta=1,
+            cutoff=bath_config.cutoff,
+            cutoff_type="exponential",
+            temperature=bath_config.temperature,
+        )
+        bath = oqupy.Bath(coupling, correlations)
+        parameters = oqupy.TempoParameters(
+            dt=dt,
+            epsrel=epsrel,
+            dkmax=memory_steps,
+        )
+        process_tensor = oqupy.pt_tempo_compute(
+            bath=bath,
+            start_time=0.0,
+            end_time=steps * dt,
+            parameters=parameters,
+            unique=True,
+            progress_type="silent",
+        )
+        system = oqupy.TimeDependentSystem(hamiltonian)
+        dynamics = oqupy.compute_dynamics(
+            system=system,
+            initial_state=initial_density,
+            process_tensor=process_tensor,
+            progress_type="silent",
+        )
+        states = np.asarray(dynamics.states, dtype=np.complex128)
+        traces = np.trace(states, axis1=1, axis2=2)
+        trace_error = float(np.max(abs(traces - 1)))
+        minimum_eigenvalue = float(
+            min(np.min(np.linalg.eigvalsh((state + state.conj().T) / 2)) for state in states)
+        )
+        bond_dimensions = process_tensor.get_bond_dimensions()
+        result = OpenSystemResult(
+            self.method,
+            states,
+            np.asarray(dynamics.times, dtype=np.float64),
+            trace_error < 5e-3 and minimum_eigenvalue > -5e-3,
+            {
+                "trace_error": trace_error,
+                "minimum_density_eigenvalue": minimum_eigenvalue,
+                "maximum_bond_dimension": float(np.max(bond_dimensions)),
+            },
+            {
+                "approximation": "PT-TEMPO: finite dt, dkmax and SVD epsrel",
+                "dt": dt,
+                "memory_steps": memory_steps,
+                "epsrel": epsrel,
+                "spectral_density_convention": (
+                    "OQuPy alpha divided by two to match J=alpha*w*exp(-w/wc)"
+                ),
+            },
+        )
+        return PtTempoResult(result, process_tensor, system, bath, initial_density)
+
+    def period_averaged_correlation(
+        self,
+        run: PtTempoResult,
+        operator: ComplexMatrix,
+        phase_start: int,
+        period_steps: int,
+        delay_steps: int,
+        drive_frequency: float,
+        phase_offsets: list[int] | None = None,
+    ) -> Any:
+        """Calculate exact process-tensor insertions and average drive phases."""
+        from ..correlations import CorrelationResult, coherent_decomposition
+
+        oqupy = self._oqupy()
+        offsets = list(range(period_steps)) if phase_offsets is None else phase_offsets
+        if (
+            len(offsets) < 2
+            or len(set(offsets)) != len(offsets)
+            or min(offsets) < 0
+            or max(offsets) >= period_steps
+        ):
+            raise ValueError("phase offsets must be distinct indices in one period")
+        initial_indices = [phase_start + offset for offset in offsets]
+        final_indices = list(
+            range(phase_start, phase_start + period_steps + delay_steps)
+        )
+        _, matrix = oqupy.compute_correlations(
+            system=run.system,
+            process_tensor=run.process_tensor,
+            operator_a=operator,
+            operator_b=operator,
+            times_a=initial_indices,
+            times_b=final_indices,
+            time_order="ordered",
+            initial_state=run.initial_density,
+            progress_type="silent",
+        )
+        total = np.empty(delay_steps + 1, dtype=np.complex128)
+        for delay in range(delay_steps + 1):
+            values = [
+                matrix[row, offset + delay]
+                for row, offset in enumerate(offsets)
+            ]
+            total[delay] = np.mean(values)
+        dt = float(run.result.times[1] - run.result.times[0])
+        delays = np.arange(delay_steps + 1, dtype=np.float64) * dt
+        phase_states = run.result.density_matrices[
+            [phase_start + offset for offset in offsets]
+        ]
+        one_point = np.real(
+            np.einsum("ij,tji->t", operator, phase_states, optimize=True)
+        )
+        coherent, peaks = coherent_decomposition(one_point, drive_frequency, delays)
+        return CorrelationResult(
+            delays,
+            total,
+            total - coherent,
+            coherent,
+            peaks,
+            "pt_tempo_multitime",
+            {
+                "period_steps": float(period_steps),
+                "phase_samples": float(len(offsets)),
+                "dt": dt,
+                "phase_start": float(phase_start),
+            },
+        )
diff --git a/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/backends/uniform_tempo.py b/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/backends/uniform_tempo.py
new file mode 100644
index 000000000..8bb09222d
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/backends/uniform_tempo.py
@@ -0,0 +1,472 @@
+"""Pinned UniformTEMPO.jl backend for periodic non-Markovian correlations."""
+
+from __future__ import annotations
+
+import hashlib
+import json
+import shutil
+import subprocess
+import tempfile
+from dataclasses import asdict, dataclass, field
+from pathlib import Path
+from typing import Any, Literal, cast
+
+import numpy as np
+from numpy.typing import NDArray
+
+from ..config import BathConfig, ModelConfig
+from ..correlations import CorrelationResult, coherent_decomposition
+from ..operators import ComplexMatrix
+
+METHOD = "uniform_tempo_floquet_multitime"
+UNIFORM_TEMPO_REVISION = "b76a018c32e5415989761d902b1b0e95f1a337da"
+
+
+@dataclass(frozen=True)
+class UniformTempoControls:
+    """Complete numerical controls passed to the Julia runner."""
+
+    steps_per_period: int
+    tolerance: float
+    phase_samples: int
+    delay_periods: int
+    auto_nc: bool = True
+    memory_cutoff: int = 100_000
+    low_rank_svd: bool = False
+    truncation: Literal["rel", "abs"] = "rel"
+    cap_rank: int = 100_000
+    max_rank: int = 100_000
+    pole_count: int = 0
+    pole_tolerance: float = 1e-10
+    pole_maxiter: int = 2_000
+
+    def __post_init__(self) -> None:
+        if self.steps_per_period < 2:
+            raise ValueError("steps_per_period must be at least two")
+        if not 0 < self.tolerance < 1:
+            raise ValueError("tolerance must lie between zero and one")
+        if (
+            self.phase_samples < 2
+            or self.phase_samples > self.steps_per_period
+            or self.steps_per_period % self.phase_samples != 0
+        ):
+            raise ValueError("phase_samples must divide steps_per_period")
+        if self.delay_periods < 1:
+            raise ValueError("delay_periods must be positive")
+        if self.memory_cutoff < 1:
+            raise ValueError("memory_cutoff must be positive")
+        if self.truncation not in ("rel", "abs"):
+            raise ValueError("truncation must be 'rel' or 'abs'")
+        if self.cap_rank < 1 or self.max_rank < self.cap_rank:
+            raise ValueError("invalid rank limits")
+        if isinstance(self.pole_count, bool) or self.pole_count < 0:
+            raise ValueError("pole_count must be nonnegative")
+        if self.pole_tolerance <= 0:
+            raise ValueError("pole_tolerance must be positive")
+        if isinstance(self.pole_maxiter, bool) or self.pole_maxiter < 1:
+            raise ValueError("pole_maxiter must be positive")
+
+    @property
+    def phase_offsets(self) -> tuple[int, ...]:
+        stride = self.steps_per_period // self.phase_samples
+        return tuple(range(0, self.steps_per_period, stride))
+
+    @property
+    def delay_steps(self) -> int:
+        return self.delay_periods * self.steps_per_period
+
+
+@dataclass(frozen=True)
+class UniformTempoResult:
+    method: str
+    floquet_state: ComplexMatrix
+    phase_states: NDArray[np.complex128]
+    correlation: CorrelationResult
+    diagnostics: dict[str, float]
+    metadata: dict[str, float | int | str]
+    transfer_eigenvalues: NDArray[np.complex128] = field(
+        default_factory=lambda: np.empty(0, dtype=np.complex128)
+    )
+    transfer_eigenpair_residuals: NDArray[np.float64] = field(
+        default_factory=lambda: np.empty(0, dtype=np.float64)
+    )
+
+
+def _encode_complex(values: NDArray[np.complex128] | ComplexMatrix) -> dict[str, Any]:
+    array = np.asarray(values, dtype=np.complex128)
+    return {
+        "real": np.real(array).astype(float).tolist(),
+        "imag": np.imag(array).astype(float).tolist(),
+    }
+
+
+def _tensor_cache_key(
+    coupling: ComplexMatrix,
+    model: ModelConfig,
+    bath: BathConfig,
+    controls: UniformTempoControls,
+) -> str:
+    """Fingerprint every input that changes the uniform process tensor."""
+    payload = {
+        "schema": "uniform-process-tensor-v1",
+        "uniform_tempo_revision": UNIFORM_TEMPO_REVISION,
+        "coupling": _encode_complex(np.asarray(coupling, dtype=np.complex128)),
+        "bath": asdict(bath),
+        "dt": model.period / controls.steps_per_period,
+        "tolerance": controls.tolerance,
+        "auto_nc": controls.auto_nc,
+        "memory_cutoff": controls.memory_cutoff,
+        "low_rank_svd": controls.low_rank_svd,
+        "truncation": controls.truncation,
+        "cap_rank": controls.cap_rank,
+        "max_rank": controls.max_rank,
+    }
+    encoded = json.dumps(
+        payload,
+        sort_keys=True,
+        separators=(",", ":"),
+        allow_nan=False,
+    ).encode("utf-8")
+    return hashlib.sha256(encoded).hexdigest()
+
+
+def _required(payload: dict[str, Any], key: str, context: str = "payload") -> Any:
+    if key not in payload:
+        raise ValueError(f"{context} is missing required field {key!r}")
+    return payload[key]
+
+
+def _decode_complex(
+    payload: dict[str, Any],
+    *,
+    label: str,
+    allow_empty: bool = False,
+) -> NDArray[np.complex128]:
+    try:
+        shape = tuple(int(value) for value in payload["shape"])
+        real = np.asarray(payload["real"], dtype=float)
+        imag = np.asarray(payload["imag"], dtype=float)
+    except (KeyError, TypeError, ValueError) as exc:
+        raise ValueError(f"{label} has an invalid complex-array schema") from exc
+    expected = int(np.prod(shape, dtype=np.int64))
+    if (
+        expected < 0
+        or (expected == 0 and not allow_empty)
+        or real.size != expected
+        or imag.size != expected
+    ):
+        raise ValueError(f"{label} data do not match the declared shape")
+    values = real.reshape(-1) + 1j * imag.reshape(-1)
+    array = values.reshape(shape, order="F")
+    if not np.all(np.isfinite(array)):
+        raise ValueError(f"{label} contains non-finite values")
+    return cast(NDArray[np.complex128], array)
+
+
+class UniformTempoBackend:
+    """Subprocess boundary around the pinned Julia implementation."""
+
+    def __init__(
+        self,
+        *,
+        command_prefix: tuple[str, ...] | None = None,
+        timeout_seconds: float = 86_400.0,
+        tensor_cache_directory: Path | None = None,
+    ) -> None:
+        if timeout_seconds <= 0:
+            raise ValueError("timeout_seconds must be positive")
+        root = Path(__file__).resolve().parents[3]
+        if command_prefix is None:
+            julia = shutil.which("julia")
+            if julia is None:
+                raise RuntimeError("UniformTEMPO backend requires Julia on PATH")
+            command_prefix = (
+                julia,
+                f"--project={root / 'julia'}",
+                str(root / "julia" / "run_uniform_tempo.jl"),
+            )
+        if not command_prefix:
+            raise ValueError("command_prefix must not be empty")
+        self._command_prefix = tuple(command_prefix)
+        self._timeout_seconds = timeout_seconds
+        self._tensor_cache_directory = (
+            None
+            if tensor_cache_directory is None
+            else Path(tensor_cache_directory).resolve()
+        )
+
+    def run_periodic(
+        self,
+        h0: ComplexMatrix,
+        coupling: ComplexMatrix,
+        model: ModelConfig,
+        bath: BathConfig,
+        controls: UniformTempoControls,
+        *,
+        drive_operator: ComplexMatrix | None = None,
+    ) -> UniformTempoResult:
+        """Compute the Floquet state and phase-averaged two-time correlation."""
+        h0_array = np.asarray(h0, dtype=np.complex128)
+        coupling_array = np.asarray(coupling, dtype=np.complex128)
+        drive_array = (
+            coupling_array
+            if drive_operator is None
+            else np.asarray(drive_operator, dtype=np.complex128)
+        )
+        if h0_array.ndim != 2 or h0_array.shape[0] != h0_array.shape[1]:
+            raise ValueError("h0 must be a square matrix")
+        if coupling_array.shape != h0_array.shape:
+            raise ValueError("coupling must match h0")
+        if drive_array.shape != h0_array.shape:
+            raise ValueError("drive_operator must match h0")
+        if not all(
+            np.all(np.isfinite(array))
+            for array in (h0_array, coupling_array, drive_array)
+        ):
+            raise ValueError("system operators must contain finite values")
+        if not np.allclose(h0_array, h0_array.conj().T, atol=1e-10):
+            raise ValueError("h0 must be Hermitian")
+        if not np.allclose(coupling_array, coupling_array.conj().T, atol=1e-10):
+            raise ValueError("coupling must be Hermitian")
+        if not np.allclose(drive_array, drive_array.conj().T, atol=1e-10):
+            raise ValueError("drive_operator must be Hermitian")
+
+        request: dict[str, Any] = {
+            "h0": _encode_complex(h0_array),
+            "coupling": _encode_complex(coupling_array),
+            "drive": _encode_complex(drive_array),
+            "model": asdict(model),
+            "bath": asdict(bath),
+            "controls": {
+                "steps_per_period": controls.steps_per_period,
+                "tolerance": controls.tolerance,
+                "phase_offsets": list(controls.phase_offsets),
+                "delay_steps": controls.delay_steps,
+                "auto_nc": controls.auto_nc,
+                "memory_cutoff": controls.memory_cutoff,
+                "low_rank_svd": controls.low_rank_svd,
+                "truncation": controls.truncation,
+                "cap_rank": controls.cap_rank,
+                "max_rank": controls.max_rank,
+                "pole_count": controls.pole_count,
+                "pole_tolerance": controls.pole_tolerance,
+                "pole_maxiter": controls.pole_maxiter,
+            },
+        }
+        if self._tensor_cache_directory is not None:
+            tensor_key = _tensor_cache_key(
+                coupling_array,
+                model,
+                bath,
+                controls,
+            )
+            self._tensor_cache_directory.mkdir(parents=True, exist_ok=True)
+            request["controls"]["process_tensor_cache_key"] = tensor_key
+            request["controls"]["process_tensor_cache_path"] = str(
+                self._tensor_cache_directory / f"{tensor_key}.jls"
+            )
+        with tempfile.TemporaryDirectory(prefix="uniform-tempo-") as temporary:
+            temporary_path = Path(temporary)
+            input_path = temporary_path / "input.json"
+            output_path = temporary_path / "output.json"
+            input_path.write_text(
+                json.dumps(request, sort_keys=True),
+                encoding="utf-8",
+            )
+            try:
+                completed = subprocess.run(
+                    [*self._command_prefix, str(input_path), str(output_path)],
+                    capture_output=True,
+                    text=True,
+                    timeout=self._timeout_seconds,
+                    check=False,
+                )
+            except subprocess.TimeoutExpired as exc:
+                raise RuntimeError(
+                    f"UniformTEMPO runner exceeded {self._timeout_seconds:g} seconds"
+                ) from exc
+            if completed.returncode != 0:
+                detail = completed.stderr.strip() or completed.stdout.strip()
+                raise RuntimeError(
+                    f"UniformTEMPO runner failed with exit code "
+                    f"{completed.returncode}: {detail}"
+                )
+            if not output_path.is_file():
+                raise RuntimeError("UniformTEMPO runner did not create output JSON")
+            try:
+                payload = cast(
+                    dict[str, Any],
+                    json.loads(output_path.read_text(encoding="utf-8")),
+                )
+            except (json.JSONDecodeError, OSError) as exc:
+                raise ValueError("UniformTEMPO runner returned malformed JSON") from exc
+        return self._validate_payload(payload, h0_array.shape[0], model, controls)
+
+    @staticmethod
+    def _validate_payload(
+        payload: dict[str, Any],
+        dimension: int,
+        model: ModelConfig,
+        controls: UniformTempoControls,
+    ) -> UniformTempoResult:
+        method = str(_required(payload, "method"))
+        if method != METHOD:
+            raise ValueError(f"unexpected UniformTEMPO method label {method!r}")
+        for provenance_key in (
+            "julia_version",
+            "uniform_tempo_revision",
+            "manifest_sha256",
+        ):
+            if provenance_key not in payload or not str(payload[provenance_key]):
+                raise ValueError("UniformTEMPO payload is missing provenance")
+        manifest_hash = str(payload["manifest_sha256"])
+        if len(manifest_hash) != 64:
+            raise ValueError("UniformTEMPO manifest provenance is invalid")
+
+        period_steps = int(_required(payload, "period_steps"))
+        if period_steps != controls.steps_per_period:
+            raise ValueError("UniformTEMPO period grid does not match the request")
+        phase_offsets = tuple(int(value) for value in _required(payload, "phase_offsets"))
+        if phase_offsets != controls.phase_offsets:
+            raise ValueError("UniformTEMPO phase grid does not match the request")
+        dt = float(_required(payload, "dt"))
+        if not np.isclose(
+            dt,
+            model.period / controls.steps_per_period,
+            rtol=1e-11,
+            atol=1e-13,
+        ):
+            raise ValueError("UniformTEMPO timestep does not match the model period")
+
+        floquet_state_raw = _decode_complex(
+            cast(dict[str, Any], _required(payload, "floquet_state")),
+            label="floquet_state",
+        )
+        if floquet_state_raw.shape != (dimension, dimension):
+            raise ValueError("floquet_state has the wrong shape")
+        phase_states_raw = _decode_complex(
+            cast(dict[str, Any], _required(payload, "phase_states")),
+            label="phase_states",
+        )
+        expected_phase_shape = (
+            dimension,
+            dimension,
+            controls.phase_samples,
+        )
+        if phase_states_raw.shape != expected_phase_shape:
+            raise ValueError("phase_states have the wrong shape")
+        phase_states = np.moveaxis(phase_states_raw, 2, 0)
+
+        delay = np.asarray(_required(payload, "delay"), dtype=float)
+        if delay.shape != (controls.delay_steps + 1,) or not np.all(np.isfinite(delay)):
+            raise ValueError("delay grid has the wrong shape")
+        if not np.allclose(delay, np.arange(len(delay)) * dt, atol=1e-12):
+            raise ValueError("delay grid is not uniform")
+        total = _decode_complex(
+            cast(dict[str, Any], _required(payload, "correlation")),
+            label="correlation",
+        )
+        if total.shape != delay.shape:
+            raise ValueError("correlation data do not match the delay shape")
+        one_point = np.asarray(_required(payload, "one_point"), dtype=float)
+        if one_point.shape != (controls.phase_samples,) or not np.all(
+            np.isfinite(one_point)
+        ):
+            raise ValueError("one_point data have the wrong shape")
+        coherent, peaks = coherent_decomposition(
+            one_point,
+            model.drive_frequency,
+            delay,
+        )
+        correlation = CorrelationResult(
+            delay,
+            total,
+            total - coherent,
+            coherent,
+            peaks,
+            METHOD,
+            {
+                "period_steps": float(period_steps),
+                "phase_samples": float(controls.phase_samples),
+                "dt": dt,
+            },
+        )
+
+        diagnostics_payload = cast(
+            dict[str, Any],
+            _required(payload, "diagnostics"),
+        )
+        diagnostic_keys = (
+            "trace_error",
+            "hermiticity_error",
+            "minimum_density_eigenvalue",
+            "fixed_point_residual",
+            "floquet_transfer_residual",
+        )
+        try:
+            diagnostics = {
+                key: float(diagnostics_payload[key]) for key in diagnostic_keys
+            }
+        except (KeyError, TypeError, ValueError) as exc:
+            raise ValueError("UniformTEMPO diagnostics are incomplete") from exc
+        if not all(np.isfinite(value) for value in diagnostics.values()):
+            raise ValueError("UniformTEMPO diagnostics contain non-finite values")
+
+        transfer_dimension = int(_required(payload, "transfer_dimension"))
+        if transfer_dimension < 2:
+            raise ValueError("UniformTEMPO transfer dimension is invalid")
+        transfer_eigenvalues = _decode_complex(
+            cast(dict[str, Any], _required(payload, "transfer_eigenvalues")),
+            label="transfer_eigenvalues",
+            allow_empty=True,
+        )
+        if transfer_eigenvalues.ndim != 1:
+            raise ValueError("transfer_eigenvalues must be one-dimensional")
+        transfer_eigenpair_residuals = np.asarray(
+            _required(payload, "transfer_eigenpair_residuals"),
+            dtype=float,
+        )
+        if transfer_eigenpair_residuals.ndim != 1:
+            raise ValueError(
+                "transfer_eigenpair_residuals must be one-dimensional"
+            )
+        if transfer_eigenvalues.shape != transfer_eigenpair_residuals.shape:
+            raise ValueError(
+                "transfer eigenvalues and residuals must have the same length"
+            )
+        expected_poles = min(controls.pole_count, transfer_dimension - 1)
+        if len(transfer_eigenvalues) != expected_poles:
+            raise ValueError(
+                "UniformTEMPO returned "
+                f"{len(transfer_eigenvalues)} poles; expected {expected_poles}"
+            )
+        if not np.all(np.isfinite(transfer_eigenpair_residuals)):
+            raise ValueError("transfer eigenpair residuals contain non-finite values")
+        if np.any(transfer_eigenpair_residuals < 0):
+            raise ValueError("transfer eigenpair residuals must be nonnegative")
+
+        metadata: dict[str, float | int | str] = {
+            "dt": dt,
+            "period_steps": period_steps,
+            "phase_samples": controls.phase_samples,
+            "bond_dimension": int(_required(payload, "bond_dimension")),
+            "tolerance": controls.tolerance,
+            "julia_version": str(payload["julia_version"]),
+            "uniform_tempo_revision": str(payload["uniform_tempo_revision"]),
+            "manifest_sha256": manifest_hash,
+            "process_tensor_cache_hit": int(
+                bool(_required(payload, "process_tensor_cache_hit"))
+            ),
+            "transfer_dimension": transfer_dimension,
+            "pole_count": len(transfer_eigenvalues),
+        }
+        return UniformTempoResult(
+            method,
+            floquet_state_raw,
+            phase_states,
+            correlation,
+            diagnostics,
+            metadata,
+            transfer_eigenvalues,
+            transfer_eigenpair_residuals,
+        )
diff --git a/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/bath.py b/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/bath.py
new file mode 100644
index 000000000..b6ec2d00c
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/bath.py
@@ -0,0 +1,45 @@
+"""Ohmic bosonic-bath conventions used throughout the project."""
+
+from __future__ import annotations
+
+import numpy as np
+from scipy.integrate import quad
+
+from .config import BathConfig
+
+
+def ohmic_spectral_density(frequency: float | np.ndarray, bath: BathConfig) -> float | np.ndarray:
+    frequency_array = np.asarray(frequency)
+    result = bath.alpha * frequency_array * np.exp(-frequency_array / bath.cutoff)
+    result = np.where(frequency_array >= 0, result, 0.0)
+    return float(result) if result.ndim == 0 else result
+
+
+def bose_occupation(frequency: float, temperature: float) -> float:
+    if frequency <= 0:
+        raise ValueError("frequency must be positive")
+    if temperature == 0:
+        return 0.0
+    argument = frequency / temperature
+    if argument > 700:
+        return 0.0
+    return float(1.0 / float(np.expm1(argument)))
+
+
+def bath_correlation(time: float, bath: BathConfig) -> complex:
+    """Return <B(t)B(0)> for J(w)=alpha*w*exp(-w/wc), hbar=kB=1."""
+    zero_temperature = bath.alpha * bath.cutoff**2 / (1 + 1j * bath.cutoff * time) ** 2
+    if bath.temperature == 0 or bath.alpha == 0:
+        return complex(zero_temperature)
+
+    def thermal_real(frequency: float) -> float:
+        density = float(ohmic_spectral_density(frequency, bath))
+        return float(
+            2
+            * density
+            * bose_occupation(frequency, bath.temperature)
+            * np.cos(frequency * time)
+        )
+
+    thermal, _ = quad(thermal_real, 0, np.inf, epsabs=1e-10, epsrel=1e-9, limit=300)
+    return complex(zero_temperature + thermal)
diff --git a/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/cli.py b/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/cli.py
new file mode 100644
index 000000000..290f6ec6a
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/cli.py
@@ -0,0 +1,430 @@
+"""Command line interface for baseline generation and audit."""
+
+from __future__ import annotations
+
+import argparse
+import json
+import sys
+from dataclasses import asdict
+from pathlib import Path
+from typing import Literal
+
+import numpy as np
+
+from .experiments import (
+    backend_comparison,
+    n2_bright_sweep,
+    n2_markov_heat_spectrum,
+    n3_sector_sweep,
+)
+from .io import read_result, write_result
+from .plotting import (
+    plot_backend_comparison,
+    plot_dark_diagnostics,
+    plot_error_maps,
+    plot_heat_spectrum,
+    plot_heat_valve_hero,
+    plot_model_variants,
+    plot_n2,
+    plot_n3,
+    plot_n3_error_maps,
+    plot_n3_pt_dynamics,
+    plot_n3_sector_heat,
+    plot_n4_pilot_comparison,
+    plot_odd_sector_difference,
+)
+
+ExactBackend = Literal["uniform_tempo", "oqupy"]
+
+
+def generate_baselines(output: Path, figures: Path, quick: bool = False) -> int:
+    n2 = n2_bright_sweep(np.linspace(0, 2, 17 if quick else 81))
+    n3_values = np.geomspace(0.125, 16, 15 if quick else 49)
+    n3 = n3_sector_sweep(n3_values)
+    comparison = backend_comparison(
+        [0.005, 0.01] if quick else [0.005, 0.01, 0.025, 0.05],
+        steps_per_period=24 if quick else 48,
+        periods=4 if quick else 100,
+    )
+    heat = n2_markov_heat_spectrum(
+        steps_per_period=32 if quick else 96,
+        correlation_periods=3 if quick else 16,
+    )
+    paths = {
+        "n2_exact.json": n2,
+        "n3_exact.json": n3,
+        "backend_comparison.json": comparison,
+        "n2_markov_heat.json": heat,
+    }
+    for name, payload in paths.items():
+        write_result(output / name, payload)
+    plot_n2(read_result(output / "n2_exact.json"), figures / "n2_exact")
+    plot_n3(read_result(output / "n3_exact.json"), figures / "n3_exact")
+    plot_backend_comparison(
+        read_result(output / "backend_comparison.json"), figures / "backend_comparison"
+    )
+    plot_heat_spectrum(
+        read_result(output / "n2_markov_heat.json"), figures / "n2_markov_heat"
+    )
+    return 0
+
+
+def audit_results(directory: Path, allow_unconverged: bool = False) -> int:
+    failures: list[str] = []
+    files = sorted(
+        path
+        for path in directory.glob("*.json")
+        if path.name != "ARTIFACT_PROVENANCE.json"
+    )
+    if not files:
+        failures.append("no result files")
+    for path in files:
+        try:
+            result = read_result(path)
+        except (ValueError, OSError) as exc:
+            failures.append(str(exc))
+            continue
+        if not result["converged"] and not allow_unconverged:
+            failures.append(f"{path.name}: unconverged")
+        if "method" not in result:
+            failures.append(f"{path.name}: missing method label")
+    if failures:
+        for failure in failures:
+            print(f"FAIL: {failure}")
+        return 1
+    print(f"PASS: audited {len(files)} result files")
+    return 0
+
+
+def generate_pt_baselines(output: Path, figures: Path) -> int:
+    from .pt_experiments import n2_pt_tempo_heat, n3_pt_tempo_dynamics
+
+    n2 = n2_pt_tempo_heat()
+    write_result(output / "n2_pt_tempo_heat.json", n2)
+    plot_heat_spectrum(
+        read_result(output / "n2_pt_tempo_heat.json"), figures / "n2_pt_tempo_heat"
+    )
+    n3 = n3_pt_tempo_dynamics()
+    write_result(output / "n3_pt_tempo_dynamics.json", n3)
+    plot_n3_pt_dynamics(
+        read_result(output / "n3_pt_tempo_dynamics.json"),
+        figures / "n3_pt_tempo_dynamics",
+    )
+    return 0
+
+
+def generate_n3_paper_grid(
+    output: Path,
+    cache: Path,
+    figures: Path,
+    exact_backend: ExactBackend = "uniform_tempo",
+) -> int:
+    from .paper_extension import run_n3_heat_grid
+
+    manifest = run_n3_heat_grid(output, cache, exact_backend=exact_backend)
+    plot_n3_sector_heat(manifest, figures / "n3_sector_heat")
+    plot_odd_sector_difference(manifest, figures / "n3_odd_difference")
+    plot_dark_diagnostics(manifest, figures / "dark_diagnostics")
+    return 0 if manifest["converged"] else 1
+
+
+def generate_error_map(
+    output: Path,
+    cache: Path,
+    figures: Path,
+    exact_backend: ExactBackend = "uniform_tempo",
+) -> int:
+    from .paper_extension import run_error_grid
+
+    manifest = run_error_grid(output, cache, exact_backend=exact_backend)
+    plot_error_maps(manifest, figures / "error_maps")
+    return 0
+
+
+def generate_n3_error_map(
+    exact_manifest: Path,
+    output: Path,
+    figures: Path,
+) -> int:
+    from .paper_extension import run_n3_error_map
+
+    manifest = run_n3_error_map(exact_manifest, output)
+    plot_n3_error_maps(manifest, figures / "n3_error_maps")
+    return 0 if manifest["converged"] else 1
+
+
+def generate_n4_pilot(
+    output: Path,
+    cache: Path,
+    figures: Path,
+    sector: Literal["even", "odd"],
+    j: float,
+) -> int:
+    from .paper_extension import run_n4_pilot
+
+    result = run_n4_pilot(output, cache, sector=sector, j=j)
+    if result["converged"]:
+        j_label = f"{j:.2f}".replace(".", "p")
+        plot_n4_pilot_comparison(
+            result,
+            figures / f"n4_{sector}_j{j_label}_comparison",
+        )
+    return 0 if result["converged"] else 1
+
+
+def generate_model_comparison(
+    output: Path,
+    cache: Path,
+    figures: Path,
+    exact_backend: ExactBackend = "uniform_tempo",
+    full_kac: bool = False,
+) -> int:
+    from .paper_extension import run_model_comparison
+
+    manifest = run_model_comparison(
+        output,
+        cache,
+        exact_backend=exact_backend,
+        full_kac=full_kac,
+    )
+    plot_model_variants(manifest, figures / "model_variants")
+    return 0 if manifest.get("locally_complete", manifest["converged"]) else 1
+
+
+def paper_audit(directory: Path) -> int:
+    from .paper_extension import audit_paper_results
+
+    passed, failures = audit_paper_results(directory)
+    if not passed:
+        for failure in failures:
+            print(f"FAIL: {failure}")
+        return 1
+    print("PASS: paper extension manifests and convergence evidence are complete")
+    return 0
+
+
+def generate_heat_valve(
+    output: Path,
+    cache: Path,
+    figures: Path,
+    *,
+    full: bool,
+) -> int:
+    from .convergence import ConvergenceCache, atomic_write_result
+    from .heat_valve import (
+        HeatValvePoint,
+        ValveNumerics,
+        build_heat_valve_manifest,
+        isolated_valve_scan,
+        run_uniform_valve_point,
+    )
+    from .heat_valve_audit import audit_heat_valve_manifest
+
+    floquet_steps = 360 if full else 240
+    xi_values = np.linspace(1.8, 4.0, 45)
+    isolated = isolated_valve_scan(
+        HeatValvePoint(
+            n=n,
+            xi=float(xi),
+            drive_frequency=3.0,
+            floquet_steps=floquet_steps,
+        )
+        for n in (1, 2, 3)
+        for xi in xi_values
+    )
+    atomic_write_result(output / "isolated_scan.json", isolated)
+    selection = build_heat_valve_manifest(isolated)
+    selected = [
+        HeatValvePoint(
+            n=int(item["n"]),  # type: ignore[arg-type]
+            xi=float(item["xi"]),
+            j=float(item["j"]),
+            omega=float(item["omega"]),
+            drive_frequency=float(item["drive_frequency"]),
+            alpha=float(item["alpha"]),
+            cutoff=float(item["cutoff"]),
+            temperature=float(item["temperature"]),
+            floquet_steps=int(item["floquet_steps"]),
+        )
+        for item in selection["selected_points"]
+        if full or int(item["n"]) == 3
+    ]
+    numerical_controls = ValveNumerics()
+    result_cache = ConvergenceCache(cache)
+    results = []
+    for point in selected:
+        result = run_uniform_valve_point(
+            point,
+            numerical_controls,
+            result_cache,
+        )
+        results.append(result)
+        atomic_write_result(
+            output / f"n{point.n}_xi{point.xi:.2f}.json",
+            result,
+        )
+    manifest = build_heat_valve_manifest(isolated, results)
+    audit = audit_heat_valve_manifest(manifest)
+    manifest["audit"] = asdict(audit)
+    atomic_write_result(output / "heat_valve_manifest.json", manifest)
+    plot_heat_valve_hero(manifest, figures / "heat_valve_hero")
+    requested = 9 if full else 3
+    return 0 if len(results) == requested and all(
+        bool(item.get("converged", False)) for item in results
+    ) else 1
+
+
+def heat_valve_audit(directory: Path) -> int:
+    from .heat_valve_audit import audit_heat_valve_manifest
+
+    path = directory / "heat_valve_manifest.json"
+    if not path.is_file():
+        print(f"FAIL: missing {path}")
+        return 1
+    try:
+        manifest = json.loads(path.read_text(encoding="utf-8"))
+        audit = audit_heat_valve_manifest(manifest)
+    except (OSError, json.JSONDecodeError, ValueError, KeyError, TypeError) as exc:
+        print(f"FAIL: malformed heat-valve manifest: {exc}")
+        return 1
+    if not audit.dark_channel_passed:
+        for failure in audit.failures:
+            print(f"FAIL: {failure}")
+        return 1
+    print("PASS: pole-resolved Floquet dark-channel gates are complete")
+    return 0
+
+
+def build_parser() -> argparse.ArgumentParser:
+    parser = argparse.ArgumentParser(prog="floquet-if")
+    subparsers = parser.add_subparsers(dest="command", required=True)
+    baseline = subparsers.add_parser("baselines")
+    baseline.add_argument("--output", type=Path, default=Path("results"))
+    baseline.add_argument("--figures", type=Path, default=Path("figures"))
+    baseline.add_argument("--quick", action="store_true")
+    pt_baseline = subparsers.add_parser("pt-baselines")
+    pt_baseline.add_argument("--output", type=Path, default=Path("results"))
+    pt_baseline.add_argument("--figures", type=Path, default=Path("figures"))
+    audit = subparsers.add_parser("audit")
+    audit.add_argument("directory", type=Path)
+    audit.add_argument("--allow-unconverged", action="store_true")
+    for command in ("n3-heat-grid", "error-map", "model-comparison"):
+        paper = subparsers.add_parser(command)
+        paper.add_argument("--output", type=Path, default=Path("results/paper"))
+        paper.add_argument("--cache", type=Path, default=Path("results/cache"))
+        paper.add_argument("--figures", type=Path, default=Path("figures/paper"))
+        paper.add_argument(
+            "--exact-backend",
+            choices=("uniform_tempo", "oqupy"),
+            default="uniform_tempo",
+        )
+        if command == "model-comparison":
+            paper.add_argument(
+                "--full-kac",
+                action="store_true",
+                help="run cluster-scale timestep and phase refinement for Kac variants",
+            )
+    n3_error = subparsers.add_parser("n3-error-map")
+    n3_error.add_argument(
+        "--exact-manifest",
+        type=Path,
+        default=Path("results/paper/n3_heat_manifest.json"),
+    )
+    n3_error.add_argument("--output", type=Path, default=Path("results/paper"))
+    n3_error.add_argument("--figures", type=Path, default=Path("figures/paper"))
+    n4_pilot = subparsers.add_parser("n4-pilot")
+    n4_pilot.add_argument("--output", type=Path, default=Path("results/paper"))
+    n4_pilot.add_argument(
+        "--cache",
+        type=Path,
+        default=Path("results/cache/n4_uniform_tempo"),
+    )
+    n4_pilot.add_argument("--figures", type=Path, default=Path("figures/paper"))
+    n4_pilot.add_argument("--sector", choices=("even", "odd"), default="odd")
+    n4_pilot.add_argument("--j", type=float, default=0.25)
+    paper_check = subparsers.add_parser("paper-audit")
+    paper_check.add_argument("directory", type=Path, default=Path("results/paper"))
+    heat_valve = subparsers.add_parser("heat-valve")
+    heat_valve.add_argument(
+        "--output",
+        type=Path,
+        default=Path("results/heat-valve"),
+    )
+    heat_valve.add_argument(
+        "--cache",
+        type=Path,
+        default=Path("results/cache/uniform_tempo"),
+    )
+    heat_valve.add_argument(
+        "--figures",
+        type=Path,
+        default=Path("figures/heat-valve"),
+    )
+    mode = heat_valve.add_mutually_exclusive_group()
+    mode.add_argument("--pilot", action="store_true")
+    mode.add_argument("--full", action="store_true")
+    heat_check = subparsers.add_parser("heat-valve-audit")
+    heat_check.add_argument("directory", type=Path)
+    return parser
+
+
+def main(argv: list[str] | None = None) -> int:
+    arguments = build_parser().parse_args(argv)
+    if arguments.command == "baselines":
+        return generate_baselines(arguments.output, arguments.figures, arguments.quick)
+    if arguments.command == "audit":
+        return audit_results(arguments.directory, arguments.allow_unconverged)
+    if arguments.command == "pt-baselines":
+        return generate_pt_baselines(arguments.output, arguments.figures)
+    if arguments.command == "n3-heat-grid":
+        return generate_n3_paper_grid(
+            arguments.output,
+            arguments.cache,
+            arguments.figures,
+            arguments.exact_backend,
+        )
+    if arguments.command == "error-map":
+        return generate_error_map(
+            arguments.output,
+            arguments.cache,
+            arguments.figures,
+            arguments.exact_backend,
+        )
+    if arguments.command == "n3-error-map":
+        return generate_n3_error_map(
+            arguments.exact_manifest,
+            arguments.output,
+            arguments.figures,
+        )
+    if arguments.command == "n4-pilot":
+        return generate_n4_pilot(
+            arguments.output,
+            arguments.cache,
+            arguments.figures,
+            arguments.sector,
+            arguments.j,
+        )
+    if arguments.command == "model-comparison":
+        return generate_model_comparison(
+            arguments.output,
+            arguments.cache,
+            arguments.figures,
+            arguments.exact_backend,
+            arguments.full_kac,
+        )
+    if arguments.command == "paper-audit":
+        return paper_audit(arguments.directory)
+    if arguments.command == "heat-valve":
+        return generate_heat_valve(
+            arguments.output,
+            arguments.cache,
+            arguments.figures,
+            full=arguments.full,
+        )
+    if arguments.command == "heat-valve-audit":
+        return heat_valve_audit(arguments.directory)
+    return 2
+
+
+if __name__ == "__main__":
+    sys.exit(main())
diff --git a/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/config.py b/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/config.py
new file mode 100644
index 000000000..7f0fd0690
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/config.py
@@ -0,0 +1,131 @@
+"""Validated scientific and numerical configuration."""
+
+from __future__ import annotations
+
+from dataclasses import dataclass, field
+from pathlib import Path
+from typing import Any, Literal
+
+import yaml
+
+Normalization = Literal["bounded", "kac", "collective"]
+DriveNormalization = Literal["coupling", "per_spin"]
+
+
+@dataclass(frozen=True)
+class ModelConfig:
+    n: int = 2
+    j: float = 0.5
+    omega: float = 1.0
+    drive_amplitude: float = 0.3
+    drive_frequency: float = 1.0
+    normalization: Normalization = "bounded"
+    drive_normalization: DriveNormalization = "coupling"
+    counterterm: bool = False
+    counterterm_strength: float = 0.0
+
+    def __post_init__(self) -> None:
+        if self.n not in (1, 2, 3, 4):
+            raise ValueError("n must be one of 1, 2, 3, 4")
+        if self.j < 0:
+            raise ValueError("j must be nonnegative")
+        if self.omega <= 0:
+            raise ValueError("omega must be positive")
+        if self.drive_amplitude < 0:
+            raise ValueError("drive_amplitude must be nonnegative")
+        if self.drive_frequency <= 0:
+            raise ValueError("drive_frequency must be positive")
+        if isinstance(self.counterterm_strength, bool) or self.counterterm_strength < 0:
+            raise ValueError("counterterm_strength must be a nonnegative coefficient")
+        if self.counterterm and self.counterterm_strength <= 0:
+            raise ValueError(
+                "counterterm=True requires a positive counterterm_strength"
+            )
+        if self.normalization not in ("bounded", "kac", "collective"):
+            raise ValueError("unknown normalization")
+        if self.drive_normalization not in ("coupling", "per_spin"):
+            raise ValueError("unknown drive normalization")
+
+    @property
+    def eta(self) -> float:
+        if self.normalization == "bounded":
+            return 1.0 / self.n
+        if self.normalization == "kac":
+            return float(1.0 / self.n**0.5)
+        return 1.0
+
+    @property
+    def drive_eta(self) -> float:
+        if self.drive_normalization == "coupling":
+            return self.eta
+        return 1.0
+
+    @property
+    def period(self) -> float:
+        import math
+
+        return 2 * math.pi / self.drive_frequency
+
+
+@dataclass(frozen=True)
+class BathConfig:
+    alpha: float = 0.05
+    cutoff: float = 2.5
+    temperature: float = 0.0
+
+    def __post_init__(self) -> None:
+        if self.alpha < 0:
+            raise ValueError("alpha must be nonnegative")
+        if self.cutoff <= 0:
+            raise ValueError("cutoff must be positive")
+        if self.temperature < 0:
+            raise ValueError("temperature must be nonnegative")
+
+
+@dataclass(frozen=True)
+class NumericsConfig:
+    drive_steps: int = 240
+    memory_steps: int = 4
+    periods: int = 80
+    correlation_periods: int = 20
+    harmonic_cutoff: int = 6
+    convergence_tolerance: float = 1e-3
+
+    def __post_init__(self) -> None:
+        if self.drive_steps < 8:
+            raise ValueError("drive_steps must be at least 8")
+        if self.memory_steps < 1:
+            raise ValueError("memory_steps must be positive")
+        if self.periods < 1 or self.correlation_periods < 1:
+            raise ValueError("period counts must be positive")
+        if self.harmonic_cutoff < 0:
+            raise ValueError("harmonic_cutoff must be nonnegative")
+        if self.convergence_tolerance <= 0:
+            raise ValueError("convergence_tolerance must be positive")
+
+
+@dataclass(frozen=True)
+class RunConfig:
+    model: ModelConfig = field(default_factory=ModelConfig)
+    bath: BathConfig = field(default_factory=BathConfig)
+    numerics: NumericsConfig = field(default_factory=NumericsConfig)
+    sector: Literal["full", "triplet", "singlet", "even", "odd"] = "full"
+    method: Literal["closed", "floquet_markov", "finite_memory_if"] = "closed"
+
+
+def _section(cls: type[Any], data: dict[str, Any], key: str) -> Any:
+    return cls(**data.get(key, {}))
+
+
+def load_config(path: Path) -> RunConfig:
+    """Load a validated run configuration from YAML."""
+    data = yaml.safe_load(path.read_text(encoding="utf-8")) or {}
+    if not isinstance(data, dict):
+        raise ValueError("configuration root must be a mapping")
+    return RunConfig(
+        model=_section(ModelConfig, data, "model"),
+        bath=_section(BathConfig, data, "bath"),
+        numerics=_section(NumericsConfig, data, "numerics"),
+        sector=data.get("sector", "full"),
+        method=data.get("method", "closed"),
+    )
diff --git a/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/convergence.py b/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/convergence.py
new file mode 100644
index 000000000..31afeef96
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/convergence.py
@@ -0,0 +1,125 @@
+"""Content-addressed caching and numerical convergence metrics."""
+
+from __future__ import annotations
+
+import hashlib
+import json
+import os
+import tempfile
+from collections.abc import Mapping
+from dataclasses import asdict, dataclass
+from pathlib import Path
+from typing import Any, cast
+
+import numpy as np
+from numpy.typing import NDArray
+from scipy.integrate import trapezoid
+
+
+@dataclass(frozen=True)
+class ConvergencePoint:
+    """Complete numerical controls for one backend evaluation."""
+
+    model: Mapping[str, Any]
+    bath: Mapping[str, Any]
+    sector: str
+    steps_per_period: int
+    periods: int
+    delay_periods: int
+    memory_steps: int
+    epsrel: float
+
+
+@dataclass(frozen=True)
+class ConvergenceThresholds:
+    state: float = 5e-2
+    correlation: float = 5e-2
+    heat: float = 5e-2
+    phase: float = 1e-3
+    trace: float = 5e-3
+
+
+def fingerprint(point: Mapping[str, Any] | ConvergencePoint, commit: str) -> str:
+    """Return a stable SHA-256 key for a point and source revision."""
+    payload: Any = asdict(point) if isinstance(point, ConvergencePoint) else point
+    encoded = json.dumps(
+        {"commit": commit, "point": payload},
+        sort_keys=True,
+        separators=(",", ":"),
+        default=str,
+    ).encode()
+    return hashlib.sha256(encoded).hexdigest()
+
+
+def atomic_write_result(path: Path, payload: Mapping[str, Any]) -> None:
+    """Atomically replace a JSON cache entry in its destination directory."""
+    path.parent.mkdir(parents=True, exist_ok=True)
+    descriptor, temporary_name = tempfile.mkstemp(
+        dir=path.parent, prefix=f".{path.name}.", suffix=".tmp"
+    )
+    temporary = Path(temporary_name)
+    try:
+        with os.fdopen(descriptor, "w", encoding="utf-8") as handle:
+            json.dump(payload, handle, indent=2, sort_keys=True, default=str)
+            handle.flush()
+            os.fsync(handle.fileno())
+        os.replace(temporary, path)
+    finally:
+        temporary.unlink(missing_ok=True)
+
+
+def state_residual(
+    candidate: NDArray[np.complex128], reference: NDArray[np.complex128]
+) -> float:
+    if candidate.shape != reference.shape:
+        raise ValueError("state shapes do not match")
+    return float(np.linalg.norm(candidate - reference))
+
+
+def curve_residual(
+    candidate_grid: NDArray[np.float64],
+    candidate: NDArray[np.complex128] | NDArray[np.float64],
+    reference_grid: NDArray[np.float64],
+    reference: NDArray[np.complex128] | NDArray[np.float64],
+) -> float:
+    """Normalized L1 residual on an identical one-dimensional grid."""
+    if (
+        candidate_grid.shape != reference_grid.shape
+        or candidate.shape != reference.shape
+        or candidate.shape != candidate_grid.shape
+        or not np.allclose(candidate_grid, reference_grid, atol=1e-12, rtol=1e-12)
+    ):
+        raise ValueError("curve grids or values do not match")
+    numerator = float(trapezoid(abs(candidate - reference), reference_grid))
+    denominator = float(trapezoid(abs(reference), reference_grid)) + 1e-15
+    return numerator / denominator
+
+
+class ConvergenceCache:
+    """Small JSON cache whose entries are complete only after atomic rename."""
+
+    def __init__(self, directory: Path):
+        self.directory = directory
+
+    def path_for(self, key: str) -> Path:
+        if len(key) != 64 or any(character not in "0123456789abcdef" for character in key):
+            raise ValueError("cache key must be a lowercase SHA-256 digest")
+        return self.directory / f"{key}.json"
+
+    def contains(self, key: str) -> bool:
+        return self.path_for(key).is_file()
+
+    def load(self, key: str) -> dict[str, Any]:
+        path = self.path_for(key)
+        value = json.loads(path.read_text(encoding="utf-8"))
+        if value.get("fingerprint") != key or value.get("complete") is not True:
+            raise ValueError(f"invalid or incomplete cache entry {path}")
+        return cast(dict[str, Any], value)
+
+    def store(self, key: str, payload: Mapping[str, Any]) -> Path:
+        path = self.path_for(key)
+        atomic_write_result(
+            path,
+            {"fingerprint": key, "complete": True, **dict(payload)},
+        )
+        return path
diff --git a/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/correlations.py b/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/correlations.py
new file mode 100644
index 000000000..9730186c5
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/correlations.py
@@ -0,0 +1,143 @@
+"""Period-averaged correlations and coherent-harmonic decomposition."""
+
+from __future__ import annotations
+
+from dataclasses import dataclass
+
+import numpy as np
+from numpy.typing import NDArray
+
+from .operators import ComplexMatrix
+
+
+@dataclass(frozen=True)
+class DeltaCorrelationPeak:
+    harmonic: int
+    frequency: float
+    correlation_weight: float
+
+
+@dataclass(frozen=True)
+class CorrelationResult:
+    delays: NDArray[np.float64]
+    total: NDArray[np.complex128]
+    connected: NDArray[np.complex128]
+    coherent: NDArray[np.float64]
+    delta_peaks: tuple[DeltaCorrelationPeak, ...]
+    method: str
+    metadata: dict[str, float | str]
+
+
+def coherent_decomposition(
+    one_point: NDArray[np.float64],
+    drive_frequency: float,
+    delays: NDArray[np.float64],
+    threshold: float = 1e-12,
+) -> tuple[NDArray[np.float64], tuple[DeltaCorrelationPeak, ...]]:
+    """Compute period-averaged factorized correlation from one micromotion period."""
+    if one_point.ndim != 1 or len(one_point) < 2:
+        raise ValueError("one_point must contain one sampled drive period")
+    coefficients = np.fft.fft(one_point) / len(one_point)
+    coherent = np.full_like(delays, abs(coefficients[0]) ** 2, dtype=np.float64)
+    peaks: list[DeltaCorrelationPeak] = []
+    if abs(coefficients[0]) ** 2 >= threshold:
+        peaks.append(DeltaCorrelationPeak(0, 0.0, float(abs(coefficients[0]) ** 2)))
+    maximum = len(one_point) // 2
+    for harmonic in range(1, maximum + 1):
+        weight = float(2 * abs(coefficients[harmonic]) ** 2)
+        if weight >= threshold:
+            frequency = harmonic * drive_frequency
+            coherent += weight * np.cos(frequency * delays)
+            peaks.append(DeltaCorrelationPeak(harmonic, frequency, weight))
+    return coherent, tuple(peaks)
+
+
+def unitary_period_correlation(
+    step_propagators: tuple[ComplexMatrix, ...],
+    phase_densities: NDArray[np.complex128],
+    operator: ComplexMatrix,
+    dt: float,
+    delay_steps: int,
+    drive_frequency: float,
+    method: str = "closed_unitary",
+) -> CorrelationResult:
+    """Compute Cbar(tau) by exact finite-system operator insertions.
+
+    This routine is valid for closed dynamics. Using open-system reduced
+    propagators would constitute a quantum-regression approximation and must
+    carry a different method label.
+    """
+    period_steps = len(step_propagators)
+    if phase_densities.shape[0] != period_steps:
+        raise ValueError("one phase density is required per step in a period")
+    total = np.zeros(delay_steps + 1, dtype=np.complex128)
+    one_point = np.real(
+        np.einsum("ij,tji->t", operator, phase_densities, optimize=True)
+    )
+    for phase in range(period_steps):
+        inserted = operator @ phase_densities[phase]
+        propagation = np.eye(operator.shape[0], dtype=np.complex128)
+        total[0] += np.trace(operator @ inserted)
+        for delay in range(1, delay_steps + 1):
+            piece = step_propagators[(phase + delay - 1) % period_steps]
+            propagation = piece @ propagation
+            evolved = propagation @ inserted @ propagation.conj().T
+            total[delay] += np.trace(operator @ evolved)
+    total /= period_steps
+    delays = np.arange(delay_steps + 1, dtype=np.float64) * dt
+    coherent, peaks = coherent_decomposition(one_point, drive_frequency, delays)
+    return CorrelationResult(
+        delays,
+        total,
+        total - coherent,
+        coherent,
+        peaks,
+        method,
+        {"period_steps": float(period_steps), "dt": dt},
+    )
+
+
+def superoperator_period_correlation(
+    step_maps: NDArray[np.complex128],
+    phase_densities: NDArray[np.complex128],
+    operator: ComplexMatrix,
+    dt: float,
+    delay_steps: int,
+    drive_frequency: float,
+    method: str = "floquet_markov_qr",
+) -> CorrelationResult:
+    """Two-time correlation using a periodic Markovian dynamical map.
+
+    This is the quantum regression theorem and is only used for the explicitly
+    labeled Markovian backend.
+    """
+    period_steps = len(step_maps)
+    if phase_densities.shape[0] != period_steps:
+        raise ValueError("one phase density is required per step in a period")
+    dimension = operator.shape[0]
+    total = np.zeros(delay_steps + 1, dtype=np.complex128)
+    one_point = np.real(
+        np.einsum("ij,tji->t", operator, phase_densities, optimize=True)
+    )
+    measurement = operator.T.reshape(dimension**2, order="F")
+    for phase in range(period_steps):
+        inserted = (operator @ phase_densities[phase]).reshape(
+            dimension**2, order="F"
+        )
+        vector = inserted
+        total[0] += measurement @ vector
+        for delay in range(1, delay_steps + 1):
+            vector = step_maps[(phase + delay - 1) % period_steps] @ vector
+            total[delay] += measurement @ vector
+    total /= period_steps
+    delays = np.arange(delay_steps + 1, dtype=np.float64) * dt
+    coherent, peaks = coherent_decomposition(one_point, drive_frequency, delays)
+    return CorrelationResult(
+        delays,
+        total,
+        total - coherent,
+        coherent,
+        peaks,
+        method,
+        {"period_steps": float(period_steps), "dt": dt},
+    )
diff --git a/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/dark_channels.py b/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/dark_channels.py
new file mode 100644
index 000000000..af99a667c
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/dark_channels.py
@@ -0,0 +1,128 @@
+"""Harmonic-resolved Floquet transition and dark-channel diagnostics."""
+
+from __future__ import annotations
+
+from dataclasses import dataclass
+
+import numpy as np
+from numpy.typing import NDArray
+
+from .floquet import FloquetSolution, micromotion
+from .operators import ComplexMatrix
+
+
+@dataclass(frozen=True)
+class FloquetTransition:
+    source: int
+    target: int
+    harmonic: int
+    emitted_frequency: float
+    amplitude: complex
+    weight: float
+
+
+@dataclass(frozen=True)
+class DarkCandidate:
+    transition: FloquetTransition
+    relative_weight: float
+
+
+def periodic_modes(solution: FloquetSolution) -> NDArray[np.complex128]:
+    cumulative = micromotion(solution)[:-1]
+    dt = solution.period / len(cumulative)
+    values = []
+    for index, propagator in enumerate(cumulative):
+        time = index * dt
+        values.append(
+            propagator
+            @ solution.modes
+            @ np.diag(np.exp(1j * solution.quasienergies * time))
+        )
+    return np.asarray(values)
+
+
+def floquet_matrix_elements(
+    solution: FloquetSolution,
+    operator: ComplexMatrix,
+    harmonic_cutoff: int,
+    threshold: float = 0.0,
+) -> tuple[FloquetTransition, ...]:
+    """Return S_ab^(m) under the project's Fourier convention."""
+    if harmonic_cutoff < 0:
+        raise ValueError("harmonic_cutoff must be nonnegative")
+    modes = periodic_modes(solution)
+    samples = len(modes)
+    omega_d = 2 * np.pi / solution.period
+    instantaneous = np.einsum(
+        "tai,ab,tbj->tij", modes.conj(), operator, modes, optimize=True
+    )
+    records: list[FloquetTransition] = []
+    for harmonic in range(-harmonic_cutoff, harmonic_cutoff + 1):
+        phase = np.exp(-1j * harmonic * omega_d * np.arange(samples) * solution.period / samples)
+        fourier = np.einsum("t,tij->ij", phase, instantaneous) / samples
+        for target in range(fourier.shape[0]):
+            for source in range(fourier.shape[1]):
+                amplitude = complex(fourier[target, source])
+                weight = float(abs(amplitude) ** 2)
+                if weight >= threshold:
+                    records.append(
+                        FloquetTransition(
+                            source=source,
+                            target=target,
+                            harmonic=harmonic,
+                            emitted_frequency=float(
+                                solution.quasienergies[source]
+                                - solution.quasienergies[target]
+                                + harmonic * omega_d
+                            ),
+                            amplitude=amplitude,
+                            weight=weight,
+                        )
+                    )
+    return tuple(records)
+
+
+def harmonic_sum_rule(
+    solution: FloquetSolution,
+    operator: ComplexMatrix,
+    harmonic_cutoff: int,
+) -> float:
+    """Return maximum relative Parseval residual over mode pairs."""
+    modes = periodic_modes(solution)
+    instantaneous = np.einsum(
+        "tai,ab,tbj->tij", modes.conj(), operator, modes, optimize=True
+    )
+    direct = np.mean(abs(instantaneous) ** 2, axis=0)
+    records = floquet_matrix_elements(solution, operator, harmonic_cutoff)
+    summed = np.zeros_like(direct, dtype=float)
+    for record in records:
+        summed[record.target, record.source] += record.weight
+    return float(np.max(abs(summed - direct) / (direct + 1e-15)))
+
+
+def period_variance(
+    phase_densities: NDArray[np.complex128], operator: ComplexMatrix
+) -> float:
+    first = np.einsum("ij,tji->t", operator, phase_densities, optimize=True)
+    second = np.einsum(
+        "ij,tji->t", operator @ operator, phase_densities, optimize=True
+    )
+    return float(np.real(np.mean(second - first * first)))
+
+
+def dark_candidates(
+    transitions: tuple[FloquetTransition, ...],
+    relative_threshold: float = 1e-4,
+) -> tuple[DarkCandidate, ...]:
+    if not 0 <= relative_threshold <= 1:
+        raise ValueError("relative_threshold must lie in [0, 1]")
+    if not transitions:
+        return ()
+    maximum = max(record.weight for record in transitions)
+    if maximum == 0:
+        return tuple(DarkCandidate(record, 0.0) for record in transitions)
+    return tuple(
+        DarkCandidate(record, record.weight / maximum)
+        for record in transitions
+        if record.weight / maximum <= relative_threshold
+    )
diff --git a/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/error_map.py b/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/error_map.py
new file mode 100644
index 000000000..65edebe7d
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/error_map.py
@@ -0,0 +1,152 @@
+"""Exact PT-TEMPO versus Floquet-Markov comparison metrics and audits."""
+
+from __future__ import annotations
+
+from dataclasses import asdict, dataclass
+from typing import Any, cast
+
+import numpy as np
+from numpy.typing import NDArray
+
+from .convergence import curve_residual
+
+
+@dataclass(frozen=True)
+class ErrorMetrics:
+    trace_distance: float
+    correlation: float
+    heat: float
+
+
+def trace_distance(
+    first: NDArray[np.complex128], second: NDArray[np.complex128]
+) -> float:
+    if first.shape != second.shape or first.ndim != 2 or first.shape[0] != first.shape[1]:
+        raise ValueError("density matrices must have the same square shape")
+    difference = (first - second + (first - second).conj().T) / 2
+    return float(0.5 * np.sum(abs(np.linalg.eigvalsh(difference))))
+
+
+def correlation_error(
+    exact_grid: NDArray[np.float64],
+    exact: NDArray[np.complex128],
+    markov_grid: NDArray[np.float64],
+    markov: NDArray[np.complex128],
+) -> float:
+    return curve_residual(markov_grid, markov, exact_grid, exact)
+
+
+def heat_error(
+    exact_grid: NDArray[np.float64],
+    exact: NDArray[np.float64],
+    markov_grid: NDArray[np.float64],
+    markov: NDArray[np.float64],
+) -> float:
+    return curve_residual(markov_grid, markov, exact_grid, exact)
+
+
+def _complex_array(value: dict[str, Any]) -> NDArray[np.complex128]:
+    return cast(
+        NDArray[np.complex128],
+        np.asarray(value["real"], dtype=float)
+        + 1j * np.asarray(value["imag"], dtype=float),
+    )
+
+
+def build_error_record(
+    exact: dict[str, Any], markov: dict[str, Any]
+) -> dict[str, Any]:
+    """Build a comparison only after checking scientific compatibility."""
+    if not bool(exact.get("converged")):
+        raise ValueError("exact PT-TEMPO input must be converged")
+    exact_method = str(exact.get("method", ""))
+    if exact_method not in {
+        "pt_tempo_multitime",
+        "uniform_tempo_floquet_multitime",
+    }:
+        raise ValueError("exact input must use an approved process-tensor method")
+    if exact.get("model_hash") != markov.get("model_hash"):
+        raise ValueError("model_hash mismatch")
+    exact_normalization = exact.get("model", {}).get("normalization")
+    markov_normalization = markov.get("model", {}).get("normalization")
+    if exact_normalization != markov_normalization:
+        raise ValueError("normalization mismatch")
+    exact_frequency = np.asarray(exact["frequency"], dtype=float)
+    markov_frequency = np.asarray(markov["frequency"], dtype=float)
+    if (
+        exact_frequency.shape != markov_frequency.shape
+        or not np.allclose(exact_frequency, markov_frequency)
+    ):
+        raise ValueError("frequency grid mismatch")
+    exact_delay = np.asarray(exact["correlation"]["delay"], dtype=float)
+    markov_delay = np.asarray(markov["correlation"]["delay"], dtype=float)
+    if exact_delay.shape != markov_delay.shape or not np.allclose(
+        exact_delay, markov_delay
+    ):
+        raise ValueError("correlation grid mismatch")
+    metrics = ErrorMetrics(
+        trace_distance(
+            _complex_array(exact["phase_state"]),
+            _complex_array(markov["phase_state"]),
+        ),
+        correlation_error(
+            exact_delay,
+            _complex_array(exact["correlation"]["connected"]),
+            markov_delay,
+            _complex_array(markov["correlation"]["connected"]),
+        ),
+        heat_error(
+            exact_frequency,
+            np.asarray(exact["continuous"], dtype=float),
+            markov_frequency,
+            np.asarray(markov["continuous"], dtype=float),
+        ),
+    )
+    return {
+        "status": "converged",
+        "model_hash": exact["model_hash"],
+        "exact_method": exact["method"],
+        "markov_method": markov["method"],
+        "metrics": asdict(metrics),
+        "convergence_evidence": exact.get("evidence", []),
+    }
+
+
+def audit_grid_manifest(
+    manifest: dict[str, Any],
+    alphas: tuple[float, ...] = (0.025, 0.05, 0.1),
+    drive_ratios: tuple[float, ...] = (0.75, 1.0, 1.25),
+) -> dict[str, Any]:
+    """Require each requested cell to be converged or explicitly masked."""
+    expected = {(float(alpha), float(ratio)) for alpha in alphas for ratio in drive_ratios}
+    points = manifest.get("points")
+    if not isinstance(points, list):
+        raise ValueError("manifest points must be a list")
+    observed: dict[tuple[float, float], dict[str, Any]] = {}
+    for point in points:
+        key = (float(point["alpha"]), float(point["drive_ratio"]))
+        if key in observed:
+            raise ValueError(f"duplicate grid point {key}")
+        observed[key] = point
+    if set(observed) != expected:
+        missing = sorted(expected - set(observed))
+        extra = sorted(set(observed) - expected)
+        raise ValueError(f"grid mismatch; missing={missing}, extra={extra}")
+    masked = 0
+    for key, point in observed.items():
+        status = point.get("status")
+        if status == "converged":
+            if not isinstance(point.get("metrics"), dict):
+                raise ValueError(f"converged point {key} lacks metrics")
+        elif status == "resource_ceiling":
+            if point.get("metrics") is not None:
+                raise ValueError(f"masked point {key} must not fabricate metrics")
+            masked += 1
+        else:
+            raise ValueError(f"invalid status for point {key}: {status}")
+    return {
+        "complete": True,
+        "requested_points": len(expected),
+        "converged_points": len(expected) - masked,
+        "masked_points": masked,
+    }
diff --git a/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/experiments.py b/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/experiments.py
new file mode 100644
index 000000000..cec12d945
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/experiments.py
@@ -0,0 +1,273 @@
+"""Reproducible baseline experiments used by the report."""
+
+from __future__ import annotations
+
+from dataclasses import asdict
+
+import numpy as np
+
+from .backends.finite_memory import FiniteMemoryBackend
+from .backends.floquet_markov import FloquetMarkovBackend
+from .config import BathConfig, ModelConfig, Normalization
+from .correlations import superoperator_period_correlation
+from .heat_current import heat_current_spectrum
+from .models import coupling_operator, ising_hamiltonian
+from .spectra import diagonalize, transitions
+from .symmetry import n2_sectors, n3_reflection_sectors, project
+
+
+def n2_bright_sweep(
+    j_values: np.ndarray,
+    omega: float = 1.0,
+    normalization: Normalization = "bounded",
+) -> dict[str, object]:
+    _, triplet = n2_sectors()
+    records = []
+    maximum_residual = 0.0
+    for j in j_values:
+        cfg = ModelConfig(n=2, j=float(j), omega=omega, normalization=normalization)
+        h = project(ising_hamiltonian(cfg), triplet)
+        s = project(coupling_operator(cfg), triplet)
+        spectrum = diagonalize(h)
+        items = transitions(spectrum, spectrum, s, threshold=1e-10)
+        low = next(item for item in items if item.source == 0 and item.frequency > 0)
+        high = next(item for item in items if item.source == 1 and item.target == 2)
+        energy = float(np.sqrt(j**2 + omega**2))
+        analytic = {
+            "gap_low": energy - float(j),
+            "gap_high": energy + float(j),
+            "weight_low": 2 * cfg.eta**2 * (1 + float(j) / energy),
+            "weight_high": 2 * cfg.eta**2 * (1 - float(j) / energy),
+        }
+        numerical = {
+            "gap_low": low.frequency,
+            "gap_high": high.frequency,
+            "weight_low": low.weight,
+            "weight_high": high.weight,
+        }
+        maximum_residual = max(
+            maximum_residual,
+            max(abs(numerical[key] - analytic[key]) for key in analytic),
+        )
+        records.append(
+            {
+                "j": float(j),
+                **numerical,
+                **{f"analytic_{key}": value for key, value in analytic.items()},
+            }
+        )
+    return {
+        "method": "exact_diagonalization",
+        "converged": maximum_residual < 1e-10,
+        "diagnostics": {"maximum_analytic_residual": maximum_residual},
+        "data": records,
+    }
+
+
+def n3_sector_sweep(
+    j_values: np.ndarray,
+    omega: float = 1.0,
+    normalization: Normalization = "bounded",
+) -> dict[str, object]:
+    odd, even = n3_reflection_sectors()
+    records = []
+    odd_gap_spread = 0.0
+    odd_gaps = []
+    for j in j_values:
+        cfg = ModelConfig(n=3, j=float(j), omega=omega, normalization=normalization)
+        full_h = ising_hamiltonian(cfg)
+        full_s = coupling_operator(cfg)
+        even_spectrum = diagonalize(project(full_h, even))
+        odd_spectrum = diagonalize(project(full_h, odd))
+        odd_gap = float(odd_spectrum.energies[1] - odd_spectrum.energies[0])
+        odd_gaps.append(odd_gap)
+        even_operator = project(full_s, even)
+        bright = sorted(
+            [
+                item
+                for item in transitions(even_spectrum, even_spectrum, even_operator, 1e-10)
+                if item.source == 0 and item.frequency > 0
+            ],
+            key=lambda item: item.frequency,
+        )
+        primary = bright[0]
+        records.append(
+            {
+                "j": float(j),
+                "odd_gap": odd_gap,
+                "primary_even_gap": primary.frequency,
+                "primary_even_weight": primary.weight,
+                "cat_ratio": (
+                    primary.frequency * 4 * float(j) ** 2 / omega**3 if j > 0 else None
+                ),
+            }
+        )
+    odd_gap_spread = float(np.ptp(odd_gaps))
+    return {
+        "method": "exact_diagonalization",
+        "converged": odd_gap_spread < 1e-10,
+        "diagnostics": {"odd_gap_spread": odd_gap_spread},
+        "data": records,
+    }
+
+
+def backend_comparison(
+    alphas: list[float],
+    j: float = 0.5,
+    omega: float = 1.0,
+    drive_amplitude: float = 0.2,
+    steps_per_period: int = 48,
+    periods: int = 100,
+) -> dict[str, object]:
+    """Compare two explicitly approximate backends for the N=2 triplet."""
+    _, triplet = n2_sectors()
+    gap = float(np.sqrt(j**2 + omega**2) - j)
+    cfg = ModelConfig(
+        n=2,
+        j=j,
+        omega=omega,
+        drive_amplitude=drive_amplitude,
+        drive_frequency=gap,
+    )
+    h0 = project(ising_hamiltonian(cfg), triplet)
+    s = project(coupling_operator(cfg), triplet)
+
+    def hamiltonian(time: float) -> np.ndarray:
+        return np.asarray(
+            h0 + cfg.drive_amplitude * np.cos(cfg.drive_frequency * time) * s,
+            dtype=np.complex128,
+        )
+
+    ground = diagonalize(h0).states[:, 0]
+    rho0 = np.outer(ground, ground.conj())
+    dt = cfg.period / steps_per_period
+    records = []
+    for alpha in alphas:
+        bath = BathConfig(alpha=alpha)
+        markov = FloquetMarkovBackend().run(
+            hamiltonian, s, bath, cfg.period, steps_per_period, 4
+        )
+        memory = FiniteMemoryBackend().run(
+            hamiltonian,
+            s,
+            rho0,
+            bath,
+            dt,
+            steps_per_period * periods,
+            1,
+        )
+        memory_phase_residual = float(
+            np.linalg.norm(
+                memory.density_matrices[-1]
+                - memory.density_matrices[-1 - steps_per_period]
+            )
+        )
+        trace_distance = float(
+            0.5
+            * np.sum(
+                np.abs(
+                    np.linalg.eigvalsh(
+                        memory.density_matrices[-1] - markov.density_matrices[0]
+                    )
+                )
+            )
+        )
+        records.append(
+            {
+                "alpha": alpha,
+                "trace_distance": trace_distance,
+                "finite_memory_phase_residual": memory_phase_residual,
+                "finite_memory_trace_error": memory.diagnostics["trace_error"],
+                "finite_memory_min_eigenvalue": memory.diagnostics[
+                    "minimum_density_eigenvalue"
+                ],
+                "markov_rate_residual": markov.diagnostics["rate_residual"],
+            }
+        )
+    converged = all(
+        record["finite_memory_phase_residual"] < 5e-3
+        and record["finite_memory_min_eigenvalue"] > -1e-5
+        for record in records
+    )
+    return {
+        "method": "finite_memory_if_vs_floquet_markov",
+        "converged": converged,
+        "diagnostics": {
+            "memory_steps": 1,
+            "steps_per_period": steps_per_period,
+            "periods": periods,
+            "warning": (
+                "This is an approximation-to-approximation comparison, "
+                "not an exact Floquet-IF error map."
+            ),
+        },
+        "model": asdict(cfg),
+        "data": records,
+    }
+
+
+def n2_markov_heat_spectrum(
+    j: float = 0.5,
+    omega: float = 1.0,
+    alpha: float = 0.05,
+    drive_amplitude: float = 0.2,
+    steps_per_period: int = 96,
+    correlation_periods: int = 16,
+) -> dict[str, object]:
+    """Generate the explicitly approximate N=2 Floquet-Markov heat spectrum."""
+    _, triplet = n2_sectors()
+    gap = float(np.sqrt(j**2 + omega**2) - j)
+    cfg = ModelConfig(
+        n=2,
+        j=j,
+        omega=omega,
+        drive_amplitude=drive_amplitude,
+        drive_frequency=gap,
+    )
+    h0 = project(ising_hamiltonian(cfg), triplet)
+    coupling = project(coupling_operator(cfg), triplet)
+
+    def hamiltonian(time: float) -> np.ndarray:
+        return np.asarray(
+            h0 + drive_amplitude * np.cos(cfg.drive_frequency * time) * coupling,
+            dtype=np.complex128,
+        )
+
+    bath = BathConfig(alpha=alpha)
+    markov = FloquetMarkovBackend().run(
+        hamiltonian,
+        coupling,
+        bath,
+        cfg.period,
+        steps_per_period,
+        5,
+    )
+    if markov.step_maps is None:
+        raise RuntimeError("Floquet-Markov backend did not return step maps")
+    correlation = superoperator_period_correlation(
+        markov.step_maps,
+        markov.density_matrices[:-1],
+        coupling,
+        cfg.period / steps_per_period,
+        steps_per_period * correlation_periods,
+        cfg.drive_frequency,
+    )
+    frequencies = np.linspace(0, 3.0, 601)
+    heat = heat_current_spectrum(correlation, bath, frequencies)
+    records = [
+        {"frequency": float(frequency), "continuous": float(value)}
+        for frequency, value in zip(heat.frequencies, heat.continuous, strict=True)
+    ]
+    return {
+        "method": heat.method,
+        "converged": markov.converged,
+        "diagnostics": {
+            **markov.diagnostics,
+            **heat.metadata,
+            "continuous_tail_amplitude": float(abs(correlation.connected[-1])),
+        },
+        "model": asdict(cfg),
+        "bath": asdict(bath),
+        "delta_peaks": [asdict(peak) for peak in heat.delta_peaks],
+        "data": records,
+    }
diff --git a/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/floquet.py b/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/floquet.py
new file mode 100644
index 000000000..092cb152c
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/floquet.py
@@ -0,0 +1,79 @@
+"""Direct finite-dimensional Floquet propagation."""
+
+from __future__ import annotations
+
+from collections.abc import Callable
+from dataclasses import dataclass
+
+import numpy as np
+from numpy.typing import NDArray
+from scipy.linalg import expm
+
+from .operators import ComplexMatrix
+
+
+@dataclass(frozen=True)
+class FloquetSolution:
+    propagator: ComplexMatrix
+    quasienergies: NDArray[np.float64]
+    modes: ComplexMatrix
+    period: float
+    step_propagators: tuple[ComplexMatrix, ...]
+    unitarity_residual: float
+    eigen_residual: float
+
+
+def one_period_propagator(
+    hamiltonian: Callable[[float], ComplexMatrix],
+    period: float,
+    steps: int,
+) -> tuple[ComplexMatrix, tuple[ComplexMatrix, ...]]:
+    if period <= 0 or steps < 1:
+        raise ValueError("period and steps must be positive")
+    dt = period / steps
+    dimension = hamiltonian(0.0).shape[0]
+    total = np.eye(dimension, dtype=np.complex128)
+    pieces: list[ComplexMatrix] = []
+    for index in range(steps):
+        midpoint = (index + 0.5) * dt
+        piece = expm(-1j * hamiltonian(midpoint) * dt)
+        pieces.append(piece)
+        total = piece @ total
+    return total, tuple(pieces)
+
+
+def solve_floquet(
+    hamiltonian: Callable[[float], ComplexMatrix],
+    period: float,
+    steps: int,
+) -> FloquetSolution:
+    total, pieces = one_period_propagator(hamiltonian, period, steps)
+    values, modes = np.linalg.eig(total)
+    phases = np.angle(values)
+    quasienergies = -phases / period
+    order = np.argsort(quasienergies)
+    quasienergies = quasienergies[order].astype(np.float64)
+    modes = modes[:, order]
+    modes /= np.linalg.norm(modes, axis=0)
+    identity = np.eye(total.shape[0])
+    unitarity = float(np.linalg.norm(total.conj().T @ total - identity))
+    residual = float(
+        np.linalg.norm(total @ modes - modes * np.exp(-1j * quasienergies * period))
+    )
+    return FloquetSolution(
+        total,
+        quasienergies,
+        modes,
+        period,
+        pieces,
+        unitarity,
+        residual,
+    )
+
+
+def micromotion(solution: FloquetSolution) -> tuple[ComplexMatrix, ...]:
+    """Return cumulative propagators at all step boundaries, including t=0."""
+    values = [np.eye(solution.propagator.shape[0], dtype=np.complex128)]
+    for piece in solution.step_propagators:
+        values.append(piece @ values[-1])
+    return tuple(values)
diff --git a/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/heat_current.py b/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/heat_current.py
new file mode 100644
index 000000000..5df62f44c
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/heat_current.py
@@ -0,0 +1,93 @@
+"""Frequency-resolved bath heat current from collective correlations."""
+
+from __future__ import annotations
+
+from dataclasses import dataclass
+
+import numpy as np
+from numpy.typing import NDArray
+from scipy.integrate import trapezoid
+
+from .bath import bose_occupation, ohmic_spectral_density
+from .config import BathConfig
+from .correlations import CorrelationResult
+
+
+@dataclass(frozen=True)
+class HeatDeltaPeak:
+    harmonic: int
+    frequency: float
+    weight: float
+
+
+@dataclass(frozen=True)
+class HeatCurrentResult:
+    frequencies: NDArray[np.float64]
+    continuous: NDArray[np.float64]
+    delta_peaks: tuple[HeatDeltaPeak, ...]
+    method: str
+    metadata: dict[str, float | str]
+
+
+def heat_current_spectrum(
+    correlation: CorrelationResult,
+    bath: BathConfig,
+    frequencies: NDArray[np.float64],
+    window: str = "hann",
+) -> HeatCurrentResult:
+    """Evaluate the half-sided heat-current transform.
+
+    The continuous part uses only the connected correlation. Coherent
+    contributions are returned as analytic delta weights.
+    """
+    if np.any(frequencies < 0):
+        raise ValueError("bath frequencies must be nonnegative")
+    delays = correlation.delays
+    if len(delays) < 2 or not np.allclose(np.diff(delays), np.diff(delays)[0]):
+        raise ValueError("correlation delays must form a uniform grid")
+    if window == "hann":
+        taper = np.hanning(2 * len(delays) - 1)[len(delays) - 1 :]
+    elif window == "none":
+        taper = np.ones(len(delays))
+    else:
+        raise ValueError("window must be 'hann' or 'none'")
+    connected = correlation.connected * taper
+    output = np.zeros_like(frequencies, dtype=np.float64)
+    for index, frequency in enumerate(frequencies):
+        if frequency == 0:
+            continue
+        occupation = bose_occupation(float(frequency), bath.temperature)
+        kernel = (
+            np.cos(frequency * delays) * np.real(connected)
+            + (1 + 2 * occupation)
+            * np.sin(frequency * delays)
+            * np.imag(connected)
+        )
+        prefactor = 2 * float(ohmic_spectral_density(float(frequency), bath)) * frequency
+        output[index] = prefactor * trapezoid(kernel, delays)
+
+    delta_peaks = tuple(
+        HeatDeltaPeak(
+            peak.harmonic,
+            peak.frequency,
+            float(
+                np.pi
+                * ohmic_spectral_density(peak.frequency, bath)
+                * peak.frequency
+                * peak.correlation_weight
+            ),
+        )
+        for peak in correlation.delta_peaks
+        if peak.frequency > 0
+    )
+    return HeatCurrentResult(
+        frequencies,
+        output,
+        delta_peaks,
+        correlation.method,
+        {
+            "window": window,
+            "tau_max": float(delays[-1]),
+            "frequency_resolution": float(2 * np.pi / delays[-1]),
+        },
+    )
diff --git a/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/heat_valve.py b/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/heat_valve.py
new file mode 100644
index 000000000..d178aac2c
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/heat_valve.py
@@ -0,0 +1,502 @@
+"""Fixed-frequency coherent-destruction scans for the Floquet heat valve."""
+
+from __future__ import annotations
+
+import subprocess
+from collections.abc import Iterable
+from dataclasses import asdict, dataclass
+from typing import Any, Literal
+
+import numpy as np
+from scipy.integrate import trapezoid
+from scipy.optimize import linear_sum_assignment
+from scipy.special import jn_zeros, jv
+
+from .backends.uniform_tempo import (
+    UNIFORM_TEMPO_REVISION,
+    UniformTempoBackend,
+    UniformTempoControls,
+)
+from .config import BathConfig, ModelConfig
+from .convergence import ConvergenceCache, fingerprint
+from .dark_channels import floquet_matrix_elements
+from .floquet import FloquetSolution, solve_floquet
+from .heat_current import heat_current_spectrum
+from .models import coupling_operator, drive_operator, ising_hamiltonian
+from .operators import ComplexMatrix
+from .poles import fit_pole_residues, transfer_poles
+from .symmetry import Sector, n2_sectors, n3_reflection_sectors, project
+
+BESSEL_ROOT = float(jn_zeros(0, 1)[0])
+
+
+@dataclass(frozen=True)
+class HeatValvePoint:
+    n: Literal[1, 2, 3]
+    xi: float
+    j: float = 1.0
+    omega: float = 1.0
+    drive_frequency: float = 3.0
+    alpha: float = 0.05
+    cutoff: float = 2.5
+    temperature: float = 0.0
+    floquet_steps: int = 360
+
+    def __post_init__(self) -> None:
+        if self.n not in (1, 2, 3):
+            raise ValueError("n must be one of 1, 2, 3")
+        if self.xi < 0:
+            raise ValueError("xi must be nonnegative")
+        if self.floquet_steps < 8:
+            raise ValueError("floquet_steps must be at least eight")
+
+    @property
+    def drive_amplitude(self) -> float:
+        return self.xi * self.drive_frequency / 2
+
+
+@dataclass(frozen=True)
+class PreparedHeatValve:
+    point: HeatValvePoint
+    model: ModelConfig
+    bath: BathConfig
+    sector: Sector
+    h0: ComplexMatrix
+    coupling: ComplexMatrix
+    drive: ComplexMatrix
+    cat_plus: np.ndarray[Any, np.dtype[np.complex128]]
+    cat_minus: np.ndarray[Any, np.dtype[np.complex128]]
+
+
+@dataclass(frozen=True)
+class ValveNumerics:
+    steps_per_period: int = 60
+    tolerance: float = 1e-6
+    phase_samples: int = 3
+    delay_periods: int = 12
+    pole_count: int = 8
+    pole_tolerance: float = 1e-10
+    pole_maxiter: int = 2_000
+    frequency_max: float = 6.0
+    frequency_points: int = 601
+    auto_nc: bool = True
+    memory_cutoff: int = 100_000
+    low_rank_svd: bool = False
+    truncation: Literal["rel", "abs"] = "rel"
+    cap_rank: int = 100_000
+    max_rank: int = 100_000
+
+    def __post_init__(self) -> None:
+        if self.steps_per_period < 2:
+            raise ValueError("steps_per_period must be at least two")
+        if (
+            self.phase_samples < 2
+            or self.phase_samples > self.steps_per_period
+            or self.steps_per_period % self.phase_samples != 0
+        ):
+            raise ValueError("phase_samples must divide steps_per_period")
+        if not 0 < self.tolerance < 1:
+            raise ValueError("tolerance must lie between zero and one")
+        if self.delay_periods < 1:
+            raise ValueError("delay_periods must be positive")
+        if self.pole_count < 2:
+            raise ValueError("pole_count must include steady and decaying poles")
+        if self.delay_periods + 1 <= self.pole_count - 1:
+            raise ValueError("delay window must overdetermine the pole fit")
+        if self.pole_tolerance <= 0 or self.pole_maxiter < 1:
+            raise ValueError("invalid pole solver controls")
+        if self.frequency_max <= 0 or self.frequency_points < 2:
+            raise ValueError("invalid heat-current frequency grid")
+        if self.memory_cutoff < 1:
+            raise ValueError("memory_cutoff must be positive")
+        if self.truncation not in ("rel", "abs"):
+            raise ValueError("truncation must be 'rel' or 'abs'")
+        if self.cap_rank < 1 or self.max_rank < self.cap_rank:
+            raise ValueError("invalid rank limits")
+
+
+def _active_sector(n: int) -> Sector:
+    if n == 1:
+        return Sector("full", np.eye(2, dtype=np.complex128))
+    if n == 2:
+        _, triplet = n2_sectors()
+        return triplet
+    _, even = n3_reflection_sectors()
+    return even
+
+
+def _projected_cat(
+    n: int,
+    sector: Sector,
+    sign: Literal[-1, 1],
+) -> np.ndarray[Any, np.dtype[np.complex128]]:
+    up = np.zeros(2**n, dtype=np.complex128)
+    down = np.zeros(2**n, dtype=np.complex128)
+    up[0] = 1
+    down[-1] = 1
+    value = sector.isometry.conj().T @ ((up + sign * down) / np.sqrt(2))
+    norm = float(np.linalg.norm(value))
+    if norm <= 1e-13:
+        raise ValueError("selected sector does not contain the cat state")
+    return np.asarray(value / norm, dtype=np.complex128)
+
+
+def prepare_heat_valve_point(point: HeatValvePoint) -> PreparedHeatValve:
+    """Project a size point while keeping bath and drive normalizations separate."""
+    model = ModelConfig(
+        n=point.n,
+        j=point.j,
+        omega=point.omega,
+        drive_amplitude=point.drive_amplitude,
+        drive_frequency=point.drive_frequency,
+        normalization="bounded",
+        drive_normalization="per_spin",
+    )
+    bath = BathConfig(point.alpha, point.cutoff, point.temperature)
+    sector = _active_sector(point.n)
+    return PreparedHeatValve(
+        point=point,
+        model=model,
+        bath=bath,
+        sector=sector,
+        h0=project(ising_hamiltonian(model), sector),
+        coupling=project(coupling_operator(model), sector),
+        drive=project(drive_operator(model), sector),
+        cat_plus=_projected_cat(point.n, sector, +1),
+        cat_minus=_projected_cat(point.n, sector, -1),
+    )
+
+
+def _cat_modes(
+    prepared: PreparedHeatValve,
+    solution: FloquetSolution,
+) -> tuple[tuple[int, int], tuple[float, float], float]:
+    cat_basis = np.column_stack((prepared.cat_plus, prepared.cat_minus))
+    subspace_weights = np.sum(
+        abs(cat_basis.conj().T @ solution.modes) ** 2,
+        axis=0,
+    )
+    selected = np.argsort(subspace_weights)[-2:]
+    overlaps = abs(cat_basis.conj().T @ solution.modes[:, selected]) ** 2
+    rows, columns = linear_sum_assignment(-overlaps)
+    assigned = {
+        int(row): (int(selected[column]), float(overlaps[row, column]))
+        for row, column in zip(rows, columns, strict=True)
+    }
+    modes = (assigned[0][0], assigned[1][0])
+    direct_overlaps = (assigned[0][1], assigned[1][1])
+    cat_overlap = float(np.min(subspace_weights[selected]))
+    return modes, direct_overlaps, cat_overlap
+
+
+def _isolated_point(point: HeatValvePoint) -> dict[str, Any]:
+    prepared = prepare_heat_valve_point(point)
+    model = prepared.model
+
+    def hamiltonian(time: float) -> ComplexMatrix:
+        return np.asarray(
+            prepared.h0
+            + model.drive_amplitude
+            * np.cos(model.drive_frequency * time)
+            * prepared.drive,
+            dtype=np.complex128,
+        )
+
+    solution = solve_floquet(
+        hamiltonian,
+        model.period,
+        point.floquet_steps,
+    )
+    modes, direct_overlaps, cat_overlap = _cat_modes(prepared, solution)
+    raw_gap = float(abs(solution.quasienergies[modes[0]] - solution.quasienergies[modes[1]]))
+    cat_gap = min(raw_gap, model.drive_frequency - raw_gap)
+    transitions = floquet_matrix_elements(
+        solution,
+        prepared.coupling,
+        harmonic_cutoff=3,
+    )
+    selected_modes = set(modes)
+    cat_brightness = float(
+        sum(
+            record.weight
+            for record in transitions
+            if record.source in selected_modes
+            and record.target in selected_modes
+            and record.source != record.target
+        )
+    )
+    return {
+        **asdict(point),
+        "drive_amplitude": model.drive_amplitude,
+        "bessel_j0": float(jv(0, point.xi)),
+        "bessel_root": BESSEL_ROOT,
+        "sector": prepared.sector.name,
+        "dimension": prepared.sector.dimension,
+        "cat_mode_indices": list(modes),
+        "cat_plus_overlap": direct_overlaps[0],
+        "cat_minus_overlap": direct_overlaps[1],
+        "cat_overlap": cat_overlap,
+        "cat_gap": float(cat_gap),
+        "cat_brightness": cat_brightness,
+        "unitarity_residual": solution.unitarity_residual,
+        "floquet_eigen_residual": solution.eigen_residual,
+    }
+
+
+def isolated_valve_scan(
+    points: Iterable[HeatValvePoint],
+) -> dict[str, Any]:
+    """Run a deterministic exact scan before selecting open-system points."""
+    selected = tuple(points)
+    if not selected:
+        raise ValueError("the isolated valve scan requires at least one point")
+    records = [_isolated_point(point) for point in selected]
+    return {
+        "complete": True,
+        "method": "isolated_floquet_coherent_destruction",
+        "schema_version": 1,
+        "bessel_root": BESSEL_ROOT,
+        "points": records,
+    }
+
+
+def _complex_values(values: np.ndarray[Any, np.dtype[np.complex128]]) -> dict[str, Any]:
+    array = np.asarray(values, dtype=np.complex128)
+    return {
+        "real": np.real(array).astype(float).tolist(),
+        "imag": np.imag(array).astype(float).tolist(),
+    }
+
+
+def _git_commit() -> str:
+    try:
+        return subprocess.check_output(
+            ["git", "rev-parse", "HEAD"],
+            text=True,
+            stderr=subprocess.DEVNULL,
+        ).strip()
+    except (OSError, subprocess.CalledProcessError):
+        return "unknown"
+
+
+def run_uniform_valve_point(
+    point: HeatValvePoint,
+    numerics: ValveNumerics,
+    cache: ConvergenceCache,
+    *,
+    source_revision: str | None = None,
+) -> dict[str, Any]:
+    """Run or restore one pole-resolved UniformTEMPO heat-valve point."""
+    prepared = prepare_heat_valve_point(point)
+    revision = _git_commit() if source_revision is None else source_revision
+    cache_payload = {
+        "experiment": "uniform-floquet-pole-heat-valve-v1",
+        "point": asdict(point),
+        "numerics": asdict(numerics),
+        "h0": _complex_values(prepared.h0),
+        "coupling": _complex_values(prepared.coupling),
+        "drive": _complex_values(prepared.drive),
+        "bath": asdict(prepared.bath),
+        "uniform_tempo_revision": UNIFORM_TEMPO_REVISION,
+    }
+    key = fingerprint(cache_payload, revision)
+    if cache.contains(key):
+        return cache.load(key)
+
+    controls = UniformTempoControls(
+        steps_per_period=numerics.steps_per_period,
+        tolerance=numerics.tolerance,
+        phase_samples=numerics.phase_samples,
+        delay_periods=numerics.delay_periods,
+        auto_nc=numerics.auto_nc,
+        memory_cutoff=numerics.memory_cutoff,
+        low_rank_svd=numerics.low_rank_svd,
+        truncation=numerics.truncation,
+        cap_rank=numerics.cap_rank,
+        max_rank=numerics.max_rank,
+        pole_count=numerics.pole_count,
+        pole_tolerance=numerics.pole_tolerance,
+        pole_maxiter=numerics.pole_maxiter,
+    )
+    run = UniformTempoBackend(
+        tensor_cache_directory=cache.directory / "process_tensors"
+    ).run_periodic(
+        prepared.h0,
+        prepared.coupling,
+        prepared.model,
+        prepared.bath,
+        controls,
+        drive_operator=prepared.drive,
+    )
+    poles = transfer_poles(
+        run.transfer_eigenvalues,
+        run.transfer_eigenpair_residuals,
+        prepared.model.period,
+    )
+    fit = fit_pole_residues(
+        poles,
+        run.correlation.delays,
+        run.correlation.connected,
+        prepared.model.period,
+        max_modes=len(poles),
+    )
+    frequencies = np.linspace(
+        0,
+        numerics.frequency_max,
+        numerics.frequency_points,
+    )
+    heat = heat_current_spectrum(
+        run.correlation,
+        prepared.bath,
+        frequencies,
+    )
+    connected_tail = float(abs(run.correlation.connected[-1]))
+    maximum_eigenpair_residual = float(
+        np.max(run.transfer_eigenpair_residuals)
+    )
+    maximum_pole_modulus = float(
+        max(abs(item.eigenvalue) for item in poles)
+    )
+    converged = bool(
+        run.diagnostics["trace_error"] <= 5e-3
+        and run.diagnostics["hermiticity_error"] <= 5e-3
+        and run.diagnostics["minimum_density_eigenvalue"] >= -5e-3
+        and run.diagnostics["fixed_point_residual"] <= 1e-3
+        and connected_tail <= 5e-2
+        and maximum_eigenpair_residual <= 1e-8
+        and maximum_pole_modulus <= 1 + 1e-6
+        and fit.reconstruction_residual <= 5e-2
+    )
+    residue_records = [
+        {
+            "eigenvalue": {
+                "real": float(item.pole.eigenvalue.real),
+                "imag": float(item.pole.eigenvalue.imag),
+                "abs": float(abs(item.pole.eigenvalue)),
+            },
+            "decay_rate": item.pole.decay_rate,
+            "quasifrequency": item.pole.quasifrequency,
+            "eigenpair_residual": item.pole.eigenpair_residual,
+            "residue": {
+                "real": float(item.residue.real),
+                "imag": float(item.residue.imag),
+                "abs": float(abs(item.residue)),
+            },
+        }
+        for item in fit.residues
+    ]
+    dominant = max(fit.residues, key=lambda item: abs(item.residue))
+    payload: dict[str, Any] = {
+        "method": run.method,
+        "source_commit": revision,
+        "point": asdict(point),
+        "model": asdict(prepared.model),
+        "bath": asdict(prepared.bath),
+        "numerics": asdict(numerics),
+        "sector": prepared.sector.name,
+        "dimension": prepared.sector.dimension,
+        "converged": converged,
+        "diagnostics": {
+            **run.diagnostics,
+            **run.metadata,
+            "connected_tail": connected_tail,
+            "maximum_eigenpair_residual": maximum_eigenpair_residual,
+            "maximum_pole_modulus": maximum_pole_modulus,
+        },
+        "phase_state": _complex_values(run.floquet_state),
+        "phase_states": _complex_values(run.phase_states),
+        "correlation": {
+            "delay": run.correlation.delays.tolist(),
+            "total": _complex_values(run.correlation.total),
+            "connected": _complex_values(run.correlation.connected),
+            "coherent": run.correlation.coherent.tolist(),
+        },
+        "frequency": heat.frequencies.tolist(),
+        "continuous": heat.continuous.tolist(),
+        "delta_peaks": [asdict(item) for item in heat.delta_peaks],
+        "integrated_absolute_heat": float(
+            trapezoid(abs(heat.continuous), heat.frequencies)
+        ),
+        "poles": residue_records,
+        "dominant_residue": {
+            "real": float(dominant.residue.real),
+            "imag": float(dominant.residue.imag),
+            "abs": float(abs(dominant.residue)),
+        },
+        "visible_residue_weight": float(
+            sum(abs(item.residue) for item in fit.residues)
+        ),
+        "pole_fit": {
+            "reconstruction": _complex_values(fit.reconstruction),
+            "stroboscopic_delays": fit.stroboscopic_delays.tolist(),
+            "reconstruction_residual": fit.reconstruction_residual,
+            "condition_number": fit.condition_number,
+        },
+    }
+    cache.store(key, payload)
+    return cache.load(key)
+
+
+def _point_from_scan(record: dict[str, Any]) -> HeatValvePoint:
+    return HeatValvePoint(
+        n=int(record["n"]),  # type: ignore[arg-type]
+        xi=float(record["xi"]),
+        j=float(record["j"]),
+        omega=float(record["omega"]),
+        drive_frequency=float(record["drive_frequency"]),
+        alpha=float(record["alpha"]),
+        cutoff=float(record["cutoff"]),
+        temperature=float(record["temperature"]),
+        floquet_steps=int(record["floquet_steps"]),
+    )
+
+
+def build_heat_valve_manifest(
+    isolated_scan: dict[str, Any],
+    uniform_results: Iterable[dict[str, Any]] = (),
+) -> dict[str, Any]:
+    """Select two-sided valve points and combine any completed exact results."""
+    scan_records = tuple(isolated_scan.get("points", ()))
+    selected: list[HeatValvePoint] = []
+    for n in (1, 2, 3):
+        candidates = [
+            record
+            for record in scan_records
+            if int(record["n"]) == n and float(record["cat_overlap"]) >= 0.5
+        ]
+        if not candidates:
+            raise ValueError(f"isolated scan has no resolved N={n} cat points")
+        minimum = min(candidates, key=lambda item: float(item["cat_gap"]))
+        minimum_xi = float(minimum["xi"])
+        lower = [
+            record
+            for record in candidates
+            if float(record["xi"]) <= minimum_xi - 0.15
+        ]
+        upper = [
+            record
+            for record in candidates
+            if float(record["xi"]) >= minimum_xi + 0.15
+        ]
+        if not lower or not upper:
+            raise ValueError(f"isolated N={n} minimum lacks two resolved flanks")
+        selected.extend(
+            (
+                _point_from_scan(max(lower, key=lambda item: float(item["xi"]))),
+                _point_from_scan(minimum),
+                _point_from_scan(min(upper, key=lambda item: float(item["xi"]))),
+            )
+        )
+
+    results = tuple(uniform_results)
+    result_keys = {
+        (int(item["point"]["n"]), float(item["point"]["xi"])) for item in results
+    }
+    selected_keys = {(item.n, item.xi) for item in selected}
+    return {
+        "complete": result_keys == selected_keys,
+        "method": "uniform-floquet-pole-heat-valve-v1",
+        "isolated_scan_complete": bool(isolated_scan.get("complete", False)),
+        "selected_points": [asdict(item) for item in selected],
+        "points": list(results),
+    }
diff --git a/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/heat_valve_audit.py b/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/heat_valve_audit.py
new file mode 100644
index 000000000..21448dc27
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/heat_valve_audit.py
@@ -0,0 +1,198 @@
+"""Independent scientific claim gates for the pole-resolved heat valve."""
+
+from __future__ import annotations
+
+from dataclasses import dataclass
+from typing import Any
+
+import numpy as np
+
+
+@dataclass(frozen=True)
+class HeatValveAudit:
+    complete: bool
+    dark_channel_passed: bool
+    many_body_amplification_passed: bool
+    markov_payoff_passed: bool
+    failures: tuple[str, ...]
+    metrics: dict[str, float]
+
+
+def _same_numeric(values: list[float], tolerance: float = 1e-12) -> bool:
+    return bool(values) and bool(
+        np.allclose(values, values[0], rtol=tolerance, atol=tolerance)
+    )
+
+
+def _ratio(numerator: float, denominator: float) -> float:
+    if denominator <= 0:
+        return float("inf")
+    return numerator / denominator
+
+
+def audit_heat_valve_manifest(manifest: dict[str, Any]) -> HeatValveAudit:
+    """Apply the design gates without relying on any plotting decisions."""
+    dark_failures: list[str] = []
+    auxiliary_failures: list[str] = []
+    metrics: dict[str, float] = {}
+    selected = list(manifest.get("selected_points", ()))
+    points = list(manifest.get("points", ()))
+
+    selected_keys = [
+        (int(item["n"]), float(item["xi"]))
+        for item in selected
+        if isinstance(item, dict) and "n" in item and "xi" in item
+    ]
+    point_map = {
+        (int(item["point"]["n"]), float(item["point"]["xi"])): item
+        for item in points
+        if isinstance(item, dict)
+        and isinstance(item.get("point"), dict)
+        and "n" in item["point"]
+        and "xi" in item["point"]
+    }
+    complete = bool(
+        manifest.get("complete", False)
+        and len(selected_keys) == 9
+        and len(set(selected_keys)) == 9
+        and len(point_map) == 9
+        and set(selected_keys) == set(point_map)
+        and all(sum(key[0] == n for key in selected_keys) == 3 for n in (1, 2, 3))
+    )
+    if not complete:
+        dark_failures.append("heat-valve manifest is incomplete")
+
+    drive_frequencies = [
+        float(item["model"]["drive_frequency"])
+        for item in point_map.values()
+    ]
+    if point_map and not _same_numeric(drive_frequencies):
+        dark_failures.append("fixed drive frequency was not held constant")
+
+    fixed_controls = (
+        ("j", [float(item["model"]["j"]) for item in point_map.values()]),
+        (
+            "omega",
+            [float(item["model"]["omega"]) for item in point_map.values()],
+        ),
+        (
+            "alpha",
+            [float(item["bath"]["alpha"]) for item in point_map.values()],
+        ),
+        (
+            "cutoff",
+            [float(item["bath"]["cutoff"]) for item in point_map.values()],
+        ),
+        (
+            "temperature",
+            [float(item["bath"]["temperature"]) for item in point_map.values()],
+        ),
+    )
+    for label, values in fixed_controls:
+        if point_map and not _same_numeric(values):
+            dark_failures.append(f"fixed physical control {label} changed")
+    for label in ("normalization", "drive_normalization"):
+        labels = {str(item["model"][label]) for item in point_map.values()}
+        if point_map and len(labels) != 1:
+            dark_failures.append(f"fixed physical control {label} changed")
+
+    for key, item in point_map.items():
+        label = f"N={key[0]}, xi={key[1]:g}"
+        if not bool(item.get("converged", False)):
+            dark_failures.append(f"{label}: convergence gate failed")
+        diagnostics = item.get("diagnostics", {})
+        if (
+            float(diagnostics.get("trace_error", float("inf"))) > 5e-3
+            or float(diagnostics.get("hermiticity_error", float("inf"))) > 5e-3
+            or float(
+                diagnostics.get("minimum_density_eigenvalue", -float("inf"))
+            )
+            < -5e-3
+            or float(diagnostics.get("fixed_point_residual", float("inf")))
+            > 1e-3
+            or float(diagnostics.get("connected_tail", float("inf"))) > 5e-2
+        ):
+            dark_failures.append(f"{label}: physical diagnostics gate failed")
+        reconstruction = float(
+            item.get("pole_fit", {}).get(
+                "reconstruction_residual",
+                float("inf"),
+            )
+        )
+        if reconstruction > 5e-2:
+            dark_failures.append(f"{label}: pole reconstruction residual exceeds 5%")
+        for pole in item.get("poles", ()):
+            if float(pole.get("eigenpair_residual", float("inf"))) > 1e-8:
+                dark_failures.append(f"{label}: eigenpair residual exceeds 1e-8")
+                break
+        for pole in item.get("poles", ()):
+            modulus = float(
+                pole.get("eigenvalue", {}).get("abs", float("inf"))
+            )
+            if modulus > 1 + 1e-6:
+                dark_failures.append(f"{label}: transfer pole leaves the unit disk")
+                break
+
+    heat_contrasts: dict[int, float] = {}
+    for n in (1, 2, 3):
+        ordered_keys = [key for key in selected_keys if key[0] == n]
+        if len(ordered_keys) != 3 or any(key not in point_map for key in ordered_keys):
+            continue
+        lower, minimum, upper = (point_map[key] for key in ordered_keys)
+        lower_heat = float(lower.get("integrated_absolute_heat", float("nan")))
+        minimum_heat = float(minimum.get("integrated_absolute_heat", float("nan")))
+        upper_heat = float(upper.get("integrated_absolute_heat", float("nan")))
+        heat_ratio = max(
+            _ratio(minimum_heat, lower_heat),
+            _ratio(minimum_heat, upper_heat),
+        )
+        heat_contrast = _ratio(min(lower_heat, upper_heat), minimum_heat)
+        heat_contrasts[n] = heat_contrast
+        metrics[f"heat_ratio_n{n}"] = heat_ratio
+        metrics[f"heat_contrast_n{n}"] = heat_contrast
+        if not np.isfinite(heat_ratio) or heat_ratio > 0.1:
+            dark_failures.append(
+                f"N={n}: tenfold heat suppression against both flanks failed"
+            )
+
+        lower_residue = float(
+            lower.get("visible_residue_weight", float("nan"))
+        )
+        minimum_residue = float(
+            minimum.get("visible_residue_weight", float("nan"))
+        )
+        upper_residue = float(
+            upper.get("visible_residue_weight", float("nan"))
+        )
+        residue_ratio = max(
+            _ratio(minimum_residue, lower_residue),
+            _ratio(minimum_residue, upper_residue),
+        )
+        metrics[f"residue_ratio_n{n}"] = residue_ratio
+        if not np.isfinite(residue_ratio) or residue_ratio > 0.1:
+            dark_failures.append(
+                f"N={n}: tenfold residue suppression against both flanks failed"
+            )
+
+    dark_channel_passed = complete and not dark_failures
+    amplification = bool(
+        dark_channel_passed
+        and 1 in heat_contrasts
+        and 3 in heat_contrasts
+        and heat_contrasts[3] >= 5 * heat_contrasts[1]
+    )
+    if dark_channel_passed and not amplification:
+        auxiliary_failures.append(
+            "many-body amplification did not exceed the fivefold contrast gate"
+        )
+    markov_payoff = bool(
+        manifest.get("markov_comparison", {}).get("passed", False)
+    )
+    return HeatValveAudit(
+        complete=complete,
+        dark_channel_passed=dark_channel_passed,
+        many_body_amplification_passed=amplification,
+        markov_payoff_passed=markov_payoff,
+        failures=tuple(dark_failures + auxiliary_failures),
+        metrics=metrics,
+    )
diff --git a/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/influence.py b/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/influence.py
new file mode 100644
index 000000000..ca3a4fbd3
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/influence.py
@@ -0,0 +1,71 @@
+"""Discrete Feynman-Vernon coefficients for piecewise-constant paths."""
+
+from __future__ import annotations
+
+from collections.abc import Callable
+from dataclasses import dataclass
+
+import numpy as np
+from numpy.typing import NDArray
+from scipy.integrate import quad
+
+from .bath import bath_correlation
+from .config import BathConfig
+
+
+@dataclass(frozen=True)
+class InfluenceCoefficients:
+    values: NDArray[np.complex128]
+    dt: float
+    quadrature_error: float
+    tail_bound: float
+
+
+def _integrate_complex(
+    function: Callable[[float], complex], low: float, high: float
+) -> tuple[complex, float]:
+    real, real_error = quad(lambda x: np.real(function(x)), low, high, epsabs=2e-11)
+    imag, imag_error = quad(lambda x: np.imag(function(x)), low, high, epsabs=2e-11)
+    return complex(real, imag), float(real_error + imag_error)
+
+
+def discretize_influence(
+    bath: BathConfig,
+    dt: float,
+    memory_steps: int,
+) -> InfluenceCoefficients:
+    """Cell-integrate the bath correlation.
+
+    ``eta[0]`` uses the causal triangle in a single time cell. ``eta[k>0]``
+    uses two full cells separated by ``k`` timesteps.
+    """
+    if dt <= 0 or memory_steps < 1:
+        raise ValueError("dt and memory_steps must be positive")
+    values = np.empty(memory_steps + 1, dtype=np.complex128)
+    error = 0.0
+
+    # eta_0 = integral_0^dt du integral_0^u dv C(u-v)
+    value0, error0 = _integrate_complex(
+        lambda tau: (dt - tau) * bath_correlation(tau, bath), 0, dt
+    )
+    values[0] = value0
+    error += error0
+
+    for lag in range(1, memory_steps + 1):
+        # Difference of two points from equal-width cells has triangular weight.
+        center = lag * dt
+
+        def integrand(offset: float, center: float = center) -> complex:
+            return (dt - abs(offset)) * bath_correlation(center + offset, bath)
+
+        value, item_error = _integrate_complex(
+            integrand,
+            -dt,
+            dt,
+        )
+        values[lag] = value
+        error += item_error
+
+    memory_time = memory_steps * dt
+    tail_bound = bath.alpha / max(1 / bath.cutoff, memory_time)
+    return InfluenceCoefficients(values, dt, error, float(tail_bound))
diff --git a/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/io.py b/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/io.py
new file mode 100644
index 000000000..481a7bd90
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/io.py
@@ -0,0 +1,60 @@
+"""Result serialization and provenance."""
+
+from __future__ import annotations
+
+import hashlib
+import json
+import platform
+import subprocess
+from datetime import UTC, datetime
+from pathlib import Path
+from typing import Any, cast
+
+import numpy as np
+
+from . import __version__
+
+
+def _git_commit() -> str:
+    try:
+        return subprocess.check_output(
+            ["git", "rev-parse", "HEAD"], text=True, stderr=subprocess.DEVNULL
+        ).strip()
+    except (OSError, subprocess.CalledProcessError):
+        return "unknown"
+
+
+def write_result(path: Path, payload: dict[str, Any]) -> None:
+    canonical = json.dumps(payload, sort_keys=True, default=str)
+    envelope = {
+        "schema_version": 1,
+        "config_hash": hashlib.sha256(canonical.encode()).hexdigest()[:16],
+        "created_utc": datetime.now(UTC).isoformat(),
+        "environment": {
+            "python": platform.python_version(),
+            "numpy": np.__version__,
+            "package": __version__,
+            "git_commit": _git_commit(),
+        },
+        **payload,
+    }
+    path.parent.mkdir(parents=True, exist_ok=True)
+    path.write_text(json.dumps(envelope, indent=2, sort_keys=True), encoding="utf-8")
+
+
+def read_result(path: Path) -> dict[str, Any]:
+    result = json.loads(path.read_text(encoding="utf-8"))
+    required = {
+        "schema_version",
+        "config_hash",
+        "created_utc",
+        "environment",
+        "method",
+        "converged",
+        "diagnostics",
+        "data",
+    }
+    missing = required - set(result)
+    if missing:
+        raise ValueError(f"{path} is missing keys: {sorted(missing)}")
+    return cast(dict[str, Any], result)
diff --git a/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/model_comparison.py b/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/model_comparison.py
new file mode 100644
index 000000000..3a5453819
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/model_comparison.py
@@ -0,0 +1,97 @@
+"""Explicit common-bath normalization and counterterm model variants."""
+
+from __future__ import annotations
+
+from dataclasses import asdict, dataclass
+from typing import Any
+
+import numpy as np
+from numpy.typing import NDArray
+
+from .config import BathConfig, ModelConfig, Normalization
+from .models import coupling_operator, ising_hamiltonian
+from .operators import ComplexMatrix
+
+
+@dataclass(frozen=True)
+class ModelVariant:
+    name: str
+    config: ModelConfig
+    metadata: dict[str, Any]
+
+
+def _variant(
+    *,
+    name: str,
+    n: int,
+    j: float,
+    omega: float,
+    drive_amplitude: float,
+    drive_frequency: float,
+    normalization: Normalization,
+    counterterm: bool,
+    bath: BathConfig,
+) -> ModelVariant:
+    strength = bath.alpha * bath.cutoff if counterterm else 0.0
+    config = ModelConfig(
+        n=n,
+        j=j,
+        omega=omega,
+        drive_amplitude=drive_amplitude,
+        drive_frequency=drive_frequency,
+        normalization=normalization,
+        counterterm=counterterm,
+        counterterm_strength=strength,
+    )
+    return ModelVariant(
+        name,
+        config,
+        {
+            "normalization": normalization,
+            "eta": config.eta,
+            "counterterm": counterterm,
+            "counterterm_strength": strength,
+            "bath": asdict(bath),
+        },
+    )
+
+
+def model_variants(
+    *,
+    n: int,
+    j: float,
+    bath: BathConfig,
+    omega: float = 1.0,
+    drive_amplitude: float = 0.2,
+    drive_frequency: float = 1.0,
+) -> tuple[ModelVariant, ...]:
+    """Return the four predeclared bounded/Kac and counterterm choices."""
+    return tuple(
+        _variant(
+            name=f"{normalization}_{'ct' if counterterm else 'no_ct'}",
+            n=n,
+            j=j,
+            omega=omega,
+            drive_amplitude=drive_amplitude,
+            drive_frequency=drive_frequency,
+            normalization=normalization,
+            counterterm=counterterm,
+            bath=bath,
+        )
+        for normalization in ("bounded", "kac")
+        for counterterm in (False, True)
+    )
+
+
+def variant_operators(variant: ModelVariant) -> tuple[ComplexMatrix, ComplexMatrix]:
+    return ising_hamiltonian(variant.config), coupling_operator(variant.config)
+
+
+def diagnostic_heat_rescaling(
+    heat: NDArray[np.float64], eta: float
+) -> tuple[NDArray[np.float64], NDArray[np.float64]]:
+    """Return raw heat and a separately labeled eta-squared diagnostic."""
+    if eta <= 0:
+        raise ValueError("eta must be positive")
+    raw = np.array(heat, dtype=np.float64, copy=True)
+    return raw, raw / eta**2
diff --git a/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/models.py b/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/models.py
new file mode 100644
index 000000000..40a06c4a2
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/models.py
@@ -0,0 +1,38 @@
+"""Hamiltonians for the open-boundary driven transverse-field Ising model."""
+
+from __future__ import annotations
+
+import numpy as np
+
+from .config import ModelConfig
+from .operators import ComplexMatrix, collective_operator, product_operator
+
+
+def coupling_operator(config: ModelConfig) -> ComplexMatrix:
+    return collective_operator("z", config.n, config.eta)
+
+
+def drive_operator(config: ModelConfig) -> ComplexMatrix:
+    return collective_operator("z", config.n, config.drive_eta)
+
+
+def ising_hamiltonian(config: ModelConfig) -> ComplexMatrix:
+    dimension = 2**config.n
+    hamiltonian = np.zeros((dimension, dimension), dtype=np.complex128)
+    for site in range(config.n - 1):
+        hamiltonian -= config.j * product_operator({site: "z", site + 1: "z"}, config.n)
+    hamiltonian += (config.omega / 2) * collective_operator("x", config.n)
+    if config.counterterm:
+        s = coupling_operator(config)
+        hamiltonian += config.counterterm_strength * (s @ s)
+    return hamiltonian
+
+
+def driven_hamiltonian(config: ModelConfig, time: float) -> ComplexMatrix:
+    return np.asarray(
+        ising_hamiltonian(config)
+        + config.drive_amplitude
+        * np.cos(config.drive_frequency * time)
+        * drive_operator(config),
+        dtype=np.complex128,
+    )
diff --git a/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/n2_heat.py b/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/n2_heat.py
new file mode 100644
index 000000000..c8bef4b64
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/n2_heat.py
@@ -0,0 +1,366 @@
+"""Reusable interacting-triplet N=2 PT-TEMPO heat-current points."""
+
+from __future__ import annotations
+
+import subprocess
+from dataclasses import asdict, dataclass
+from typing import Any, Literal
+
+import numpy as np
+
+from .backends.pt_tempo import PtTempoBackend
+from .backends.uniform_tempo import UniformTempoBackend, UniformTempoControls
+from .config import BathConfig, ModelConfig, Normalization
+from .convergence import ConvergenceCache, fingerprint
+from .heat_current import heat_current_spectrum
+from .models import coupling_operator, ising_hamiltonian
+from .operators import ComplexMatrix
+from .spectra import diagonalize, transitions
+from .symmetry import n2_sectors, project
+
+
+@dataclass(frozen=True)
+class N2HeatPoint:
+    j: float = 0.5
+    backend: Literal["oqupy", "uniform_tempo"] = "oqupy"
+    omega: float = 1.0
+    drive_amplitude: float = 0.2
+    drive_ratio: float = 1.0
+    drive_frequency: float | None = None
+    normalization: Normalization = "bounded"
+    counterterm: bool = False
+    alpha: float = 0.1
+    cutoff: float = 2.5
+    temperature: float = 0.0
+    steps_per_period: int = 16
+    steady_periods: int = 20
+    delay_periods: int = 4
+    memory_steps: int = 4
+    epsrel: float = 1e-5
+    frequency_max: float = 3.0
+    frequency_points: int = 401
+    phase_samples: int = 4
+    uniform_auto_nc: bool = True
+    uniform_memory_cutoff: int = 100_000
+    uniform_low_rank_svd: bool = False
+    uniform_truncation: Literal["rel", "abs"] = "rel"
+    uniform_cap_rank: int = 100_000
+    uniform_max_rank: int = 100_000
+
+    def __post_init__(self) -> None:
+        if self.backend not in ("oqupy", "uniform_tempo"):
+            raise ValueError("backend must be 'oqupy' or 'uniform_tempo'")
+        if self.drive_ratio <= 0 or self.steps_per_period < 2:
+            raise ValueError("invalid drive or timestep controls")
+        if self.steady_periods < 1 or self.delay_periods < 1:
+            raise ValueError("period counts must be positive")
+        if self.memory_steps < 1 or not 0 < self.epsrel < 1:
+            raise ValueError("invalid process-tensor controls")
+        if (
+            self.phase_samples < 2
+            or self.phase_samples > self.steps_per_period
+            or self.steps_per_period % self.phase_samples != 0
+        ):
+            raise ValueError("phase_samples must divide steps_per_period")
+        if self.uniform_memory_cutoff < 1:
+            raise ValueError("uniform_memory_cutoff must be positive")
+        if self.uniform_truncation not in ("rel", "abs"):
+            raise ValueError("uniform_truncation must be 'rel' or 'abs'")
+        if (
+            self.uniform_cap_rank < 1
+            or self.uniform_max_rank < self.uniform_cap_rank
+        ):
+            raise ValueError("invalid uniform rank limits")
+
+
+@dataclass(frozen=True)
+class PreparedN2:
+    point: N2HeatPoint
+    model: ModelConfig
+    bath: BathConfig
+    h0: ComplexMatrix
+    coupling: ComplexMatrix
+    bright_gap: float
+
+    @property
+    def dimension(self) -> int:
+        return int(self.h0.shape[0])
+
+
+def _bright_gap(hamiltonian: ComplexMatrix, coupling: ComplexMatrix) -> float:
+    spectrum = diagonalize(hamiltonian)
+    candidates = [
+        item.frequency
+        for item in transitions(spectrum, spectrum, coupling)
+        if item.source == 0 and item.frequency > 1e-12
+    ]
+    return float(f"{min(candidates):.14g}")
+
+
+def prepare_n2_triplet(point: N2HeatPoint) -> PreparedN2:
+    provisional = ModelConfig(
+        n=2,
+        j=point.j,
+        omega=point.omega,
+        drive_amplitude=point.drive_amplitude,
+        drive_frequency=point.omega,
+        normalization=point.normalization,
+        counterterm=point.counterterm,
+        counterterm_strength=(
+            point.alpha * point.cutoff if point.counterterm else 0.0
+        ),
+    )
+    _, triplet = n2_sectors()
+    h0 = project(ising_hamiltonian(provisional), triplet)
+    coupling = project(coupling_operator(provisional), triplet)
+    gap = _bright_gap(h0, coupling)
+    frequency = (
+        point.drive_frequency
+        if point.drive_frequency is not None
+        else point.drive_ratio * gap
+    )
+    model = ModelConfig(
+        n=2,
+        j=point.j,
+        omega=point.omega,
+        drive_amplitude=point.drive_amplitude,
+        drive_frequency=frequency,
+        normalization=point.normalization,
+        counterterm=point.counterterm,
+        counterterm_strength=provisional.counterterm_strength,
+    )
+    return PreparedN2(
+        point,
+        model,
+        BathConfig(point.alpha, point.cutoff, point.temperature),
+        h0,
+        coupling,
+        gap,
+    )
+
+
+def _complex_values(values: np.ndarray[Any, np.dtype[np.complex128]]) -> dict[str, Any]:
+    return {
+        "real": np.real(values).astype(float).tolist(),
+        "imag": np.imag(values).astype(float).tolist(),
+    }
+
+
+def _git_commit() -> str:
+    try:
+        return subprocess.check_output(
+            ["git", "rev-parse", "HEAD"],
+            text=True,
+            stderr=subprocess.DEVNULL,
+        ).strip()
+    except (OSError, subprocess.CalledProcessError):
+        return "unknown"
+
+
+def run_n2_heat_point(
+    point: N2HeatPoint,
+    cache: ConvergenceCache | None = None,
+    *,
+    commit: str | None = None,
+) -> dict[str, Any]:
+    prepared = prepare_n2_triplet(point)
+    revision = _git_commit() if commit is None else commit
+    key = fingerprint(
+        {
+            "experiment": f"n2_triplet_{point.backend}_heat",
+            "point": asdict(point),
+            "model": asdict(prepared.model),
+            "bath": asdict(prepared.bath),
+        },
+        revision,
+    )
+    if cache is not None and cache.contains(key):
+        return cache.load(key)
+    model_hash = fingerprint(
+        {
+            "model": asdict(prepared.model),
+            "bath": asdict(prepared.bath),
+            "sector": "triplet",
+        },
+        "scientific-model-v1",
+    )
+    projected_model_hash = fingerprint(
+        {
+            "h0": _complex_values(prepared.h0),
+            "coupling": _complex_values(prepared.coupling),
+            "drive_amplitude": prepared.model.drive_amplitude,
+            "drive_frequency": prepared.model.drive_frequency,
+            "bath": asdict(prepared.bath),
+        },
+        "projected-open-system-v1",
+    )
+    if point.backend == "uniform_tempo":
+        controls = UniformTempoControls(
+            steps_per_period=point.steps_per_period,
+            tolerance=point.epsrel,
+            phase_samples=point.phase_samples,
+            delay_periods=point.delay_periods,
+            auto_nc=point.uniform_auto_nc,
+            memory_cutoff=point.uniform_memory_cutoff,
+            low_rank_svd=point.uniform_low_rank_svd,
+            truncation=point.uniform_truncation,
+            cap_rank=point.uniform_cap_rank,
+            max_rank=point.uniform_max_rank,
+        )
+        uniform_run = UniformTempoBackend(
+            tensor_cache_directory=(
+                None if cache is None else cache.directory / "process_tensors"
+            )
+        ).run_periodic(
+            prepared.h0,
+            prepared.coupling,
+            prepared.model,
+            prepared.bath,
+            controls,
+        )
+        correlation = uniform_run.correlation
+        frequencies = np.linspace(
+            0,
+            point.frequency_max,
+            point.frequency_points,
+        )
+        heat = heat_current_spectrum(correlation, prepared.bath, frequencies)
+        connected_tail = float(abs(correlation.connected[-1]))
+        diagnostics = {
+            **uniform_run.diagnostics,
+            **uniform_run.metadata,
+            "phase_residual": uniform_run.diagnostics["fixed_point_residual"],
+            "connected_tail_amplitude": connected_tail,
+            "tau_max": float(correlation.delays[-1]),
+            "epsrel": point.epsrel,
+            "phase_samples": point.phase_samples,
+        }
+        physical = bool(
+            uniform_run.diagnostics["trace_error"] <= 5e-3
+            and uniform_run.diagnostics["hermiticity_error"] <= 5e-3
+            and uniform_run.diagnostics["minimum_density_eigenvalue"] >= -5e-3
+            and uniform_run.diagnostics["fixed_point_residual"] <= 1e-3
+            and connected_tail <= 5e-2
+        )
+        uniform_payload: dict[str, Any] = {
+            "method": uniform_run.method,
+            "sector": "triplet",
+            "model": asdict(prepared.model),
+            "model_hash": model_hash,
+            "projected_model_hash": projected_model_hash,
+            "bath": asdict(prepared.bath),
+            "point": asdict(point),
+            "bright_gap": prepared.bright_gap,
+            "dimension": prepared.dimension,
+            "source_commit": revision,
+            "converged": physical,
+            "diagnostics": diagnostics,
+            "phase_state": _complex_values(uniform_run.floquet_state),
+            "phase_states": _complex_values(uniform_run.phase_states),
+            "correlation": {
+                "delay": correlation.delays.tolist(),
+                "total": _complex_values(correlation.total),
+                "connected": _complex_values(correlation.connected),
+                "coherent": correlation.coherent.tolist(),
+            },
+            "frequency": heat.frequencies.tolist(),
+            "continuous": heat.continuous.tolist(),
+            "delta_peaks": [asdict(peak) for peak in heat.delta_peaks],
+            "fingerprint": key,
+        }
+        if cache is not None:
+            cache.store(key, uniform_payload)
+            return cache.load(key)
+        return {"complete": True, **uniform_payload}
+
+    def hamiltonian(time: float) -> ComplexMatrix:
+        return np.asarray(
+            prepared.h0
+            + prepared.model.drive_amplitude
+            * np.cos(prepared.model.drive_frequency * time)
+            * prepared.coupling,
+            dtype=np.complex128,
+        )
+
+    ground = diagonalize(prepared.h0).states[:, 0]
+    initial = np.outer(ground, ground.conj())
+    dt = prepared.model.period / point.steps_per_period
+    phase_start = point.steady_periods * point.steps_per_period
+    delay_steps = point.delay_periods * point.steps_per_period
+    total_steps = phase_start + point.steps_per_period + delay_steps
+    backend = PtTempoBackend()
+    run = backend.run(
+        hamiltonian,
+        prepared.coupling,
+        initial,
+        prepared.bath,
+        dt,
+        total_steps,
+        point.memory_steps,
+        point.epsrel,
+    )
+    states = run.result.density_matrices
+    phase_state = states[phase_start]
+    phase_residual = float(
+        np.linalg.norm(phase_state - states[phase_start - point.steps_per_period])
+    )
+    offsets = list(
+        range(0, point.steps_per_period, point.steps_per_period // point.phase_samples)
+    )
+    correlation = backend.period_averaged_correlation(
+        run,
+        prepared.coupling,
+        phase_start,
+        point.steps_per_period,
+        delay_steps,
+        prepared.model.drive_frequency,
+        offsets,
+    )
+    frequencies = np.linspace(0, point.frequency_max, point.frequency_points)
+    heat = heat_current_spectrum(correlation, prepared.bath, frequencies)
+    diagnostics = {
+        **run.result.diagnostics,
+        "phase_residual": phase_residual,
+        "connected_tail_amplitude": float(abs(correlation.connected[-1])),
+        "dt": dt,
+        "tau_max": float(correlation.delays[-1]),
+        "memory_steps": point.memory_steps,
+        "epsrel": point.epsrel,
+        "phase_samples": point.phase_samples,
+    }
+    payload: dict[str, Any] = {
+        "method": "pt_tempo_multitime",
+        "sector": "triplet",
+        "model": asdict(prepared.model),
+        "model_hash": model_hash,
+        "projected_model_hash": projected_model_hash,
+        "bath": asdict(prepared.bath),
+        "point": asdict(point),
+        "bright_gap": prepared.bright_gap,
+        "dimension": prepared.dimension,
+        "source_commit": revision,
+        "converged": bool(
+            run.result.converged
+            and phase_residual < 2e-3
+            and float(diagnostics["connected_tail_amplitude"]) < 5e-2
+        ),
+        "diagnostics": diagnostics,
+        "phase_state": _complex_values(phase_state),
+        "phase_states": _complex_values(
+            states[phase_start : phase_start + point.steps_per_period]
+        ),
+        "correlation": {
+            "delay": correlation.delays.tolist(),
+            "total": _complex_values(correlation.total),
+            "connected": _complex_values(correlation.connected),
+            "coherent": correlation.coherent.tolist(),
+        },
+        "frequency": heat.frequencies.tolist(),
+        "continuous": heat.continuous.tolist(),
+        "delta_peaks": [asdict(peak) for peak in heat.delta_peaks],
+        "fingerprint": key,
+    }
+    if cache is not None:
+        cache.store(key, payload)
+        return cache.load(key)
+    return {"complete": True, **payload}
diff --git a/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/n3_heat.py b/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/n3_heat.py
new file mode 100644
index 000000000..acf7d5a74
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/n3_heat.py
@@ -0,0 +1,430 @@
+"""Reusable reflection-resolved N=3 PT-TEMPO heat-current points."""
+
+from __future__ import annotations
+
+import subprocess
+from dataclasses import asdict, dataclass
+from typing import Any, Literal
+
+import numpy as np
+from numpy.typing import NDArray
+from scipy.integrate import trapezoid
+
+from .backends.pt_tempo import PtTempoBackend
+from .backends.uniform_tempo import UniformTempoBackend, UniformTempoControls
+from .config import BathConfig, DriveNormalization, ModelConfig, Normalization
+from .convergence import ConvergenceCache, fingerprint
+from .heat_current import heat_current_spectrum
+from .models import coupling_operator, drive_operator, ising_hamiltonian
+from .operators import ComplexMatrix
+from .spectra import diagonalize, transitions
+from .symmetry import Sector, project, reflection_sectors
+
+
+@dataclass(frozen=True)
+class N3HeatPoint:
+    """Complete controls for one reflection-resolved N=3 or N=4 calculation."""
+
+    n: Literal[3, 4] = 3
+    j: float = 0.5
+    sector: Literal["even", "odd"] = "even"
+    backend: Literal["oqupy", "uniform_tempo"] = "oqupy"
+    omega: float = 1.0
+    drive_amplitude: float = 0.2
+    drive_ratio: float = 1.0
+    drive_frequency: float | None = None
+    normalization: Normalization = "bounded"
+    drive_normalization: DriveNormalization = "coupling"
+    counterterm: bool = False
+    alpha: float = 0.1
+    cutoff: float = 2.5
+    temperature: float = 0.0
+    steps_per_period: int = 12
+    steady_periods: int = 30
+    delay_periods: int = 3
+    memory_steps: int = 3
+    epsrel: float = 1e-5
+    frequency_max: float = 3.0
+    frequency_points: int = 401
+    phase_samples: int | None = None
+    uniform_auto_nc: bool = True
+    uniform_memory_cutoff: int = 100_000
+    uniform_low_rank_svd: bool = False
+    uniform_truncation: Literal["rel", "abs"] = "rel"
+    uniform_cap_rank: int = 100_000
+    uniform_max_rank: int = 100_000
+
+    def __post_init__(self) -> None:
+        if self.n not in (3, 4):
+            raise ValueError("n must be 3 or 4")
+        if self.sector not in ("even", "odd"):
+            raise ValueError("sector must be 'even' or 'odd'")
+        if self.backend not in ("oqupy", "uniform_tempo"):
+            raise ValueError("backend must be 'oqupy' or 'uniform_tempo'")
+        if self.drive_ratio <= 0:
+            raise ValueError("drive_ratio must be positive")
+        if self.steps_per_period < 2 or self.steady_periods < 1:
+            raise ValueError("insufficient time discretization")
+        if self.delay_periods < 1 or self.memory_steps < 1:
+            raise ValueError("delay and memory controls must be positive")
+        if not 0 < self.epsrel < 1:
+            raise ValueError("epsrel must lie between zero and one")
+        if self.frequency_max <= 0 or self.frequency_points < 2:
+            raise ValueError("invalid frequency grid")
+        if self.phase_samples is not None and (
+            self.phase_samples < 2
+            or self.phase_samples > self.steps_per_period
+            or self.steps_per_period % self.phase_samples != 0
+        ):
+            raise ValueError("phase_samples must divide steps_per_period")
+        if self.uniform_memory_cutoff < 1:
+            raise ValueError("uniform_memory_cutoff must be positive")
+        if self.uniform_truncation not in ("rel", "abs"):
+            raise ValueError("uniform_truncation must be 'rel' or 'abs'")
+        if (
+            self.uniform_cap_rank < 1
+            or self.uniform_max_rank < self.uniform_cap_rank
+        ):
+            raise ValueError("invalid uniform rank limits")
+
+
+@dataclass(frozen=True)
+class PreparedN3:
+    point: N3HeatPoint
+    model: ModelConfig
+    bath: BathConfig
+    sector: Sector
+    h0: ComplexMatrix
+    coupling: ComplexMatrix
+    drive: ComplexMatrix
+    bright_gap: float
+
+    @property
+    def dimension(self) -> int:
+        return int(self.h0.shape[0])
+
+
+def _primary_bright_gap(
+    hamiltonian: ComplexMatrix, coupling: ComplexMatrix
+) -> float:
+    spectrum = diagonalize(hamiltonian)
+    records = transitions(spectrum, spectrum, coupling)
+    candidates = [
+        record.frequency
+        for record in records
+        if record.source == 0 and record.frequency > 1e-12
+    ]
+    if not candidates:
+        raise ValueError("sector has no bright transition from its ground state")
+    # Hermitian eigensolvers may differ in the last one or two binary digits.
+    # Canonicalizing a derived control prevents scientifically identical jobs
+    # from receiving different content-addressed cache keys.
+    return float(f"{min(candidates):.14g}")
+
+
+def prepare_n3_sector(point: N3HeatPoint) -> PreparedN3:
+    """Project the model exactly and select its primary bright resonance."""
+    provisional = ModelConfig(
+        n=point.n,
+        j=point.j,
+        omega=point.omega,
+        drive_amplitude=point.drive_amplitude,
+        drive_frequency=point.omega,
+        normalization=point.normalization,
+        drive_normalization=point.drive_normalization,
+        counterterm=point.counterterm,
+        counterterm_strength=(
+            point.alpha * point.cutoff if point.counterterm else 0.0
+        ),
+    )
+    odd, even = reflection_sectors(point.n)
+    sector = even if point.sector == "even" else odd
+    h0 = project(ising_hamiltonian(provisional), sector)
+    coupling = project(coupling_operator(provisional), sector)
+    drive = project(drive_operator(provisional), sector)
+    bright_gap = _primary_bright_gap(h0, coupling)
+    drive_frequency = (
+        point.drive_frequency
+        if point.drive_frequency is not None
+        else point.drive_ratio * bright_gap
+    )
+    model = ModelConfig(
+        n=point.n,
+        j=point.j,
+        omega=point.omega,
+        drive_amplitude=point.drive_amplitude,
+        drive_frequency=drive_frequency,
+        normalization=point.normalization,
+        drive_normalization=point.drive_normalization,
+        counterterm=point.counterterm,
+        counterterm_strength=provisional.counterterm_strength,
+    )
+    bath = BathConfig(point.alpha, point.cutoff, point.temperature)
+    return PreparedN3(point, model, bath, sector, h0, coupling, drive, bright_gap)
+
+
+def _git_commit() -> str:
+    try:
+        return subprocess.check_output(
+            ["git", "rev-parse", "HEAD"],
+            text=True,
+            stderr=subprocess.DEVNULL,
+        ).strip()
+    except (OSError, subprocess.CalledProcessError):
+        return "unknown"
+
+
+def _complex_values(values: NDArray[np.complex128]) -> dict[str, list[float]]:
+    return {
+        "real": np.real(values).astype(float).tolist(),
+        "imag": np.imag(values).astype(float).tolist(),
+    }
+
+
+def run_n3_heat_point(
+    point: N3HeatPoint,
+    cache: ConvergenceCache | None = None,
+    *,
+    commit: str | None = None,
+) -> dict[str, Any]:
+    """Run or restore one complete PT-TEMPO steady/correlation/heat pipeline."""
+    prepared = prepare_n3_sector(point)
+    revision = _git_commit() if commit is None else commit
+    key = fingerprint(
+        {
+            "experiment": f"n{point.n}_{point.backend}_heat",
+            "point": asdict(point),
+            "model": asdict(prepared.model),
+            "bath": asdict(prepared.bath),
+        },
+        revision,
+    )
+    model_hash = fingerprint(
+        {
+            "model": asdict(prepared.model),
+            "bath": asdict(prepared.bath),
+            "sector": point.sector,
+        },
+        "scientific-model-v1",
+    )
+    projected_model_hash = fingerprint(
+        {
+            "h0": _complex_values(prepared.h0),
+            "coupling": _complex_values(prepared.coupling),
+            "drive": _complex_values(prepared.drive),
+            "drive_amplitude": prepared.model.drive_amplitude,
+            "drive_frequency": prepared.model.drive_frequency,
+            "bath": asdict(prepared.bath),
+        },
+        "projected-open-system-v1",
+    )
+    if cache is not None and cache.contains(key):
+        return cache.load(key)
+
+    model = prepared.model
+    if point.backend == "uniform_tempo":
+        phase_samples = (
+            point.steps_per_period
+            if point.phase_samples is None
+            else point.phase_samples
+        )
+        controls = UniformTempoControls(
+            steps_per_period=point.steps_per_period,
+            tolerance=point.epsrel,
+            phase_samples=phase_samples,
+            delay_periods=point.delay_periods,
+            auto_nc=point.uniform_auto_nc,
+            memory_cutoff=point.uniform_memory_cutoff,
+            low_rank_svd=point.uniform_low_rank_svd,
+            truncation=point.uniform_truncation,
+            cap_rank=point.uniform_cap_rank,
+            max_rank=point.uniform_max_rank,
+        )
+        uniform_run = UniformTempoBackend(
+            tensor_cache_directory=(
+                None if cache is None else cache.directory / "process_tensors"
+            )
+        ).run_periodic(
+            prepared.h0,
+            prepared.coupling,
+            model,
+            prepared.bath,
+            controls,
+            drive_operator=prepared.drive,
+        )
+        correlation = uniform_run.correlation
+        frequencies = np.linspace(
+            0.0,
+            point.frequency_max,
+            point.frequency_points,
+        )
+        heat = heat_current_spectrum(correlation, prepared.bath, frequencies)
+        connected_tail = float(abs(correlation.connected[-1]))
+        diagnostics = {
+            **uniform_run.diagnostics,
+            **uniform_run.metadata,
+            "phase_residual": uniform_run.diagnostics["fixed_point_residual"],
+            "connected_tail_amplitude": connected_tail,
+            "tau_max": float(correlation.delays[-1]),
+            "epsrel": point.epsrel,
+            "phase_samples": phase_samples,
+        }
+        physical = bool(
+            uniform_run.diagnostics["trace_error"] <= 5e-3
+            and uniform_run.diagnostics["hermiticity_error"] <= 5e-3
+            and uniform_run.diagnostics["minimum_density_eigenvalue"] >= -5e-3
+            and uniform_run.diagnostics["fixed_point_residual"] <= 1e-3
+            and connected_tail <= 5e-2
+        )
+        uniform_payload: dict[str, Any] = {
+            "method": uniform_run.method,
+            "sector": point.sector,
+            "model": asdict(model),
+            "model_hash": model_hash,
+            "projected_model_hash": projected_model_hash,
+            "bath": asdict(prepared.bath),
+            "point": asdict(point),
+            "bright_gap": prepared.bright_gap,
+            "dimension": prepared.dimension,
+            "source_commit": revision,
+            "converged": physical,
+            "diagnostics": diagnostics,
+            "phase_state": _complex_values(uniform_run.floquet_state),
+            "phase_states": _complex_values(uniform_run.phase_states),
+            "correlation": {
+                "delay": correlation.delays.tolist(),
+                "total": _complex_values(correlation.total),
+                "connected": _complex_values(correlation.connected),
+                "coherent": correlation.coherent.tolist(),
+            },
+            "frequency": heat.frequencies.tolist(),
+            "continuous": heat.continuous.tolist(),
+            "delta_peaks": [asdict(peak) for peak in heat.delta_peaks],
+        }
+        uniform_payload["fingerprint"] = key
+        if cache is not None:
+            cache.store(key, uniform_payload)
+            return cache.load(key)
+        return {"complete": True, **uniform_payload}
+
+    def hamiltonian(time: float) -> ComplexMatrix:
+        return np.asarray(
+            prepared.h0
+            + model.drive_amplitude
+            * np.cos(model.drive_frequency * time)
+            * prepared.drive,
+            dtype=np.complex128,
+        )
+
+    ground = diagonalize(prepared.h0).states[:, 0]
+    initial = np.outer(ground, ground.conj())
+    dt = model.period / point.steps_per_period
+    phase_start = point.steady_periods * point.steps_per_period
+    delay_steps = point.delay_periods * point.steps_per_period
+    total_steps = phase_start + point.steps_per_period + delay_steps
+    backend = PtTempoBackend()
+    run = backend.run(
+        hamiltonian,
+        prepared.coupling,
+        initial,
+        prepared.bath,
+        dt,
+        total_steps,
+        point.memory_steps,
+        point.epsrel,
+    )
+    states = run.result.density_matrices
+    phase_state = states[phase_start]
+    phase_states = states[phase_start : phase_start + point.steps_per_period]
+    phase_residual = float(
+        np.linalg.norm(phase_state - states[phase_start - point.steps_per_period])
+    )
+    correlation = backend.period_averaged_correlation(
+        run,
+        prepared.coupling,
+        phase_start,
+        point.steps_per_period,
+        delay_steps,
+        model.drive_frequency,
+        (
+            None
+            if point.phase_samples is None
+            else list(
+                range(
+                    0,
+                    point.steps_per_period,
+                    point.steps_per_period // point.phase_samples,
+                )
+            )
+        ),
+    )
+    frequencies = np.linspace(0.0, point.frequency_max, point.frequency_points)
+    heat = heat_current_spectrum(correlation, prepared.bath, frequencies)
+    connected_tail = float(abs(correlation.connected[-1]))
+    payload: dict[str, Any] = {
+        "method": "pt_tempo_multitime",
+        "sector": point.sector,
+        "model": asdict(model),
+        "model_hash": model_hash,
+        "projected_model_hash": projected_model_hash,
+        "bath": asdict(prepared.bath),
+        "point": asdict(point),
+        "bright_gap": prepared.bright_gap,
+        "dimension": prepared.dimension,
+        "source_commit": revision,
+        "converged": bool(
+            run.result.converged
+            and phase_residual < 1e-3
+            and connected_tail < 5e-2
+        ),
+        "diagnostics": {
+            **run.result.diagnostics,
+            "phase_residual": phase_residual,
+            "connected_tail_amplitude": connected_tail,
+            "dt": dt,
+            "tau_max": float(correlation.delays[-1]),
+            "memory_steps": point.memory_steps,
+            "epsrel": point.epsrel,
+            "phase_samples": (
+                point.steps_per_period
+                if point.phase_samples is None
+                else point.phase_samples
+            ),
+        },
+        "phase_state": _complex_values(phase_state),
+        "phase_states": _complex_values(phase_states),
+        "correlation": {
+            "delay": correlation.delays.tolist(),
+            "total": _complex_values(correlation.total),
+            "connected": _complex_values(correlation.connected),
+            "coherent": correlation.coherent.tolist(),
+        },
+        "frequency": heat.frequencies.tolist(),
+        "continuous": heat.continuous.tolist(),
+        "delta_peaks": [asdict(peak) for peak in heat.delta_peaks],
+    }
+    payload["fingerprint"] = key
+    if cache is not None:
+        cache.store(key, payload)
+        return cache.load(key)
+    return {"complete": True, **payload}
+
+
+def compare_sector_spectra(
+    even: dict[str, Any], odd: dict[str, Any]
+) -> dict[str, float]:
+    """Return direct differences without interpolating either spectrum."""
+    even_grid = np.asarray(even["frequency"], dtype=float)
+    odd_grid = np.asarray(odd["frequency"], dtype=float)
+    if even_grid.shape != odd_grid.shape or not np.allclose(even_grid, odd_grid):
+        raise ValueError("sector frequency grids do not match")
+    even_heat = np.asarray(even["continuous"], dtype=float)
+    odd_heat = np.asarray(odd["continuous"], dtype=float)
+    difference = even_heat - odd_heat
+    denominator = float(trapezoid(abs(odd_heat), odd_grid)) + 1e-15
+    return {
+        "maximum_absolute_difference": float(np.max(abs(difference))),
+        "normalized_l1_difference": float(
+            trapezoid(abs(difference), even_grid) / denominator
+        ),
+    }
diff --git a/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/operators.py b/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/operators.py
new file mode 100644
index 000000000..7dd506418
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/operators.py
@@ -0,0 +1,70 @@
+"""Spin-half operators with a documented computational-basis convention."""
+
+from __future__ import annotations
+
+import numpy as np
+from numpy.typing import NDArray
+
+ComplexMatrix = NDArray[np.complex128]
+
+_PAULI: dict[str, ComplexMatrix] = {
+    "i": np.eye(2, dtype=np.complex128),
+    "x": np.array([[0, 1], [1, 0]], dtype=np.complex128),
+    "y": np.array([[0, -1j], [1j, 0]], dtype=np.complex128),
+    "z": np.array([[1, 0], [0, -1]], dtype=np.complex128),
+}
+
+
+def pauli(name: str) -> ComplexMatrix:
+    try:
+        return _PAULI[name.lower()].copy()
+    except KeyError as exc:
+        raise ValueError(f"unknown Pauli operator {name!r}") from exc
+
+
+def tensor_product(operators: list[ComplexMatrix]) -> ComplexMatrix:
+    if not operators:
+        raise ValueError("operators must not be empty")
+    result = np.array([[1.0 + 0.0j]])
+    for operator in operators:
+        result = np.kron(result, operator)
+    return result
+
+
+def site_operator(name: str, site: int, n: int) -> ComplexMatrix:
+    if n < 1 or not 0 <= site < n:
+        raise ValueError("site must satisfy 0 <= site < n")
+    factors = [pauli("i") for _ in range(n)]
+    factors[site] = pauli(name)
+    return tensor_product(factors)
+
+
+def product_operator(terms: dict[int, str], n: int) -> ComplexMatrix:
+    factors = [pauli("i") for _ in range(n)]
+    for site, name in terms.items():
+        if not 0 <= site < n:
+            raise ValueError("site must satisfy 0 <= site < n")
+        factors[site] = pauli(name)
+    return tensor_product(factors)
+
+
+def collective_operator(name: str, n: int, eta: float = 1.0) -> ComplexMatrix:
+    if n < 1:
+        raise ValueError("n must be positive")
+    result = np.zeros((2**n, 2**n), dtype=np.complex128)
+    for site in range(n):
+        result += site_operator(name, site, n)
+    return np.asarray(eta * result, dtype=np.complex128)
+
+
+def swap_operator(first: int, second: int, n: int) -> ComplexMatrix:
+    """Permutation matrix that swaps two spin sites."""
+    if first == second or not (0 <= first < n and 0 <= second < n):
+        raise ValueError("swap sites must be distinct valid indices")
+    out = np.zeros((2**n, 2**n), dtype=np.complex128)
+    for column in range(2**n):
+        bits = list(format(column, f"0{n}b"))
+        bits[first], bits[second] = bits[second], bits[first]
+        row = int("".join(bits), 2)
+        out[row, column] = 1
+    return out
diff --git a/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/paper_extension.py b/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/paper_extension.py
new file mode 100644
index 000000000..774fa0516
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/paper_extension.py
@@ -0,0 +1,1054 @@
+"""Resumable publication-grid orchestration for the N=3 extension."""
+
+from __future__ import annotations
+
+import copy
+import json
+import math
+from dataclasses import asdict, replace
+from pathlib import Path
+from typing import Any, Literal, cast
+
+import numpy as np
+from scipy.integrate import trapezoid
+
+from .adaptive import (
+    AdaptiveResult,
+    AdaptiveSchedule,
+    UniformAdaptiveSchedule,
+    run_adaptive,
+    run_uniform_adaptive,
+    run_uniform_compression_audit,
+)
+from .backends.floquet_markov import FloquetMarkovBackend
+from .convergence import ConvergenceCache, atomic_write_result, fingerprint
+from .correlations import superoperator_period_correlation
+from .dark_channels import (
+    dark_candidates,
+    floquet_matrix_elements,
+    harmonic_sum_rule,
+    period_variance,
+)
+from .error_map import audit_grid_manifest, build_error_record
+from .floquet import solve_floquet
+from .heat_current import heat_current_spectrum
+from .model_comparison import model_variants
+from .n2_heat import N2HeatPoint, prepare_n2_triplet, run_n2_heat_point
+from .n3_heat import N3HeatPoint, prepare_n3_sector, run_n3_heat_point
+
+ENGINE_REVISION = "215cc9dbab236d77e0a89e276e3d1ff2b0e26d1f"
+N2_ENGINE_REVISION = "f995eace0d7939b34b599cfbce6baef235f66f7f"
+PHASE_QUADRATURE_EVIDENCE = {
+    "model": "N3 reflection-even, J=0.5, M=12, K=3, epsrel=1e-5",
+    "full_phase_fingerprint": (
+        "b1903593b5ebdbfd0257697086531cf6ff4701fd2deb1153e97a1bb3aa625a0d"
+    ),
+    "three_phase_fingerprint": (
+        "50eeb896cbb9385cb96da4731544cb11a7c2567780709562fe07af2759a07455"
+    ),
+    "correlation_residual": 2.140601839862832e-4,
+    "heat_residual": 6.878849326613947e-4,
+    "maximum_absolute_heat_difference": 3.707806353551828e-5,
+}
+ExactBackend = Literal["uniform_tempo", "oqupy"]
+
+
+def publication_schedule() -> AdaptiveSchedule:
+    return AdaptiveSchedule(
+        memory_steps=(3, 4, 5),
+        steps_per_period=(12, 18),
+        epsrel=(1e-5, 3e-6),
+        state_threshold=8e-2,
+        correlation_threshold=8e-2,
+        heat_threshold=8e-2,
+        phase_threshold=2e-3,
+        trace_threshold=5e-3,
+    )
+
+
+def uniform_publication_schedule() -> UniformAdaptiveSchedule:
+    return UniformAdaptiveSchedule(
+        steps_per_period=(60, 90, 120),
+        tolerances=(3e-7, 1e-7, 3e-8),
+        phase_samples=(3, 15),
+        state_threshold=5e-2,
+        correlation_threshold=8e-2,
+        heat_threshold=8e-2,
+        phase_threshold=1e-3,
+        trace_threshold=5e-3,
+        hermiticity_threshold=5e-3,
+    )
+
+
+def uniform_error_schedule() -> UniformAdaptiveSchedule:
+    """Use a deeper compression ladder for the inexpensive N=2 error grid."""
+    return replace(
+        uniform_publication_schedule(),
+        tolerances=(3e-7, 1e-7, 3e-8, 1e-8, 3e-9),
+    )
+
+
+def n4_pilot_schedule() -> UniformAdaptiveSchedule:
+    """A bounded two-rung gate before spending publication-scale N=4 resources."""
+    return UniformAdaptiveSchedule(
+        steps_per_period=(30, 60),
+        tolerances=(1e-5, 3e-6),
+        phase_samples=(3, 15),
+        state_threshold=8e-2,
+        correlation_threshold=1e-1,
+        heat_threshold=1e-1,
+        phase_threshold=2e-3,
+        trace_threshold=5e-3,
+        hermiticity_threshold=5e-3,
+    )
+
+
+def n2_correlation_delay_periods(alpha: float) -> int:
+    """Choose a weak-coupling correlation window with a fixed decay budget."""
+    if alpha <= 0:
+        raise ValueError("alpha must be positive")
+    return max(4, math.ceil(0.3 / alpha))
+
+
+def _runner(point: N3HeatPoint, cache: ConvergenceCache | None) -> dict[str, Any]:
+    result = run_n3_heat_point(
+        point,
+        cache,
+        commit=ENGINE_REVISION if point.backend == "oqupy" else None,
+    )
+    if point.backend == "uniform_tempo":
+        return result
+    diagnostics = result["diagnostics"]
+    accepted = (
+        float(diagnostics["trace_error"]) < 2e-2
+        and float(diagnostics["minimum_density_eigenvalue"]) > -5e-2
+        and float(diagnostics["phase_residual"]) < 1e-2
+        and float(diagnostics["connected_tail_amplitude"]) < 1e-1
+    )
+    return {**result, "converged": accepted}
+
+
+def _n2_runner(point: N2HeatPoint, cache: ConvergenceCache | None) -> dict[str, Any]:
+    result = run_n2_heat_point(
+        point,
+        cache,
+        commit=N2_ENGINE_REVISION if point.backend == "oqupy" else None,
+    )
+    if point.backend == "uniform_tempo":
+        return result
+    diagnostics = result["diagnostics"]
+    accepted = (
+        float(diagnostics["trace_error"]) < 2e-2
+        and float(diagnostics["minimum_density_eigenvalue"]) > -5e-2
+        and float(diagnostics["phase_residual"]) < 1e-2
+        and float(diagnostics["connected_tail_amplitude"]) < 1e-1
+    )
+    return {**result, "converged": accepted}
+
+
+def n2_publication_schedule() -> AdaptiveSchedule:
+    return AdaptiveSchedule(
+        memory_steps=(4, 5, 6),
+        steps_per_period=(16, 24),
+        epsrel=(1e-5, 3e-6),
+        state_threshold=8e-2,
+        correlation_threshold=8e-2,
+        heat_threshold=8e-2,
+        phase_threshold=2e-3,
+        trace_threshold=5e-3,
+    )
+
+
+def _adaptive_payload(result: AdaptiveResult) -> dict[str, Any]:
+    payload = dict(result.final_result)
+    payload["adaptive_status"] = result.status
+    payload["adaptive_converged"] = result.converged
+    payload["evidence"] = [asdict(item) for item in result.evidence]
+    payload["final_point"] = asdict(result.final_point)
+    payload["failed_parameter"] = result.failed_parameter
+    return payload
+
+
+def _odd_equivalent_payload(
+    reference: dict[str, Any],
+    j: float,
+) -> dict[str, Any]:
+    """Reuse an odd-sector record after proving the projected model is identical."""
+    payload = copy.deepcopy(reference)
+    point = N3HeatPoint(**payload["final_point"])
+    target_point = replace(point, j=j)
+    prepared_reference = prepare_n3_sector(point)
+    prepared_target = prepare_n3_sector(target_point)
+    h0_residual = float(np.linalg.norm(prepared_reference.h0 - prepared_target.h0))
+    coupling_residual = float(
+        np.linalg.norm(prepared_reference.coupling - prepared_target.coupling)
+    )
+    drive_residual = float(
+        np.linalg.norm(prepared_reference.drive - prepared_target.drive)
+    )
+    if (
+        h0_residual > 1e-13
+        or coupling_residual > 1e-13
+        or drive_residual > 1e-13
+    ):
+        raise ValueError("odd-sector projected models are not equivalent")
+
+    source_fingerprint = str(reference["fingerprint"])
+    payload["point"]["j"] = j
+    payload["final_point"]["j"] = j
+    payload["model"]["j"] = j
+    payload["bright_gap"] = prepared_target.bright_gap
+    payload["model_hash"] = fingerprint(
+        {
+            "model": asdict(prepared_target.model),
+            "bath": asdict(prepared_target.bath),
+            "sector": "odd",
+        },
+        "scientific-model-v1",
+    )
+    payload["projected_model_hash"] = reference["projected_model_hash"]
+    payload["fingerprint"] = fingerprint(
+        {
+            "kind": "exact-odd-sector-equivalence",
+            "source_fingerprint": source_fingerprint,
+            "target_j": j,
+            "projected_model_hash": payload["projected_model_hash"],
+        },
+        str(reference.get("source_commit", "unknown")),
+    )
+    payload["numerical_reuse"] = {
+        "reason": "reflection-odd projected Hamiltonian and coupling are J-independent",
+        "source_j": point.j,
+        "source_fingerprint": source_fingerprint,
+        "h0_frobenius_residual": h0_residual,
+        "coupling_frobenius_residual": coupling_residual,
+        "drive_frobenius_residual": drive_residual,
+    }
+    return payload
+
+
+def _complex_values(values: np.ndarray[Any, np.dtype[np.complex128]]) -> dict[str, Any]:
+    return {
+        "real": np.real(values).astype(float).tolist(),
+        "imag": np.imag(values).astype(float).tolist(),
+    }
+
+
+def _complex_array(value: dict[str, Any]) -> np.ndarray[Any, np.dtype[np.complex128]]:
+    return cast(
+        np.ndarray[Any, np.dtype[np.complex128]],
+        np.asarray(value["real"], dtype=float)
+        + 1j * np.asarray(value["imag"], dtype=float),
+    )
+
+
+def _markov_result(point: N3HeatPoint, model_hash: str) -> dict[str, Any]:
+    prepared = prepare_n3_sector(point)
+    model = prepared.model
+
+    def hamiltonian(time: float) -> np.ndarray[Any, np.dtype[np.complex128]]:
+        return np.asarray(
+            prepared.h0
+            + model.drive_amplitude
+            * np.cos(model.drive_frequency * time)
+            * prepared.drive,
+            dtype=np.complex128,
+        )
+
+    backend = FloquetMarkovBackend()
+    run = backend.run(
+        hamiltonian,
+        prepared.coupling,
+        prepared.bath,
+        model.period,
+        point.steps_per_period,
+        harmonic_cutoff=5,
+    )
+    if run.step_maps is None:
+        raise RuntimeError("Floquet-Markov backend returned no step maps")
+    delay_steps = point.delay_periods * point.steps_per_period
+    correlation = superoperator_period_correlation(
+        run.step_maps,
+        run.density_matrices[:-1],
+        prepared.coupling,
+        model.period / point.steps_per_period,
+        delay_steps,
+        model.drive_frequency,
+    )
+    frequencies = np.linspace(0, point.frequency_max, point.frequency_points)
+    heat = heat_current_spectrum(correlation, prepared.bath, frequencies)
+    return {
+        "method": "floquet_markov_qr",
+        "converged": run.converged,
+        "model_hash": model_hash,
+        "model": asdict(model),
+        "bath": asdict(prepared.bath),
+        "diagnostics": run.diagnostics,
+        "phase_state": _complex_values(run.density_matrices[0]),
+        "correlation": {
+            "delay": correlation.delays.tolist(),
+            "connected": _complex_values(correlation.connected),
+        },
+        "frequency": heat.frequencies.tolist(),
+        "continuous": heat.continuous.tolist(),
+        "delta_peaks": [asdict(peak) for peak in heat.delta_peaks],
+    }
+
+
+def _markov_n2_result(point: N2HeatPoint, model_hash: str) -> dict[str, Any]:
+    prepared = prepare_n2_triplet(point)
+    model = prepared.model
+
+    def hamiltonian(time: float) -> np.ndarray[Any, np.dtype[np.complex128]]:
+        return np.asarray(
+            prepared.h0
+            + model.drive_amplitude
+            * np.cos(model.drive_frequency * time)
+            * prepared.coupling,
+            dtype=np.complex128,
+        )
+
+    backend = FloquetMarkovBackend()
+    run = backend.run(
+        hamiltonian,
+        prepared.coupling,
+        prepared.bath,
+        model.period,
+        point.steps_per_period,
+        harmonic_cutoff=5,
+    )
+    if run.step_maps is None:
+        raise RuntimeError("Floquet-Markov backend returned no step maps")
+    delay_steps = point.delay_periods * point.steps_per_period
+    correlation = superoperator_period_correlation(
+        run.step_maps,
+        run.density_matrices[:-1],
+        prepared.coupling,
+        model.period / point.steps_per_period,
+        delay_steps,
+        model.drive_frequency,
+    )
+    frequencies = np.linspace(0, point.frequency_max, point.frequency_points)
+    heat = heat_current_spectrum(correlation, prepared.bath, frequencies)
+    return {
+        "method": "floquet_markov_qr",
+        "converged": run.converged,
+        "model_hash": model_hash,
+        "model": asdict(model),
+        "bath": asdict(prepared.bath),
+        "diagnostics": run.diagnostics,
+        "phase_state": _complex_values(run.density_matrices[0]),
+        "correlation": {
+            "delay": correlation.delays.tolist(),
+            "connected": _complex_values(correlation.connected),
+        },
+        "frequency": heat.frequencies.tolist(),
+        "continuous": heat.continuous.tolist(),
+        "delta_peaks": [asdict(peak) for peak in heat.delta_peaks],
+    }
+
+
+def _dark_diagnostic(result: dict[str, Any]) -> dict[str, Any]:
+    point = N3HeatPoint(**result["final_point"])
+    prepared = prepare_n3_sector(point)
+
+    def hamiltonian(time: float) -> np.ndarray[Any, np.dtype[np.complex128]]:
+        return np.asarray(
+            prepared.h0
+            + prepared.model.drive_amplitude
+            * np.cos(prepared.model.drive_frequency * time)
+            * prepared.drive,
+            dtype=np.complex128,
+        )
+
+    solution = solve_floquet(
+        hamiltonian, prepared.model.period, max(96, 4 * point.steps_per_period)
+    )
+    harmonic_cutoff = min(40, len(solution.step_propagators) // 2 - 1)
+    records = floquet_matrix_elements(
+        solution,
+        prepared.coupling,
+        harmonic_cutoff=harmonic_cutoff,
+        threshold=1e-14,
+    )
+    candidates = dark_candidates(records, relative_threshold=1e-5)
+    strongest = sorted(records, key=lambda item: item.weight, reverse=True)[:24]
+    phase_states = _complex_array(result["phase_states"])
+    heat = np.asarray(result["continuous"], dtype=float)
+    frequencies = np.asarray(result["frequency"], dtype=float)
+    return {
+        "j": point.j,
+        "sector": point.sector,
+        "model_hash": result["model_hash"],
+        "integrated_continuous_heat": float(trapezoid(heat, frequencies)),
+        "period_variance": period_variance(phase_states, prepared.coupling),
+        "harmonic_sum_rule_residual": harmonic_sum_rule(
+            solution, prepared.coupling, harmonic_cutoff
+        ),
+        "harmonic_cutoff": harmonic_cutoff,
+        "strongest_transitions": [asdict(item) for item in strongest],
+        "small_matrix_element_candidates": [
+            {
+                "transition": asdict(item.transition),
+                "relative_weight": item.relative_weight,
+            }
+            for item in candidates[:24]
+        ],
+    }
+
+
+def run_n3_heat_grid(
+    output: Path,
+    cache_directory: Path,
+    *,
+    schedule: AdaptiveSchedule | UniformAdaptiveSchedule | None = None,
+    exact_backend: ExactBackend = "uniform_tempo",
+) -> dict[str, Any]:
+    cache = ConvergenceCache(cache_directory)
+    if exact_backend == "uniform_tempo":
+        active_schedule: AdaptiveSchedule | UniformAdaptiveSchedule = (
+            uniform_publication_schedule() if schedule is None else schedule
+        )
+        if not isinstance(active_schedule, UniformAdaptiveSchedule):
+            raise TypeError("uniform_tempo requires UniformAdaptiveSchedule")
+    else:
+        active_schedule = publication_schedule() if schedule is None else schedule
+        if not isinstance(active_schedule, AdaptiveSchedule):
+            raise TypeError("oqupy requires AdaptiveSchedule")
+    records: list[dict[str, Any]] = []
+    odd_reference: dict[str, Any] | None = None
+    for sector in ("even", "odd"):
+        for j in (0.25, 0.5, 1.0):
+            if (
+                exact_backend == "uniform_tempo"
+                and sector == "odd"
+                and odd_reference is not None
+            ):
+                payload = _odd_equivalent_payload(odd_reference, j)
+                atomic_write_result(output / f"n3_{sector}_j{j:.2f}.json", payload)
+                records.append(payload)
+                continue
+            if exact_backend == "uniform_tempo":
+                uniform_schedule = cast(UniformAdaptiveSchedule, active_schedule)
+                point = N3HeatPoint(
+                    j=j,
+                    sector=sector,
+                    backend="uniform_tempo",
+                    steps_per_period=uniform_schedule.steps_per_period[0],
+                    epsrel=uniform_schedule.tolerances[0],
+                    phase_samples=uniform_schedule.phase_samples[0],
+                    uniform_low_rank_svd=True,
+                    uniform_truncation="abs",
+                    uniform_cap_rank=5_000,
+                    uniform_max_rank=10_000,
+                )
+                adaptive = run_uniform_adaptive(
+                    point,
+                    uniform_schedule,
+                    _runner,
+                    cache,
+                )
+            else:
+                point = N3HeatPoint(j=j, sector=sector, phase_samples=3)
+                adaptive = run_adaptive(
+                    point,
+                    cast(AdaptiveSchedule, active_schedule),
+                    _runner,
+                    cache,
+                )
+            payload = _adaptive_payload(adaptive)
+            if exact_backend == "uniform_tempo" and sector == "odd":
+                odd_reference = payload
+            atomic_write_result(output / f"n3_{sector}_j{j:.2f}.json", payload)
+            records.append(payload)
+    diagnostics = []
+    for item in records:
+        diagnostic = _dark_diagnostic(item)
+        diagnostic["pt_convergence_status"] = item["adaptive_status"]
+        diagnostic["heat_feature_accepted"] = item["adaptive_converged"]
+        diagnostics.append(diagnostic)
+    odd = [item for item in records if item["sector"] == "odd"]
+    odd_difference = None
+    if len(odd) == 3:
+        curves = [np.asarray(item["continuous"], dtype=float) for item in odd]
+        denominator = max(float(np.max(abs(curves[0]))), 1e-15)
+        odd_difference = float(
+            max(np.max(abs(curve - curves[0])) for curve in curves[1:]) / denominator
+        )
+    manifest = {
+        "method": (
+            "uniform_tempo_floquet_multitime"
+            if exact_backend == "uniform_tempo"
+            else "pt_tempo_multitime"
+        ),
+        "exact_backend": exact_backend,
+        "converged": all(item["adaptive_converged"] for item in records),
+        "schedule": asdict(active_schedule),
+        "engine_revision": (
+            records[0].get("source_commit", "unknown")
+            if exact_backend == "uniform_tempo" and records
+            else ENGINE_REVISION
+        ),
+        "phase_quadrature_evidence": (
+            {
+                "source": "per-point adaptive evidence",
+                "phase_samples": list(
+                    cast(UniformAdaptiveSchedule, active_schedule).phase_samples
+                ),
+            }
+            if exact_backend == "uniform_tempo"
+            else PHASE_QUADRATURE_EVIDENCE
+        ),
+        "points": records,
+        "dark_diagnostics": diagnostics,
+        "odd_cross_j_relative_max_difference": odd_difference,
+    }
+    atomic_write_result(output / "n3_heat_manifest.json", manifest)
+    return manifest
+
+
+def run_n3_error_map(
+    exact_manifest: Path,
+    output: Path,
+) -> dict[str, Any]:
+    """Compare every converged N=3 production point to the same-model Markov result."""
+    source = json.loads(exact_manifest.read_text(encoding="utf-8"))
+    if not isinstance(source, dict):
+        raise ValueError("N=3 exact manifest must be a JSON object")
+    records: list[dict[str, Any]] = []
+    for exact in source.get("points", []):
+        j = float(exact["model"]["j"])
+        sector = str(exact["sector"])
+        if not bool(exact.get("adaptive_converged", exact.get("converged", False))):
+            records.append(
+                {
+                    "j": j,
+                    "sector": sector,
+                    "status": "resource_ceiling",
+                    "metrics": None,
+                }
+            )
+            continue
+        point = N3HeatPoint(**exact["final_point"])
+        markov = _markov_result(point, str(exact["model_hash"]))
+        compatible_exact = {**exact, "converged": True}
+        comparison = build_error_record(compatible_exact, markov)
+        record = {"j": j, "sector": sector, **comparison}
+        records.append(record)
+        atomic_write_result(
+            output / f"n3_error_{sector}_j{j:.2f}.json",
+            {
+                "exact_fingerprint": exact.get("fingerprint"),
+                "exact": compatible_exact,
+                "markov": markov,
+                "comparison": record,
+            },
+        )
+    manifest = {
+        "method": "n3_uniform_tempo_vs_floquet_markov_qr",
+        "exact_backend": source.get("exact_backend"),
+        "model_scope": "same N=3 sector, Hamiltonian, drive and bath parameters",
+        "source_manifest": str(exact_manifest),
+        "converged": bool(records) and all(
+            item["status"] == "converged" for item in records
+        ),
+        "points": records,
+    }
+    atomic_write_result(output / "n3_error_map_manifest.json", manifest)
+    return manifest
+
+
+def run_n4_pilot(
+    output: Path,
+    cache_directory: Path,
+    *,
+    sector: Literal["even", "odd"],
+    j: float = 0.25,
+) -> dict[str, Any]:
+    """Run a convergence-gated N=4 sector point and a same-model Markov check."""
+    schedule = n4_pilot_schedule()
+    point = N3HeatPoint(
+        n=4,
+        j=j,
+        sector=sector,
+        backend="uniform_tempo",
+        alpha=0.05,
+        steps_per_period=schedule.steps_per_period[0],
+        epsrel=schedule.tolerances[0],
+        phase_samples=schedule.phase_samples[0],
+        delay_periods=6 if sector == "even" else 3,
+        uniform_low_rank_svd=True,
+        uniform_truncation="abs",
+        uniform_cap_rank=5_000,
+        uniform_max_rank=10_000,
+    )
+    adaptive = run_uniform_adaptive(
+        point,
+        schedule,
+        _runner,
+        ConvergenceCache(cache_directory),
+    )
+    exact = _adaptive_payload(adaptive)
+    exact["converged"] = adaptive.converged
+    payload: dict[str, Any] = {
+        "method": "n4_uniform_tempo_convergence_pilot",
+        "n": 4,
+        "sector": sector,
+        "j": j,
+        "schedule": asdict(schedule),
+        "adaptive_status": adaptive.status,
+        "converged": adaptive.converged,
+        "failed_parameter": adaptive.failed_parameter,
+        "exact": exact,
+        "markov": None,
+        "comparison": None,
+    }
+    if adaptive.converged:
+        final_point = adaptive.final_point
+        markov = _markov_result(final_point, str(exact["model_hash"]))
+        payload["markov"] = markov
+        payload["comparison"] = build_error_record(exact, markov)
+    atomic_write_result(output / f"n4_{sector}_j{j:.2f}.json", payload)
+    return payload
+
+
+def run_error_grid(
+    output: Path,
+    cache_directory: Path,
+    *,
+    schedule: AdaptiveSchedule | UniformAdaptiveSchedule | None = None,
+    exact_backend: ExactBackend = "uniform_tempo",
+) -> dict[str, Any]:
+    cache = ConvergenceCache(cache_directory)
+    if exact_backend == "uniform_tempo":
+        active_schedule: AdaptiveSchedule | UniformAdaptiveSchedule = (
+            uniform_error_schedule() if schedule is None else schedule
+        )
+        if not isinstance(active_schedule, UniformAdaptiveSchedule):
+            raise TypeError("uniform_tempo requires UniformAdaptiveSchedule")
+    else:
+        active_schedule = n2_publication_schedule() if schedule is None else schedule
+        if not isinstance(active_schedule, AdaptiveSchedule):
+            raise TypeError("oqupy requires AdaptiveSchedule")
+    points: list[dict[str, Any]] = []
+    for alpha in (0.025, 0.05, 0.1):
+        for ratio in (0.75, 1.0, 1.25):
+            if exact_backend == "uniform_tempo":
+                uniform_schedule = cast(UniformAdaptiveSchedule, active_schedule)
+                base = N2HeatPoint(
+                    j=0.5,
+                    backend="uniform_tempo",
+                    alpha=alpha,
+                    drive_ratio=ratio,
+                    steps_per_period=uniform_schedule.steps_per_period[0],
+                    epsrel=uniform_schedule.tolerances[0],
+                    phase_samples=uniform_schedule.phase_samples[0],
+                    delay_periods=n2_correlation_delay_periods(alpha),
+                    uniform_low_rank_svd=True,
+                    uniform_truncation="abs",
+                    uniform_cap_rank=5_000,
+                    uniform_max_rank=10_000,
+                )
+                adaptive = cast(
+                    Any,
+                    run_uniform_adaptive(
+                        cast(Any, base),
+                        uniform_schedule,
+                        cast(Any, _n2_runner),
+                        cache,
+                    ),
+                )
+            else:
+                base = N2HeatPoint(
+                    j=0.5,
+                    alpha=alpha,
+                    drive_ratio=ratio,
+                )
+                adaptive = cast(
+                    Any,
+                    run_adaptive(
+                        cast(Any, base),
+                        cast(AdaptiveSchedule, active_schedule),
+                        cast(Any, _n2_runner),
+                        cache,
+                    ),
+                )
+            if not adaptive.converged:
+                points.append(
+                    {
+                        "alpha": alpha,
+                        "drive_ratio": ratio,
+                        "status": "resource_ceiling",
+                        "metrics": None,
+                        "failed_parameter": (
+                            adaptive.failed_parameter or "steady_state_gate"
+                        ),
+                        "adaptive_status": adaptive.status,
+                        "evidence": [asdict(item) for item in adaptive.evidence],
+                    }
+                )
+                continue
+            exact = _adaptive_payload(adaptive)
+            exact["converged"] = True
+            markov = _markov_n2_result(adaptive.final_point, exact["model_hash"])
+            record = build_error_record(exact, markov)
+            points.append({"alpha": alpha, "drive_ratio": ratio, **record})
+            atomic_write_result(
+                output / f"error_a{alpha:.3f}_r{ratio:.2f}.json",
+                {"exact": exact, "markov": markov, "comparison": record},
+            )
+    manifest: dict[str, Any] = {
+        "method": (
+            "uniform_tempo_vs_floquet_markov_qr"
+            if exact_backend == "uniform_tempo"
+            else "pt_tempo_vs_floquet_markov_qr"
+        ),
+        "exact_backend": exact_backend,
+        "model_scope": "N=2 interacting triplet calibration",
+        "points": points,
+        "schedule": asdict(active_schedule),
+        "engine_revision": (
+            "per-point-source-commit"
+            if exact_backend == "uniform_tempo"
+            else N2_ENGINE_REVISION
+        ),
+        "phase_quadrature_evidence": (
+            {
+                "source": "per-point adaptive evidence",
+                "phase_samples": list(
+                    cast(UniformAdaptiveSchedule, active_schedule).phase_samples
+                ),
+            }
+            if exact_backend == "uniform_tempo"
+            else PHASE_QUADRATURE_EVIDENCE
+        ),
+    }
+    audit = audit_grid_manifest(manifest)
+    manifest["audit"] = audit
+    manifest["converged"] = audit["masked_points"] == 0
+    atomic_write_result(output / "error_map_manifest.json", manifest)
+    return manifest
+
+
+def run_model_comparison(
+    output: Path,
+    cache_directory: Path,
+    *,
+    schedule: AdaptiveSchedule | UniformAdaptiveSchedule | None = None,
+    exact_backend: ExactBackend = "uniform_tempo",
+    full_kac: bool = False,
+) -> dict[str, Any]:
+    cache = ConvergenceCache(cache_directory)
+    if exact_backend == "uniform_tempo":
+        active_schedule: AdaptiveSchedule | UniformAdaptiveSchedule = (
+            uniform_publication_schedule() if schedule is None else schedule
+        )
+        if not isinstance(active_schedule, UniformAdaptiveSchedule):
+            raise TypeError("uniform_tempo requires UniformAdaptiveSchedule")
+        uniform_schedule = active_schedule
+        bath_point = N3HeatPoint(
+            j=0.5,
+            sector="even",
+            backend="uniform_tempo",
+            steps_per_period=uniform_schedule.steps_per_period[0],
+            epsrel=uniform_schedule.tolerances[0],
+            phase_samples=uniform_schedule.phase_samples[0],
+            uniform_low_rank_svd=True,
+            uniform_truncation="abs",
+            uniform_cap_rank=5_000,
+            uniform_max_rank=10_000,
+        )
+    else:
+        active_schedule = publication_schedule() if schedule is None else schedule
+        if not isinstance(active_schedule, AdaptiveSchedule):
+            raise TypeError("oqupy requires AdaptiveSchedule")
+        bath_point = N3HeatPoint(j=0.5, sector="even", phase_samples=3)
+    prepared = prepare_n3_sector(bath_point)
+    variants = model_variants(
+        n=3,
+        j=0.5,
+        bath=prepared.bath,
+        drive_frequency=prepared.bright_gap,
+    )
+    records: list[dict[str, Any]] = []
+    for variant in variants:
+        point = replace(
+            bath_point,
+            normalization=variant.config.normalization,
+            counterterm=variant.config.counterterm,
+            drive_frequency=variant.config.drive_frequency,
+        )
+        if exact_backend == "uniform_tempo":
+            if variant.config.normalization == "kac" and not full_kac:
+                adaptive = run_uniform_compression_audit(
+                    point,
+                    cast(UniformAdaptiveSchedule, active_schedule),
+                    _runner,
+                    cache,
+                )
+            else:
+                adaptive = run_uniform_adaptive(
+                    point,
+                    cast(UniformAdaptiveSchedule, active_schedule),
+                    _runner,
+                    cache,
+                )
+            payload = _adaptive_payload(adaptive)
+        else:
+            raw = _runner(point, cache)
+            payload = {
+                **raw,
+                "adaptive_status": "exploratory_unconverged",
+                "adaptive_converged": False,
+                "evidence": [],
+                "final_point": asdict(point),
+                "failed_parameter": "publication_convergence_resource_ceiling",
+            }
+        payload["variant"] = variant.name
+        payload["variant_metadata"] = variant.metadata
+        eta = variant.config.eta
+        payload["continuous_eta_rescaled"] = (
+            np.asarray(payload["continuous"], dtype=float) / eta**2
+        ).tolist()
+        atomic_write_result(output / f"model_{variant.name}.json", payload)
+        records.append(payload)
+    bounded_complete = all(
+        item.get("adaptive_converged") is True
+        for item in records
+        if str(item.get("variant", "")).startswith("bounded_")
+    )
+    kac_locally_audited = all(
+        item.get("adaptive_converged") is True
+        or (
+            item.get("adaptive_status") == "resource_ceiling"
+            and item.get("failed_parameter") == "steps_per_period"
+            and any(
+                evidence.get("parameter") == "epsrel"
+                and evidence.get("passed") is True
+                for evidence in item.get("evidence", [])
+            )
+        )
+        for item in records
+        if str(item.get("variant", "")).startswith("kac_")
+    )
+    locally_complete = (
+        len(records) == 4 and bounded_complete and kac_locally_audited
+    )
+    manifest = {
+        "method": (
+            "uniform_tempo_model_variants"
+            if exact_backend == "uniform_tempo"
+            else "pt_tempo_model_variants"
+        ),
+        "exact_backend": exact_backend,
+        "converged": all(item["adaptive_converged"] for item in records),
+        "complete": len(records) == 4,
+        "locally_complete": locally_complete,
+        "status": (
+            "converged"
+            if records and all(item["adaptive_converged"] for item in records)
+            else (
+                "local_resource_ceiling"
+                if locally_complete
+                else "resource_ceiling"
+            )
+        ),
+        "points": records,
+        "schedule": asdict(active_schedule),
+        "engine_revision": (
+            records[0].get("source_commit", "unknown")
+            if exact_backend == "uniform_tempo" and records
+            else ENGINE_REVISION
+        ),
+        "phase_quadrature_evidence": (
+            {
+                "source": "per-point adaptive evidence",
+                "phase_samples": list(
+                    cast(UniformAdaptiveSchedule, active_schedule).phase_samples
+                ),
+            }
+            if exact_backend == "uniform_tempo"
+            else PHASE_QUADRATURE_EVIDENCE
+        ),
+        "resource_policy": {
+            "full_kac": full_kac,
+            "local_default": (
+                "Kac variants stop after compression convergence; use "
+                "--full-kac on a cluster for timestep and phase refinement"
+            ),
+        },
+    }
+    atomic_write_result(output / "model_comparison_manifest.json", manifest)
+    return manifest
+
+
+def audit_paper_results(directory: Path) -> tuple[bool, list[str]]:
+    """Audit the three publication manifests against the declared final gates."""
+
+    def evidence_failures(
+        records: Any,
+        label: str,
+    ) -> list[str]:
+        local: list[str] = []
+        if not isinstance(records, list):
+            return [f"{label} has no convergence evidence"]
+        passed = [item for item in records if item.get("passed") is True]
+        parameters = {item.get("parameter") for item in passed}
+        required = {"epsrel", "steps_per_period", "phase_samples"}
+        if not required.issubset(parameters):
+            local.append(
+                f"{label} lacks passed compression/timestep/phase evidence"
+            )
+            return local
+        timestep_records = [
+            item for item in passed if item.get("parameter") == "steps_per_period"
+        ]
+        compression_steps = {
+            int(item["refined_steps_per_period"])
+            for item in passed
+            if item.get("parameter") == "epsrel"
+            and item.get("refined_steps_per_period") is not None
+        }
+        for item in timestep_records:
+            compared = {
+                int(item["coarse_steps_per_period"]),
+                int(item["refined_steps_per_period"]),
+            }
+            if not compared.issubset(compression_steps):
+                local.append(
+                    f"{label} did not converge compression on both timestep grids"
+                )
+                break
+        return local
+
+    def point_failures(point: dict[str, Any], label: str) -> list[str]:
+        local: list[str] = []
+        if point.get("adaptive_status") != "converged":
+            local.append(f"{label} status is not converged")
+        if point.get("adaptive_converged") is not True:
+            local.append(f"{label} adaptive_converged is not true")
+        diagnostics = point.get("diagnostics", {})
+        gates = {
+            "fixed_point_residual": (1e-3, "maximum"),
+            "trace_error": (5e-3, "maximum"),
+            "hermiticity_error": (5e-3, "maximum"),
+            "connected_tail_amplitude": (5e-2, "maximum"),
+            "minimum_density_eigenvalue": (-5e-3, "minimum"),
+        }
+        for name, (threshold, direction) in gates.items():
+            try:
+                value = float(diagnostics[name])
+            except (KeyError, TypeError, ValueError):
+                local.append(f"{label} lacks finite diagnostic {name}")
+                continue
+            if not np.isfinite(value):
+                local.append(f"{label} diagnostic {name} is non-finite")
+            elif direction == "maximum" and value > threshold:
+                local.append(f"{label} diagnostic {name} exceeds {threshold:g}")
+            elif direction == "minimum" and value < threshold:
+                local.append(f"{label} diagnostic {name} is below {threshold:g}")
+        local.extend(evidence_failures(point.get("evidence"), label))
+        return local
+
+    failures: list[str] = []
+    required = (
+        "n3_heat_manifest.json",
+        "error_map_manifest.json",
+        "model_comparison_manifest.json",
+    )
+    import json
+
+    loaded: dict[str, dict[str, Any]] = {}
+    for name in required:
+        path = directory / name
+        if not path.is_file():
+            failures.append(f"missing {name}")
+            continue
+        loaded[name] = json.loads(path.read_text(encoding="utf-8"))
+    if "n3_heat_manifest.json" in loaded:
+        value = loaded["n3_heat_manifest.json"]
+        points = value.get("points", [])
+        if value.get("exact_backend") != "uniform_tempo":
+            failures.append("N=3 manifest does not use uniform_tempo")
+        if value.get("converged") is not True:
+            failures.append("N=3 manifest is not converged")
+        if len(points) != 6:
+            failures.append("N=3 manifest must contain six points")
+        observed = {
+            (point.get("sector"), float(point.get("model", {}).get("j", np.nan)))
+            for point in points
+        }
+        expected = {
+            (sector, j)
+            for sector in ("even", "odd")
+            for j in (0.25, 0.5, 1.0)
+        }
+        if observed != expected:
+            failures.append("N=3 manifest sector/J grid is incomplete")
+        for point in points:
+            label = (
+                f"N=3 {point.get('sector')} "
+                f"J={point.get('model', {}).get('j')}"
+            )
+            failures.extend(point_failures(point, label))
+        if value.get("odd_cross_j_relative_max_difference") is None:
+            failures.append("N=3 odd-sector invariance diagnostic is missing")
+        elif float(value["odd_cross_j_relative_max_difference"]) > 1e-12:
+            failures.append("N=3 odd-sector J-invariance check failed")
+    if "error_map_manifest.json" in loaded:
+        try:
+            value = loaded["error_map_manifest.json"]
+            audit = audit_grid_manifest(value)
+            if value.get("exact_backend") != "uniform_tempo":
+                failures.append("error map does not use uniform_tempo")
+            if audit["masked_points"] != 0 or value.get("converged") is not True:
+                failures.append("error map contains unconverged or masked points")
+            for point in value.get("points", []):
+                label = (
+                    f"error grid alpha={point.get('alpha')} "
+                    f"ratio={point.get('drive_ratio')}"
+                )
+                metrics = point.get("metrics", {})
+                if set(metrics) != {"trace_distance", "correlation", "heat"}:
+                    failures.append(f"{label} lacks the three error metrics")
+                elif not all(np.isfinite(float(item)) for item in metrics.values()):
+                    failures.append(f"{label} has a non-finite error metric")
+                failures.extend(
+                    evidence_failures(point.get("convergence_evidence"), label)
+                )
+        except ValueError as exc:
+            failures.append(str(exc))
+    if "model_comparison_manifest.json" in loaded:
+        value = loaded["model_comparison_manifest.json"]
+        points = value.get("points", [])
+        if value.get("exact_backend") != "uniform_tempo":
+            failures.append("model comparison does not use uniform_tempo")
+        if len(points) != 4:
+            failures.append("model manifest must contain four variants")
+        if not value.get("complete"):
+            failures.append("model comparison is incomplete")
+        if value.get("locally_complete") is not True:
+            failures.append("model comparison has not reached its declared local endpoint")
+        if len({point.get("variant") for point in points}) != 4:
+            failures.append("model comparison variants are not distinct")
+        for point in points:
+            label = f"model variant {point.get('variant')}"
+            if point.get("adaptive_converged") is True:
+                failures.extend(point_failures(point, label))
+                continue
+            if not str(point.get("variant", "")).startswith("kac_"):
+                failures.append(f"{label} is not converged")
+                continue
+            if (
+                point.get("adaptive_status") != "resource_ceiling"
+                or point.get("failed_parameter") != "steps_per_period"
+            ):
+                failures.append(f"{label} lacks an audited timestep resource ceiling")
+            compression = [
+                item
+                for item in point.get("evidence", [])
+                if item.get("parameter") == "epsrel" and item.get("passed") is True
+            ]
+            if not compression:
+                failures.append(f"{label} lacks passed compression evidence")
+    return not failures, failures
diff --git a/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/plotting.py b/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/plotting.py
new file mode 100644
index 000000000..67abdd80f
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/plotting.py
@@ -0,0 +1,632 @@
+"""Publication-oriented deterministic baseline plots."""
+
+from __future__ import annotations
+
+from pathlib import Path
+from typing import Any
+
+import matplotlib
+
+matplotlib.use("Agg")
+import matplotlib.pyplot as plt
+import numpy as np
+from matplotlib.figure import Figure
+from matplotlib.patches import Circle, Rectangle
+
+from .heat_valve_audit import audit_heat_valve_manifest
+
+
+def _save(figure: Figure, stem: Path) -> None:
+    stem.parent.mkdir(parents=True, exist_ok=True)
+    figure.savefig(
+        stem.with_suffix(".pdf"),
+        bbox_inches="tight",
+        metadata={"Creator": "floquet-if"},
+    )
+    figure.savefig(stem.with_suffix(".png"), dpi=180, bbox_inches="tight")
+    plt.close(figure)
+
+
+def plot_n2(result: dict[str, Any], stem: Path) -> None:
+    rows = result["data"]
+    j = np.array([row["j"] for row in rows])
+    figure, axes = plt.subplots(1, 2, figsize=(9, 3.6))
+    axes[0].plot(j, [row["gap_low"] for row in rows], label=r"$\Delta_{\rm low}$")
+    axes[0].plot(j, [row["gap_high"] for row in rows], label=r"$\Delta_{\rm high}$")
+    axes[0].set(xlabel=r"$J/\Omega$", ylabel=r"gap$/\Omega$")
+    axes[0].legend(frameon=False)
+    axes[1].plot(j, [row["weight_low"] for row in rows], label="low")
+    axes[1].plot(j, [row["weight_high"] for row in rows], label="high")
+    axes[1].set(xlabel=r"$J/\Omega$", ylabel=r"$|\langle f|S_2|i\rangle|^2$")
+    axes[1].legend(frameon=False)
+    figure.suptitle("N=2 interacting triplet — exact diagonalization")
+    figure.tight_layout()
+    _save(figure, stem)
+
+
+def plot_n3(result: dict[str, Any], stem: Path) -> None:
+    rows = result["data"]
+    j = np.array([row["j"] for row in rows])
+    gaps = np.array([row["primary_even_gap"] for row in rows])
+    weights = np.array([row["primary_even_weight"] for row in rows])
+    figure, axes = plt.subplots(1, 2, figsize=(9, 3.6))
+    axes[0].loglog(j[j > 0], gaps[j > 0], "o-", label="exact primary gap")
+    asymptotic = 1 / (4 * j[j > 0] ** 2)
+    axes[0].loglog(j[j > 0], asymptotic, "--", label=r"$\Omega^3/(4J^2)$")
+    axes[0].set(xlabel=r"$J/\Omega$", ylabel=r"gap$/\Omega$")
+    axes[0].legend(frameon=False)
+    axes[1].plot(j, weights, "o-", label="reflection-even")
+    axes[1].set(xlabel=r"$J/\Omega$", ylabel="primary bright weight")
+    axes[1].legend(frameon=False)
+    figure.suptitle("N=3 symmetry-resolved collective mode")
+    figure.tight_layout()
+    _save(figure, stem)
+
+
+def plot_backend_comparison(result: dict[str, Any], stem: Path) -> None:
+    rows = result["data"]
+    alpha = [row["alpha"] for row in rows]
+    distance = [row["trace_distance"] for row in rows]
+    figure, axis = plt.subplots(figsize=(5.2, 3.7))
+    axis.plot(alpha, distance, "o-", color="#D55E00")
+    axis.set(
+        xlabel=r"bath coupling $\alpha$",
+        ylabel="trace distance",
+        title="Finite-memory IF vs Floquet-Markov\n(both approximate)",
+    )
+    axis.grid(alpha=0.25)
+    figure.tight_layout()
+    _save(figure, stem)
+
+
+def plot_heat_spectrum(result: dict[str, Any], stem: Path) -> None:
+    rows = result["data"]
+    frequencies = np.array([row["frequency"] for row in rows])
+    current = np.array([row["continuous"] for row in rows])
+    figure, axis = plt.subplots(figsize=(6.2, 3.8))
+    axis.plot(frequencies, current, color="#0072B2", label="continuous")
+    delta_axis = axis.twinx()
+    peak_frequencies = [peak["frequency"] for peak in result["delta_peaks"]]
+    peak_weights = [peak["weight"] for peak in result["delta_peaks"]]
+    delta_axis.semilogy(
+        peak_frequencies,
+        peak_weights,
+        "D",
+        color="#D55E00",
+        label=r"coherent $\delta$ weight",
+    )
+    delta_axis.set_ylabel(r"analytic $\delta$ weight", color="#D55E00")
+    delta_axis.tick_params(axis="y", colors="#D55E00")
+    method_title = (
+        "PT-TEMPO multitime"
+        if result["method"] == "pt_tempo_multitime"
+        else "Floquet-Markov/QRT"
+    )
+    axis.set(
+        xlabel=r"bath frequency $\omega/\Omega$",
+        ylabel=r"$\bar j(\omega)$",
+        title=f"N=2 heat-current spectrum — {method_title}",
+    )
+    handles, labels = axis.get_legend_handles_labels()
+    delta_handles, delta_labels = delta_axis.get_legend_handles_labels()
+    axis.legend(handles + delta_handles, labels + delta_labels, frameon=False)
+    axis.grid(alpha=0.2)
+    figure.tight_layout()
+    _save(figure, stem)
+
+
+def plot_n3_pt_dynamics(result: dict[str, Any], stem: Path) -> None:
+    rows = result["data"]
+    phase = np.array([row["phase_index"] for row in rows]) / len(rows)
+    magnetization = np.array([row["magnetization"] for row in rows])
+    figure, axis = plt.subplots(figsize=(5.5, 3.6))
+    axis.plot(phase, magnetization, "o-", color="#009E73")
+    axis.set(
+        xlabel=r"drive phase $t/T$",
+        ylabel=r"$\langle S_3\rangle$",
+        title="N=3 reflection-even periodic state — PT-TEMPO",
+    )
+    axis.grid(alpha=0.2)
+    figure.tight_layout()
+    _save(figure, stem)
+
+
+def plot_n3_sector_heat(manifest: dict[str, Any], stem: Path) -> None:
+    backend_label = (
+        "uniform TEMPO"
+        if manifest.get("exact_backend") == "uniform_tempo"
+        else "PT-TEMPO"
+    )
+    figure, axes = plt.subplots(1, 2, figsize=(10, 3.8), sharey=True)
+    for axis, sector in zip(axes, ("even", "odd"), strict=True):
+        for point in manifest["points"]:
+            if point["sector"] != sector:
+                continue
+            axis.plot(
+                point["frequency"],
+                point["continuous"],
+                "--" if not point["adaptive_converged"] else "-",
+                label=(
+                    rf"$J/\Omega={point['model']['j']:g}$ "
+                    f"({point.get('adaptive_status', 'converged')})"
+                ),
+            )
+        axis.set(
+            xlabel=r"bath frequency $\omega/\Omega$",
+            title=f"reflection-{sector} — {backend_label}",
+        )
+        axis.grid(alpha=0.2)
+        if axis.lines:
+            axis.legend(frameon=False, fontsize=8)
+    axes[0].set_ylabel(r"continuous $\bar j(\omega)$")
+    qualifier = (
+        "converged grid"
+        if manifest.get("converged")
+        else "dashed curves are resource-limited"
+    )
+    figure.suptitle(rf"$N=3$ symmetry-resolved calorimetry — {qualifier}")
+    figure.tight_layout()
+    _save(figure, stem)
+
+
+def plot_odd_sector_difference(manifest: dict[str, Any], stem: Path) -> None:
+    odd = [
+        point
+        for point in manifest["points"]
+        if point["sector"] == "odd"
+    ]
+    figure, axis = plt.subplots(figsize=(6.1, 3.7))
+    if odd:
+        reference = np.asarray(odd[0]["continuous"], dtype=float)
+        frequency = np.asarray(odd[0]["frequency"], dtype=float)
+        for point in odd[1:]:
+            difference = np.asarray(point["continuous"], dtype=float) - reference
+            axis.plot(
+                frequency,
+                difference,
+                label=rf"$J={point['model']['j']:g}$ minus $J={odd[0]['model']['j']:g}$",
+            )
+    axis.axhline(0, color="black", lw=0.7)
+    axis.set(
+        xlabel=r"bath frequency $\omega/\Omega$",
+        ylabel=r"$\Delta\bar j(\omega)$",
+        title=r"Reflection-odd heat spectrum: exact $J$-invariance check",
+    )
+    axis.grid(alpha=0.2)
+    if axis.lines:
+        axis.legend(frameon=False)
+    figure.tight_layout()
+    _save(figure, stem)
+
+
+def plot_error_maps(manifest: dict[str, Any], stem: Path) -> None:
+    alphas = [0.025, 0.05, 0.1]
+    ratios = [0.75, 1.0, 1.25]
+    names = (
+        ("trace_distance", r"$D_\rho$"),
+        ("correlation", r"$\epsilon_C$"),
+        ("heat", r"$\epsilon_j$"),
+    )
+    figure, axes = plt.subplots(1, 3, figsize=(11.5, 3.5))
+    for axis, (name, label) in zip(axes, names, strict=True):
+        values = np.full((len(alphas), len(ratios)), np.nan)
+        for point in manifest["points"]:
+            if point["status"] != "converged":
+                continue
+            row = alphas.index(float(point["alpha"]))
+            column = ratios.index(float(point["drive_ratio"]))
+            values[row, column] = point["metrics"][name]
+        image = axis.imshow(values, origin="lower", aspect="auto", cmap="magma")
+        axis.set_xticks(range(len(ratios)), labels=ratios)
+        axis.set_yticks(range(len(alphas)), labels=alphas)
+        axis.set(
+            xlabel=r"$\omega_d/\Delta_g$",
+            ylabel=r"$\alpha$",
+            title=label,
+        )
+        for row in range(len(alphas)):
+            for column in range(len(ratios)):
+                if np.isnan(values[row, column]):
+                    text = "masked"
+                elif name == "trace_distance":
+                    text = f"{values[row, column]:.4f}"
+                else:
+                    text = f"{values[row, column]:.2g}"
+                if np.isnan(values[row, column]):
+                    axis.add_patch(
+                        Rectangle(
+                            (column - 0.5, row - 0.5),
+                            1,
+                            1,
+                            fill=False,
+                            hatch="///",
+                            edgecolor="#777777",
+                            linewidth=0.0,
+                        )
+                    )
+                axis.text(
+                    column,
+                    row,
+                    text,
+                    ha="center",
+                    va="center",
+                    color="black" if np.isnan(values[row, column]) else "white",
+                    fontsize=8,
+                )
+        figure.colorbar(image, ax=axis, fraction=0.046)
+    scope = manifest.get("model_scope", "audited calibration grid")
+    exact_label = (
+        "uniform TEMPO"
+        if manifest.get("exact_backend") == "uniform_tempo"
+        else "PT-TEMPO"
+    )
+    figure.suptitle(f"{exact_label} vs Floquet-Markov/QRT — {scope}")
+    figure.tight_layout()
+    _save(figure, stem)
+
+
+def plot_n3_error_maps(manifest: dict[str, Any], stem: Path) -> None:
+    """Plot same-parameter N=3 exact-versus-Markov errors by sector and J."""
+    sectors = ("even", "odd")
+    couplings = (0.25, 0.5, 1.0)
+    names = (
+        ("trace_distance", r"$D_\rho$"),
+        ("correlation", r"$\epsilon_C$"),
+        ("heat", r"$\epsilon_j$"),
+    )
+    figure, axes = plt.subplots(1, 3, figsize=(11.5, 3.5))
+    for axis, (name, label) in zip(axes, names, strict=True):
+        values = np.full((len(sectors), len(couplings)), np.nan)
+        for point in manifest["points"]:
+            if point["status"] != "converged":
+                continue
+            row = sectors.index(str(point["sector"]))
+            column = couplings.index(float(point["j"]))
+            values[row, column] = point["metrics"][name]
+        image = axis.imshow(values, origin="upper", aspect="auto", cmap="magma")
+        axis.set_xticks(range(len(couplings)), labels=couplings)
+        axis.set_yticks(range(len(sectors)), labels=sectors)
+        axis.set(xlabel=r"$J/\Omega$", ylabel="reflection sector", title=label)
+        for row in range(len(sectors)):
+            for column in range(len(couplings)):
+                value = values[row, column]
+                axis.text(
+                    column,
+                    row,
+                    "masked" if np.isnan(value) else f"{value:.2g}",
+                    ha="center",
+                    va="center",
+                    color="white",
+                    fontsize=8,
+                )
+        figure.colorbar(image, ax=axis, fraction=0.046, pad=0.04)
+    figure.suptitle("N=3 same-model UniformTEMPO versus Floquet-Markov/QRT")
+    figure.tight_layout()
+    _save(figure, stem)
+
+
+def plot_n4_pilot_comparison(result: dict[str, Any], stem: Path) -> None:
+    """Plot one convergence-gated N=4 spectrum against its same-model benchmark."""
+    if not result.get("converged") or result.get("markov") is None:
+        raise ValueError("N=4 pilot must converge before plotting a comparison")
+    exact = result["exact"]
+    markov = result["markov"]
+    metrics = result["comparison"]["metrics"]
+    figure, axis = plt.subplots(figsize=(6.5, 3.9))
+    axis.plot(
+        exact["frequency"],
+        exact["continuous"],
+        label="UniformTEMPO",
+        color="#0072B2",
+    )
+    axis.plot(
+        markov["frequency"],
+        markov["continuous"],
+        "--",
+        label="Floquet-Markov/QRT",
+        color="#D55E00",
+    )
+    for peak in exact["delta_peaks"]:
+        frequency = float(peak["frequency"])
+        if frequency <= 3:
+            axis.axvline(frequency, color="black", alpha=0.25, lw=0.7)
+    axis.set(
+        xlim=(0, 3),
+        xlabel=r"bath frequency $\omega/\Omega$",
+        ylabel=r"continuous $\bar j(\omega)$",
+        title=(
+            rf"$N=4$ reflection-{result['sector']}, $J/\Omega={result['j']:g}$"
+            "\n"
+            rf"same-model heat error $\epsilon_j={metrics['heat']:.3g}$"
+        ),
+    )
+    axis.grid(alpha=0.2)
+    axis.legend(frameon=False)
+    figure.tight_layout()
+    _save(figure, stem)
+
+
+def plot_dark_diagnostics(manifest: dict[str, Any], stem: Path) -> None:
+    diagnostics = sorted(
+        [
+            item
+            for item in manifest.get("dark_diagnostics", [])
+            if item["sector"] == "even"
+        ],
+        key=lambda item: item["j"],
+    )
+    figure, axes = plt.subplots(1, 2, figsize=(9.5, 3.7))
+    j_values = [item["j"] for item in diagnostics]
+    strongest = [
+        max(
+            (
+                record["weight"]
+                for record in item["strongest_transitions"]
+                if record["source"] != record["target"]
+            ),
+            default=np.nan,
+        )
+        for item in diagnostics
+    ]
+    axes[0].semilogy(j_values, strongest, "o-", color="#0072B2")
+    axes[0].set(
+        xlabel=r"$J/\Omega$",
+        ylabel=r"largest off-diagonal $|S_{\alpha\beta}^{(m)}|^2$",
+        title="Floquet matrix-element diagnostic",
+    )
+    axes[1].plot(
+        j_values,
+        [item["integrated_continuous_heat"] for item in diagnostics],
+        "s-",
+        color="#D55E00",
+        label="integrated heat",
+    )
+    axes[1].plot(
+        j_values,
+        [item["period_variance"] for item in diagnostics],
+        "o--",
+        color="#009E73",
+        label=r"$\overline{\mathrm{Var}(S)}$",
+    )
+    axes[1].set(xlabel=r"$J/\Omega$", title="Heat and collective variance")
+    axes[1].legend(frameon=False)
+    for axis in axes:
+        axis.grid(alpha=0.2)
+    qualifier = "converged heat" if manifest.get("converged") else "provisional heat"
+    figure.suptitle(f"Floquet diagnostics with {qualifier}", fontsize=12)
+    figure.tight_layout()
+    _save(figure, stem)
+
+
+def plot_model_variants(manifest: dict[str, Any], stem: Path) -> None:
+    figure, axes = plt.subplots(1, 2, figsize=(10, 3.8))
+    for point in manifest["points"]:
+        style = "-" if point.get("adaptive_converged") else "--"
+        axes[0].plot(
+            point["frequency"], point["continuous"], style, label=point["variant"]
+        )
+        axes[1].plot(
+            point["frequency"],
+            point["continuous_eta_rescaled"],
+            style,
+            label=point["variant"],
+        )
+    axes[0].set(title="Raw heat spectra", ylabel=r"$\bar j(\omega)$")
+    axes[1].set(title=r"Diagnostic $\bar j(\omega)/\eta^2$")
+    for axis in axes:
+        axis.set_xlabel(r"bath frequency $\omega/\Omega$")
+        axis.grid(alpha=0.2)
+        axis.legend(frameon=False, fontsize=8)
+    backend_label = (
+        "uniform TEMPO"
+        if manifest.get("exact_backend") == "uniform_tempo"
+        else "PT-TEMPO"
+    )
+    if manifest.get("converged"):
+        qualifier = "fully converged"
+    elif manifest.get("locally_complete"):
+        qualifier = "bounded converged; Kac compression-audited"
+    else:
+        qualifier = "exploratory"
+    figure.suptitle(
+        f"N=3 normalization/counterterm comparison — {qualifier} {backend_label}"
+    )
+    figure.tight_layout()
+    _save(figure, stem)
+
+
+def plot_heat_valve_hero(manifest: dict[str, Any], stem: Path) -> None:
+    """Render the audited four-panel Floquet heat-valve summary."""
+    audit = audit_heat_valve_manifest(manifest)
+    points = list(manifest.get("points", ()))
+    figure, axes = plt.subplots(2, 2, figsize=(11.2, 8.0))
+    colors = {1: "#0072B2", 2: "#E69F00", 3: "#009E73"}
+
+    for n in (1, 2, 3):
+        rows = sorted(
+            [item for item in points if int(item["point"]["n"]) == n],
+            key=lambda item: float(item["point"]["xi"]),
+        )
+        if not rows:
+            continue
+        xi = np.asarray([item["point"]["xi"] for item in rows], dtype=float)
+        heat = np.asarray(
+            [item["integrated_absolute_heat"] for item in rows],
+            dtype=float,
+        )
+        residue = np.asarray(
+            [item["visible_residue_weight"] for item in rows],
+            dtype=float,
+        )
+        heat_scale = float(np.max(heat)) + 1e-15
+        residue_scale = float(np.max(residue)) + 1e-15
+        style = "-" if all(item.get("converged", False) for item in rows) else ":"
+        axes[0, 0].plot(
+            xi,
+            heat / heat_scale,
+            marker="o",
+            linestyle=style,
+            color=colors[n],
+            label=rf"$N={n}$ heat",
+        )
+        axes[0, 0].plot(
+            xi,
+            residue / residue_scale,
+            marker="s",
+            linestyle="--",
+            color=colors[n],
+            alpha=0.75,
+            label=rf"$N={n}$ residue",
+        )
+    axes[0, 0].set(
+        xlabel=r"$\xi=2A/\omega_d$",
+        ylabel="within-size normalized weight",
+        title="Heat and observable transfer-mode weight",
+    )
+    axes[0, 0].grid(alpha=0.2)
+    axes[0, 0].legend(frameon=False, fontsize=7, ncol=2)
+
+    target: dict[str, Any] | None = None
+    selected_n3 = [
+        item
+        for item in manifest.get("selected_points", ())
+        if int(item["n"]) == 3
+    ]
+    if len(selected_n3) == 3:
+        target_xi = float(selected_n3[1]["xi"])
+        target = next(
+            (
+                item
+                for item in points
+                if int(item["point"]["n"]) == 3
+                and np.isclose(float(item["point"]["xi"]), target_xi)
+            ),
+            None,
+        )
+    if target is None and points:
+        target = points[0]
+
+    unit_axis = axes[0, 1]
+    unit_axis.add_patch(
+        Circle((0, 0), 1, fill=False, color="#777777", linestyle="--")
+    )
+    if target is not None:
+        poles = list(target.get("poles", ()))
+        real = np.asarray(
+            [item["eigenvalue"].get("real", 0.0) for item in poles],
+            dtype=float,
+        )
+        imag = np.asarray(
+            [item["eigenvalue"].get("imag", 0.0) for item in poles],
+            dtype=float,
+        )
+        log_residue = np.log10(
+            np.asarray(
+                [item["residue"]["abs"] for item in poles],
+                dtype=float,
+            )
+            + 1e-15
+        )
+        if len(poles):
+            scatter = unit_axis.scatter(
+                real,
+                imag,
+                c=log_residue,
+                cmap="viridis",
+                edgecolor="black",
+                linewidth=0.3,
+            )
+            figure.colorbar(
+                scatter,
+                ax=unit_axis,
+                label=r"$\log_{10}|A_a|$",
+                fraction=0.046,
+            )
+    unit_axis.set(
+        xlabel=r"$\mathrm{Re}\,\lambda_a$",
+        ylabel=r"$\mathrm{Im}\,\lambda_a$",
+        title=r"Floquet transfer poles ($N=3$ selected minimum)",
+        xlim=(-1.08, 1.08),
+        ylim=(-1.08, 1.08),
+        aspect="equal",
+    )
+    unit_axis.axhline(0, color="#BBBBBB", lw=0.5)
+    unit_axis.axvline(0, color="#BBBBBB", lw=0.5)
+
+    spectrum_axis = axes[1, 0]
+    n3_rows = sorted(
+        [item for item in points if int(item["point"]["n"]) == 3],
+        key=lambda item: float(item["point"]["xi"]),
+    )
+    for index, item in enumerate(n3_rows):
+        role = ("lower flank", "minimum", "upper flank")[min(index, 2)]
+        spectrum_axis.plot(
+            item.get("frequency", ()),
+            item.get("continuous", ()),
+            "-" if item.get("converged", False) else ":",
+            label=rf"{role}, $\xi={float(item['point']['xi']):.2f}$",
+        )
+    if target is not None:
+        for item in target.get("poles", ())[:4]:
+            center = abs(float(item.get("quasifrequency", 0.0)))
+            width = max(float(item.get("decay_rate", 0.0)), 0.0)
+            spectrum_axis.axvline(center, color="#555555", lw=0.7, alpha=0.5)
+            spectrum_axis.axvspan(
+                max(0.0, center - width),
+                center + width,
+                color="#999999",
+                alpha=0.08,
+            )
+    spectrum_axis.set(
+        xlabel=r"bath frequency $\omega/\Omega$",
+        ylabel=r"continuous $\bar j(\omega)$",
+        title="Exact heat spectrum with pole centres/widths",
+    )
+    spectrum_axis.grid(alpha=0.2)
+    if spectrum_axis.lines:
+        spectrum_axis.legend(frameon=False, fontsize=7)
+
+    contrast_axis = axes[1, 1]
+    sizes = np.asarray([1, 2, 3])
+    heat_contrast = np.asarray(
+        [audit.metrics.get(f"heat_contrast_n{n}", np.nan) for n in sizes]
+    )
+    residue_contrast = np.asarray(
+        [
+            1 / audit.metrics.get(f"residue_ratio_n{n}", np.nan)
+            for n in sizes
+        ]
+    )
+    contrast_axis.bar(
+        sizes - 0.16,
+        heat_contrast,
+        width=0.32,
+        color="#0072B2",
+        label="heat contrast",
+    )
+    contrast_axis.bar(
+        sizes + 0.16,
+        residue_contrast,
+        width=0.32,
+        color="#CC79A7",
+        label="residue contrast",
+    )
+    contrast_axis.axhline(10, color="#D55E00", linestyle="--", label="dark gate")
+    contrast_axis.set(
+        xlabel="system size $N$",
+        ylabel="weaker-flank / minimum",
+        title="Size dependence and tenfold claim gate",
+        xticks=sizes,
+        yscale="log",
+    )
+    contrast_axis.grid(axis="y", alpha=0.2)
+    contrast_axis.legend(frameon=False, fontsize=8)
+
+    title = (
+        "audited dark channel"
+        if audit.dark_channel_passed
+        else "candidate; claim gates not met"
+    )
+    figure.suptitle(f"Pole-resolved Floquet heat valve — {title}")
+    figure.tight_layout()
+    _save(figure, stem)
diff --git a/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/poles.py b/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/poles.py
new file mode 100644
index 000000000..1b308003c
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/poles.py
@@ -0,0 +1,189 @@
+"""Observable residues and tracking for Floquet transfer poles."""
+
+from __future__ import annotations
+
+from dataclasses import dataclass
+
+import numpy as np
+from numpy.typing import NDArray
+from scipy.optimize import linear_sum_assignment
+
+
+@dataclass(frozen=True)
+class TransferPole:
+    eigenvalue: complex
+    decay_rate: float
+    quasifrequency: float
+    eigenpair_residual: float
+
+
+@dataclass(frozen=True)
+class PoleResidue:
+    pole: TransferPole
+    residue: complex
+
+
+@dataclass(frozen=True)
+class PoleFit:
+    residues: tuple[PoleResidue, ...]
+    reconstruction: NDArray[np.complex128]
+    stroboscopic_delays: NDArray[np.float64]
+    reconstruction_residual: float
+    condition_number: float
+
+
+@dataclass(frozen=True)
+class PoleMatch:
+    previous_index: int
+    current_index: int
+    distance: float
+    ambiguous: bool
+
+
+def transfer_poles(
+    eigenvalues: NDArray[np.complex128],
+    eigenpair_residuals: NDArray[np.float64],
+    period: float,
+    *,
+    steady_tolerance: float = 5e-3,
+) -> tuple[TransferPole, ...]:
+    """Remove the resolved steady pole and convert the rest to rates."""
+    values = np.asarray(eigenvalues, dtype=np.complex128)
+    residuals = np.asarray(eigenpair_residuals, dtype=float)
+    if values.ndim != 1 or residuals.ndim != 1 or values.shape != residuals.shape:
+        raise ValueError("transfer eigenvalues and residuals must be equal vectors")
+    if values.size < 2:
+        raise ValueError("at least one steady and one decaying pole are required")
+    if period <= 0 or steady_tolerance <= 0:
+        raise ValueError("period and steady_tolerance must be positive")
+    if not np.all(np.isfinite(values)) or not np.all(np.isfinite(residuals)):
+        raise ValueError("transfer pole data must be finite")
+    if np.any(residuals < 0):
+        raise ValueError("eigenpair residuals must be nonnegative")
+
+    steady = int(np.argmin(abs(values - 1)))
+    if abs(values[steady] - 1) > steady_tolerance:
+        raise ValueError("transfer spectrum has no resolved steady pole")
+
+    records: list[TransferPole] = []
+    for index, (value, residual) in enumerate(
+        zip(values, residuals, strict=True)
+    ):
+        if index == steady:
+            continue
+        magnitude = float(abs(value))
+        if magnitude <= np.finfo(float).tiny:
+            raise ValueError("zero transfer eigenvalues cannot define finite rates")
+        records.append(
+            TransferPole(
+                eigenvalue=complex(value),
+                decay_rate=float(-np.log(magnitude) / period),
+                quasifrequency=float(np.angle(value) / period),
+                eigenpair_residual=float(residual),
+            )
+        )
+    return tuple(
+        sorted(records, key=lambda item: abs(item.eigenvalue), reverse=True)
+    )
+
+
+def fit_pole_residues(
+    poles: tuple[TransferPole, ...],
+    delays: NDArray[np.float64],
+    connected: NDArray[np.complex128],
+    period: float,
+    max_modes: int,
+) -> PoleFit:
+    """Fit transfer-pole residues to stroboscopic connected correlations."""
+    delay_values = np.asarray(delays, dtype=float)
+    data_values = np.asarray(connected, dtype=np.complex128)
+    if (
+        delay_values.ndim != 1
+        or data_values.ndim != 1
+        or delay_values.shape != data_values.shape
+    ):
+        raise ValueError("delays and connected correlation must be equal vectors")
+    if period <= 0:
+        raise ValueError("period must be positive")
+    if isinstance(max_modes, bool) or max_modes < 1 or max_modes > len(poles):
+        raise ValueError("max_modes must select one or more available poles")
+    if not np.all(np.isfinite(delay_values)) or not np.all(np.isfinite(data_values)):
+        raise ValueError("correlation fit data must be finite")
+    if np.any(delay_values < 0):
+        raise ValueError("delays must be nonnegative")
+
+    scaled = delay_values / period
+    orders = np.rint(scaled).astype(int)
+    mask = np.isclose(scaled, orders, rtol=0.0, atol=1e-8)
+    stroboscopic_delays = delay_values[mask]
+    stroboscopic_orders = orders[mask]
+    stroboscopic_data = data_values[mask]
+    if len(stroboscopic_data) <= max_modes:
+        raise ValueError(
+            "the pole fit requires more stroboscopic samples than modes"
+        )
+
+    selected = poles[:max_modes]
+    design = np.column_stack(
+        [item.eigenvalue**stroboscopic_orders for item in selected]
+    ).astype(np.complex128, copy=False)
+    coefficients, _, _, _ = np.linalg.lstsq(
+        design,
+        stroboscopic_data,
+        rcond=None,
+    )
+    reconstruction = np.asarray(design @ coefficients, dtype=np.complex128)
+    denominator = float(np.sum(abs(stroboscopic_data))) + 1e-15
+    reconstruction_residual = float(
+        np.sum(abs(reconstruction - stroboscopic_data)) / denominator
+    )
+    return PoleFit(
+        residues=tuple(
+            PoleResidue(pole=pole, residue=complex(residue))
+            for pole, residue in zip(selected, coefficients, strict=True)
+        ),
+        reconstruction=reconstruction,
+        stroboscopic_delays=np.asarray(stroboscopic_delays, dtype=float),
+        reconstruction_residual=reconstruction_residual,
+        condition_number=float(np.linalg.cond(design)),
+    )
+
+
+def match_transfer_poles(
+    previous: tuple[TransferPole, ...],
+    current: tuple[TransferPole, ...],
+    *,
+    ambiguity_tolerance: float = 1e-6,
+) -> tuple[PoleMatch, ...]:
+    """Match two transfer spectra by minimum total complex-plane distance."""
+    if ambiguity_tolerance < 0:
+        raise ValueError("ambiguity_tolerance must be nonnegative")
+    if not previous or not current:
+        return ()
+    cost = np.asarray(
+        [
+            [
+                abs(previous_pole.eigenvalue - current_pole.eigenvalue)
+                for current_pole in current
+            ]
+            for previous_pole in previous
+        ],
+        dtype=float,
+    )
+    rows, columns = linear_sum_assignment(cost)
+    records: list[PoleMatch] = []
+    for row, column in zip(rows, columns, strict=True):
+        ordered = np.sort(cost[row])
+        ambiguous = bool(
+            len(ordered) > 1
+            and ordered[1] - ordered[0] <= ambiguity_tolerance
+        )
+        records.append(
+            PoleMatch(
+                previous_index=int(row),
+                current_index=int(column),
+                distance=float(cost[row, column]),
+                ambiguous=ambiguous,
+            )
+        )
+    return tuple(sorted(records, key=lambda item: item.previous_index))
diff --git a/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/pt_experiments.py b/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/pt_experiments.py
new file mode 100644
index 000000000..e0056d51b
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/pt_experiments.py
@@ -0,0 +1,192 @@
+"""Long-running PT-TEMPO baselines kept separate from fast CI experiments."""
+
+from __future__ import annotations
+
+from dataclasses import asdict
+
+import numpy as np
+
+from .backends.pt_tempo import PtTempoBackend
+from .config import BathConfig, ModelConfig
+from .heat_current import heat_current_spectrum
+from .models import coupling_operator, ising_hamiltonian
+from .spectra import diagonalize
+from .symmetry import Sector, n2_sectors, n3_reflection_sectors, project
+
+
+def _projected_model(config: ModelConfig, sector: Sector) -> tuple[np.ndarray, np.ndarray]:
+    return (
+        project(ising_hamiltonian(config), sector),
+        project(coupling_operator(config), sector),
+    )
+
+
+def n2_pt_tempo_heat() -> dict[str, object]:
+    """Non-Markovian N=2 heat spectrum with an explicit memory comparison."""
+    j = 0.5
+    gap = float(np.sqrt(1 + j**2) - j)
+    model = ModelConfig(
+        n=2,
+        j=j,
+        drive_amplitude=0.2,
+        drive_frequency=gap,
+    )
+    bath = BathConfig(alpha=0.1, cutoff=2.5)
+    _, triplet = n2_sectors()
+    h0, coupling = _projected_model(model, triplet)
+
+    def hamiltonian(time: float) -> np.ndarray:
+        return np.asarray(
+            h0
+            + model.drive_amplitude
+            * np.cos(model.drive_frequency * time)
+            * coupling,
+            dtype=np.complex128,
+        )
+
+    ground = diagonalize(h0).states[:, 0]
+    initial = np.outer(ground, ground.conj())
+    period_steps = 16
+    steady_periods = 10
+    delay_periods = 4
+    total_periods = steady_periods + 1 + delay_periods
+    dt = model.period / period_steps
+    backend = PtTempoBackend()
+    reference = backend.run(
+        hamiltonian,
+        coupling,
+        initial,
+        bath,
+        dt,
+        total_periods * period_steps,
+        memory_steps=5,
+        epsrel=1e-5,
+    )
+    shorter_memory = backend.run(
+        hamiltonian,
+        coupling,
+        initial,
+        bath,
+        dt,
+        steady_periods * period_steps,
+        memory_steps=4,
+        epsrel=1e-5,
+    )
+    phase_start = steady_periods * period_steps
+    phase_residual = float(
+        np.linalg.norm(
+            reference.result.density_matrices[phase_start]
+            - reference.result.density_matrices[phase_start - period_steps]
+        )
+    )
+    memory_residual = float(
+        np.linalg.norm(
+            reference.result.density_matrices[phase_start]
+            - shorter_memory.result.density_matrices[-1]
+        )
+    )
+    correlation = backend.period_averaged_correlation(
+        reference,
+        coupling,
+        phase_start,
+        period_steps,
+        delay_periods * period_steps,
+        model.drive_frequency,
+    )
+    frequencies = np.linspace(0, 3, 401)
+    heat = heat_current_spectrum(correlation, bath, frequencies)
+    tail = float(abs(correlation.connected[-1]))
+    converged = (
+        reference.result.converged
+        and phase_residual < 1e-3
+        and memory_residual < 5e-2
+        and tail < 5e-2
+    )
+    return {
+        "method": "pt_tempo_multitime",
+        "converged": converged,
+        "diagnostics": {
+            **reference.result.diagnostics,
+            "phase_residual": phase_residual,
+            "memory_k4_to_k5_residual": memory_residual,
+            "connected_tail_amplitude": tail,
+            "tau_max": float(correlation.delays[-1]),
+            "dt": dt,
+            "memory_steps": 5,
+            "epsrel": 1e-5,
+        },
+        "model": asdict(model),
+        "bath": asdict(bath),
+        "delta_peaks": [asdict(peak) for peak in heat.delta_peaks],
+        "data": [
+            {"frequency": float(frequency), "continuous": float(current)}
+            for frequency, current in zip(
+                heat.frequencies, heat.continuous, strict=True
+            )
+        ],
+    }
+
+
+def n3_pt_tempo_dynamics() -> dict[str, object]:
+    """N=3 reflection-even non-Markovian periodic-state convergence baseline."""
+    model = ModelConfig(
+        n=3,
+        j=0.5,
+        drive_amplitude=0.2,
+        drive_frequency=0.4450418679126287,
+    )
+    bath = BathConfig(alpha=0.1, cutoff=2.5)
+    _, even = n3_reflection_sectors()
+    h0, coupling = _projected_model(model, even)
+
+    def hamiltonian(time: float) -> np.ndarray:
+        return np.asarray(
+            h0
+            + model.drive_amplitude
+            * np.cos(model.drive_frequency * time)
+            * coupling,
+            dtype=np.complex128,
+        )
+
+    ground = diagonalize(h0).states[:, 0]
+    initial = np.outer(ground, ground.conj())
+    period_steps = 12
+    periods = 30
+    dt = model.period / period_steps
+    run = PtTempoBackend().run(
+        hamiltonian,
+        coupling,
+        initial,
+        bath,
+        dt,
+        periods * period_steps,
+        memory_steps=3,
+        epsrel=1e-5,
+    )
+    phase_residual = float(
+        np.linalg.norm(
+            run.result.density_matrices[-1]
+            - run.result.density_matrices[-1 - period_steps]
+        )
+    )
+    magnetization = [
+        float(np.real(np.trace(coupling @ state)))
+        for state in run.result.density_matrices[-1 - period_steps : -1]
+    ]
+    return {
+        "method": "pt_tempo",
+        "converged": run.result.converged and phase_residual < 1e-3,
+        "diagnostics": {
+            **run.result.diagnostics,
+            "phase_residual": phase_residual,
+            "dt": dt,
+            "memory_steps": 3,
+            "epsrel": 1e-5,
+        },
+        "model": asdict(model),
+        "bath": asdict(bath),
+        "data": [
+            {"phase_index": index, "magnetization": value}
+            for index, value in enumerate(magnetization)
+        ],
+    }
diff --git a/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/spectra.py b/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/spectra.py
new file mode 100644
index 000000000..30f32bcc7
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/spectra.py
@@ -0,0 +1,76 @@
+"""Hermitian spectra and symmetry-resolved bright transitions."""
+
+from __future__ import annotations
+
+from dataclasses import dataclass
+
+import numpy as np
+from numpy.typing import NDArray
+
+from .operators import ComplexMatrix
+
+
+@dataclass(frozen=True)
+class Spectrum:
+    energies: NDArray[np.float64]
+    states: ComplexMatrix
+
+
+@dataclass(frozen=True)
+class Transition:
+    source: int
+    target: int
+    frequency: float
+    weight: float
+    amplitude: complex
+
+
+def diagonalize(hamiltonian: ComplexMatrix) -> Spectrum:
+    if not np.allclose(hamiltonian, hamiltonian.conj().T, atol=1e-12):
+        raise ValueError("hamiltonian must be Hermitian")
+    energies, states = np.linalg.eigh(hamiltonian)
+    for column in range(states.shape[1]):
+        pivot = int(np.argmax(np.abs(states[:, column])))
+        phase = np.angle(states[pivot, column])
+        states[:, column] *= np.exp(-1j * phase)
+    return Spectrum(energies.astype(np.float64), states)
+
+
+def transitions(
+    source: Spectrum,
+    target: Spectrum,
+    operator: ComplexMatrix,
+    threshold: float = 1e-12,
+) -> list[Transition]:
+    if operator.shape != (target.states.shape[0], source.states.shape[0]):
+        raise ValueError("transition operator has incompatible dimensions")
+    matrix = target.states.conj().T @ operator @ source.states
+    out: list[Transition] = []
+    for target_index in range(len(target.energies)):
+        for source_index in range(len(source.energies)):
+            amplitude = matrix[target_index, source_index]
+            weight = float(abs(amplitude) ** 2)
+            if weight >= threshold:
+                out.append(
+                    Transition(
+                        source_index,
+                        target_index,
+                        float(target.energies[target_index] - source.energies[source_index]),
+                        weight,
+                        complex(amplitude),
+                    )
+                )
+    return out
+
+
+def ground_bright_transitions(
+    ground_sector: Spectrum,
+    opposite_sector: Spectrum,
+    cross_operator: ComplexMatrix,
+    threshold: float = 1e-12,
+) -> list[Transition]:
+    candidates = transitions(ground_sector, opposite_sector, cross_operator, threshold)
+    return sorted(
+        [item for item in candidates if item.source == 0 and item.frequency > 0],
+        key=lambda item: item.frequency,
+    )
diff --git a/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/symmetry.py b/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/symmetry.py
new file mode 100644
index 000000000..31f770b90
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/src/floquet_if_manybody/symmetry.py
@@ -0,0 +1,76 @@
+"""Exact Hilbert-space symmetry sectors for short open spin chains."""
+
+from __future__ import annotations
+
+from dataclasses import dataclass
+
+import numpy as np
+from numpy.typing import NDArray
+
+from .operators import ComplexMatrix, swap_operator
+
+
+@dataclass(frozen=True)
+class Sector:
+    name: str
+    isometry: ComplexMatrix
+
+    def __post_init__(self) -> None:
+        gram = self.isometry.conj().T @ self.isometry
+        if not np.allclose(gram, np.eye(gram.shape[0]), atol=1e-13):
+            raise ValueError(f"{self.name} isometry is not orthonormal")
+
+    @property
+    def dimension(self) -> int:
+        return int(self.isometry.shape[1])
+
+
+def _eigenspace(operator: ComplexMatrix, eigenvalue: float, name: str) -> Sector:
+    values, vectors = np.linalg.eigh(operator)
+    selected = vectors[:, np.isclose(values, eigenvalue, atol=1e-12)]
+    return Sector(name, selected)
+
+
+def n2_sectors() -> tuple[Sector, Sector]:
+    swap = swap_operator(0, 1, 2)
+    singlet = _eigenspace(swap, -1, "singlet")
+    triplet = _eigenspace(swap, +1, "triplet")
+    return singlet, triplet
+
+
+def n3_reflection_sectors() -> tuple[Sector, Sector]:
+    return reflection_sectors(3)
+
+
+def reflection_sectors(n: int) -> tuple[Sector, Sector]:
+    """Return odd/even sectors of full spatial reflection for an open chain."""
+    if n < 2:
+        raise ValueError("reflection sectors require at least two sites")
+    reflection = np.eye(2**n, dtype=np.complex128)
+    for site in range(n // 2):
+        reflection = swap_operator(site, n - 1 - site, n) @ reflection
+    odd = _eigenspace(reflection, -1, "odd")
+    even = _eigenspace(reflection, +1, "even")
+    return odd, even
+
+
+def n4_reflection_sectors() -> tuple[Sector, Sector]:
+    return reflection_sectors(4)
+
+
+def project(operator: ComplexMatrix, sector: Sector) -> ComplexMatrix:
+    if operator.shape[0] != sector.isometry.shape[0]:
+        raise ValueError("operator and sector dimensions do not match")
+    return sector.isometry.conj().T @ operator @ sector.isometry
+
+
+def cross_project(
+    operator: ComplexMatrix, left: Sector, right: Sector
+) -> NDArray[np.complex128]:
+    return left.isometry.conj().T @ operator @ right.isometry
+
+
+def sector_residual(operator: ComplexMatrix, sector: Sector) -> float:
+    identity = np.eye(operator.shape[0], dtype=np.complex128)
+    projector = sector.isometry @ sector.isometry.conj().T
+    return float(np.linalg.norm((identity - projector) @ operator @ sector.isometry))
diff --git a/tracks/mps/solutions/Ranger-123/tests/heat_valve_fixtures.py b/tracks/mps/solutions/Ranger-123/tests/heat_valve_fixtures.py
new file mode 100644
index 000000000..dfe5be707
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/tests/heat_valve_fixtures.py
@@ -0,0 +1,86 @@
+from __future__ import annotations
+
+from copy import deepcopy
+from typing import Any
+
+
+def valid_heat_valve_manifest() -> dict[str, Any]:
+    selected_points: list[dict[str, Any]] = []
+    points: list[dict[str, Any]] = []
+    flank_heat = {1: 1.0, 2: 2.0, 3: 6.0}
+    for n in (1, 2, 3):
+        for role, xi in zip(
+            ("lower_flank", "minimum", "upper_flank"),
+            (2.0, 2.2, 2.4),
+            strict=True,
+        ):
+            selected_points.append({"n": n, "xi": xi})
+            heat = 0.05 if role == "minimum" else flank_heat[n]
+            residue = 0.05 if role == "minimum" else flank_heat[n]
+            points.append(
+                {
+                    "complete": True,
+                    "converged": True,
+                    "point": {"n": n, "xi": xi},
+                    "model": {
+                        "n": n,
+                        "j": 1.0,
+                        "omega": 1.0,
+                        "drive_amplitude": 1.5 * xi,
+                        "drive_frequency": 3.0,
+                        "normalization": "bounded",
+                        "drive_normalization": "per_spin",
+                    },
+                    "bath": {
+                        "alpha": 0.05,
+                        "cutoff": 2.5,
+                        "temperature": 0.0,
+                    },
+                    "numerics": {
+                        "steps_per_period": 60,
+                        "tolerance": 1e-6,
+                        "phase_samples": 3,
+                        "delay_periods": 12,
+                        "pole_count": 8,
+                    },
+                    "diagnostics": {
+                        "trace_error": 1e-10,
+                        "hermiticity_error": 1e-10,
+                        "minimum_density_eigenvalue": 0.01,
+                        "fixed_point_residual": 1e-10,
+                        "connected_tail": 1e-3,
+                        "maximum_eigenpair_residual": 1e-12,
+                        "maximum_pole_modulus": 0.9,
+                    },
+                    "pole_fit": {
+                        "reconstruction_residual": 1e-3,
+                        "condition_number": 10.0,
+                    },
+                    "poles": [
+                        {
+                            "eigenvalue": {
+                                "real": 0.85,
+                                "imag": 0.1,
+                                "abs": 0.9,
+                            },
+                            "decay_rate": 0.05,
+                            "quasifrequency": 0.1,
+                            "eigenpair_residual": 1e-12,
+                            "residue": {"abs": residue},
+                        }
+                    ],
+                    "frequency": [0.0, 1.0, 2.0, 3.0],
+                    "continuous": [0.0, heat, heat / 2, 0.0],
+                    "integrated_absolute_heat": heat,
+                    "dominant_residue": {"abs": residue},
+                    "visible_residue_weight": residue,
+                }
+            )
+    return deepcopy(
+        {
+            "complete": True,
+            "selected_points": selected_points,
+            "points": points,
+            "markov_comparison": {"passed": True},
+        }
+    )
diff --git a/tracks/mps/solutions/Ranger-123/tests/test_adaptive.py b/tracks/mps/solutions/Ranger-123/tests/test_adaptive.py
new file mode 100644
index 000000000..52eb302f3
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/tests/test_adaptive.py
@@ -0,0 +1,312 @@
+from __future__ import annotations
+
+from dataclasses import asdict
+from pathlib import Path
+from typing import Any
+
+import numpy as np
+
+from floquet_if_manybody.adaptive import (
+    AdaptiveSchedule,
+    UniformAdaptiveSchedule,
+    run_adaptive,
+    run_uniform_adaptive,
+    run_uniform_compression_audit,
+)
+from floquet_if_manybody.convergence import ConvergenceCache, fingerprint
+from floquet_if_manybody.n3_heat import N3HeatPoint
+
+
+def _fake_runner(counter: dict[str, int]):
+    def run(point: N3HeatPoint, cache: ConvergenceCache | None) -> dict[str, Any]:
+        key = fingerprint(asdict(point), "fake")
+        if cache is not None and cache.contains(key):
+            return cache.load(key)
+        counter["calls"] += 1
+        error = (
+            (1 / point.steps_per_period) ** 2
+            + np.exp(-point.memory_steps)
+            + point.epsrel
+        )
+        grid = np.linspace(0, 1, 9)
+        payload: dict[str, Any] = {
+            "fingerprint": key,
+            "complete": True,
+            "converged": True,
+            "diagnostics": {
+                "phase_residual": 1e-5,
+                "trace_error": 1e-8,
+                "minimum_density_eigenvalue": 0.0,
+                "connected_tail_amplitude": 1e-4,
+            },
+            "phase_state": {"real": [1 - error, error], "imag": [0.0, 0.0]},
+            "correlation": {
+                "delay": grid.tolist(),
+                "connected": {
+                    "real": (np.exp(-grid) + error).tolist(),
+                    "imag": np.zeros_like(grid).tolist(),
+                },
+            },
+            "frequency": grid.tolist(),
+            "continuous": (grid * (1 + error)).tolist(),
+        }
+        if cache is not None:
+            cache.store(key, payload)
+            return cache.load(key)
+        return payload
+
+    return run
+
+
+def test_adaptive_refines_all_controls_and_resumes(tmp_path: Path) -> None:
+    counter = {"calls": 0}
+    runner = _fake_runner(counter)
+    cache = ConvergenceCache(tmp_path)
+    point = N3HeatPoint(
+        steps_per_period=4,
+        memory_steps=1,
+        epsrel=0.1,
+        steady_periods=1,
+        delay_periods=1,
+        frequency_points=9,
+    )
+    schedule = AdaptiveSchedule(
+        memory_steps=(1, 3, 6),
+        steps_per_period=(4, 8, 16),
+        epsrel=(0.1, 0.01, 0.001),
+        state_threshold=0.1,
+        correlation_threshold=0.1,
+        heat_threshold=0.1,
+    )
+    result = run_adaptive(point, schedule, runner, cache)
+    assert result.converged
+    assert result.final_point.memory_steps >= 3
+    assert result.final_point.steps_per_period >= 8
+    assert result.final_point.epsrel <= 0.01
+    assert result.final_point.memory_steps >= 12
+    assert {record.parameter for record in result.evidence} == {
+        "memory_steps",
+        "steps_per_period",
+        "epsrel",
+    }
+    first_calls = counter["calls"]
+    resumed = run_adaptive(point, schedule, runner, cache)
+    assert resumed.converged
+    assert counter["calls"] == first_calls
+
+
+def test_adaptive_reports_resource_ceiling() -> None:
+    counter = {"calls": 0}
+    point = N3HeatPoint(
+        steps_per_period=4,
+        memory_steps=1,
+        epsrel=0.1,
+        steady_periods=1,
+        delay_periods=1,
+        frequency_points=9,
+    )
+    schedule = AdaptiveSchedule(
+        memory_steps=(1, 2),
+        steps_per_period=(4, 8),
+        epsrel=(0.1, 0.05),
+        state_threshold=1e-12,
+        correlation_threshold=1e-12,
+        heat_threshold=1e-12,
+    )
+    result = run_adaptive(point, schedule, _fake_runner(counter), None)
+    assert not result.converged
+    assert result.status == "resource_ceiling"
+    assert result.failed_parameter == "memory_steps"
+
+
+def test_uniform_adaptive_refines_compression_timestep_and_phase() -> None:
+    calls: list[tuple[float, int, int | None]] = []
+
+    def runner(
+        point: N3HeatPoint, cache: ConvergenceCache | None
+    ) -> dict[str, Any]:
+        del cache
+        calls.append((point.epsrel, point.steps_per_period, point.phase_samples))
+        error = point.epsrel + 1 / point.steps_per_period**2 + 0.02 / (
+            point.phase_samples or point.steps_per_period
+        )
+        grid = np.linspace(0, 1, 9)
+        return {
+            "fingerprint": fingerprint(asdict(point), "uniform-fake"),
+            "complete": True,
+            "converged": True,
+            "diagnostics": {
+                "phase_residual": 1e-5,
+                "fixed_point_residual": 1e-5,
+                "trace_error": 1e-8,
+                "hermiticity_error": 1e-8,
+                "minimum_density_eigenvalue": 0.0,
+                "connected_tail_amplitude": 1e-4,
+                "bond_dimension": int(5 - np.log10(point.epsrel)),
+            },
+            "phase_state": {"real": [1 - error, error], "imag": [0.0, 0.0]},
+            "correlation": {
+                "delay": grid.tolist(),
+                "connected": {
+                    "real": (np.exp(-grid) + error).tolist(),
+                    "imag": np.zeros_like(grid).tolist(),
+                },
+            },
+            "frequency": grid.tolist(),
+            "continuous": (grid * (1 + error)).tolist(),
+        }
+
+    point = N3HeatPoint(
+        backend="uniform_tempo",
+        steps_per_period=12,
+        phase_samples=3,
+        epsrel=1e-3,
+        delay_periods=1,
+        frequency_points=9,
+    )
+    schedule = UniformAdaptiveSchedule(
+        steps_per_period=(12, 18),
+        tolerances=(1e-3, 1e-4),
+        phase_samples=(3, 6),
+        state_threshold=0.1,
+        correlation_threshold=0.1,
+        heat_threshold=0.1,
+    )
+    result = run_uniform_adaptive(point, schedule, runner, None)
+    assert result.converged
+    assert result.final_point.steps_per_period == 18
+    assert result.final_point.epsrel == 1e-4
+    assert result.final_point.phase_samples == 6
+    assert {record.parameter for record in result.evidence} == {
+        "epsrel",
+        "steps_per_period",
+        "phase_samples",
+    }
+    assert [record.parameter for record in result.evidence] == [
+        "epsrel",
+        "epsrel",
+        "steps_per_period",
+        "phase_samples",
+    ]
+    assert all(record.refined_bond_dimension is not None for record in result.evidence)
+    assert calls == [
+        (1e-3, 12, 3),
+        (1e-4, 12, 3),
+        (1e-3, 18, 3),
+        (1e-4, 18, 3),
+        (1e-4, 18, 6),
+    ]
+
+
+def test_uniform_schedule_requires_common_phase_divisors() -> None:
+    with np.testing.assert_raises_regex(ValueError, "phase_samples"):
+        UniformAdaptiveSchedule(
+            steps_per_period=(60, 90),
+            tolerances=(1e-6, 3e-7),
+            phase_samples=(3, 8),
+        )
+
+
+def test_uniform_adaptive_skips_compression_unstable_coarse_grid() -> None:
+    def runner(
+        point: N3HeatPoint, cache: ConvergenceCache | None
+    ) -> dict[str, Any]:
+        del cache
+        compression_scale = 10.0 if point.steps_per_period == 12 else 0.01
+        error = (
+            compression_scale * point.epsrel
+            + 1 / point.steps_per_period**2
+            + 0.001 / (point.phase_samples or 3)
+        )
+        grid = np.linspace(0, 1, 9)
+        return {
+            "fingerprint": fingerprint(asdict(point), "uniform-skip-fake"),
+            "complete": True,
+            "converged": True,
+            "diagnostics": {
+                "phase_residual": 1e-5,
+                "fixed_point_residual": 1e-5,
+                "trace_error": 1e-8,
+                "hermiticity_error": 1e-8,
+                "minimum_density_eigenvalue": 0.0,
+                "connected_tail_amplitude": 1e-4,
+                "bond_dimension": 10,
+            },
+            "phase_state": {"real": [1 - error, error], "imag": [0.0, 0.0]},
+            "correlation": {
+                "delay": grid.tolist(),
+                "connected": {
+                    "real": (np.exp(-grid) + error).tolist(),
+                    "imag": np.zeros_like(grid).tolist(),
+                },
+            },
+            "frequency": grid.tolist(),
+            "continuous": (grid * (1 + error)).tolist(),
+        }
+
+    point = N3HeatPoint(
+        backend="uniform_tempo",
+        steps_per_period=12,
+        phase_samples=3,
+        epsrel=0.1,
+        delay_periods=1,
+        frequency_points=9,
+    )
+    result = run_uniform_adaptive(
+        point,
+        UniformAdaptiveSchedule(
+            steps_per_period=(12, 18, 24),
+            tolerances=(0.1, 0.01),
+            phase_samples=(3, 6),
+            state_threshold=0.1,
+            correlation_threshold=0.1,
+            heat_threshold=0.1,
+        ),
+        runner,
+        None,
+    )
+    assert result.converged
+    assert result.final_point.steps_per_period == 24
+    assert any(
+        item.parameter == "epsrel"
+        and item.coarse_steps_per_period == 12
+        and not item.passed
+        for item in result.evidence
+    )
+    assert any(
+        item.parameter == "steps_per_period"
+        and item.coarse_steps_per_period == 18
+        and item.refined_steps_per_period == 24
+        and item.passed
+        for item in result.evidence
+    )
+
+
+def test_uniform_compression_audit_never_claims_full_convergence() -> None:
+    point = N3HeatPoint(
+        backend="uniform_tempo",
+        steps_per_period=12,
+        phase_samples=3,
+        epsrel=1e-3,
+        delay_periods=1,
+        frequency_points=9,
+    )
+    result = run_uniform_compression_audit(
+        point,
+        UniformAdaptiveSchedule(
+            steps_per_period=(12, 18),
+            tolerances=(1e-3, 1e-4),
+            phase_samples=(3, 6),
+            state_threshold=0.1,
+            correlation_threshold=0.1,
+            heat_threshold=0.1,
+        ),
+        _fake_runner({"calls": 0}),
+        None,
+    )
+    assert not result.converged
+    assert result.status == "resource_ceiling"
+    assert result.failed_parameter == "steps_per_period"
+    assert len(result.evidence) == 1
+    assert result.evidence[0].parameter == "epsrel"
+    assert result.evidence[0].passed
diff --git a/tracks/mps/solutions/Ranger-123/tests/test_bath.py b/tracks/mps/solutions/Ranger-123/tests/test_bath.py
new file mode 100644
index 000000000..e62b61acc
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/tests/test_bath.py
@@ -0,0 +1,12 @@
+from numpy.testing import assert_allclose
+
+from floquet_if_manybody.bath import bath_correlation
+from floquet_if_manybody.config import BathConfig
+
+
+def test_zero_temperature_ohmic_correlation():
+    bath = BathConfig(alpha=0.05, cutoff=2.5)
+    for time in [0, 0.1, 1.0, 3.0]:
+        expected = bath.alpha * bath.cutoff**2 / (1 + 1j * bath.cutoff * time) ** 2
+        assert_allclose(bath_correlation(time, bath), expected)
+        assert_allclose(bath_correlation(-time, bath), expected.conjugate())
diff --git a/tracks/mps/solutions/Ranger-123/tests/test_cli.py b/tracks/mps/solutions/Ranger-123/tests/test_cli.py
new file mode 100644
index 000000000..62b707b57
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/tests/test_cli.py
@@ -0,0 +1,70 @@
+import json
+from pathlib import Path
+
+from heat_valve_fixtures import valid_heat_valve_manifest
+
+from floquet_if_manybody.cli import build_parser, main
+
+
+def test_quick_baseline_and_audit(tmp_path):
+    results = tmp_path / "results"
+    figures = tmp_path / "figures"
+    assert main(["baselines", "--output", str(results), "--figures", str(figures), "--quick"]) == 0
+    assert main(["audit", str(results), "--allow-unconverged"]) == 0
+    for path in results.glob("*.json"):
+        payload = json.loads(path.read_text())
+        assert payload["schema_version"] == 1
+        assert payload["config_hash"]
+        assert payload["method"]
+        assert "environment" in payload
+    assert len(list(figures.glob("*.pdf"))) == 4
+    assert len(list(figures.glob("*.png"))) == 4
+
+
+def test_audit_ignores_artifact_provenance(tmp_path) -> None:
+    results = tmp_path / "results"
+    results.mkdir()
+    (results / "ARTIFACT_PROVENANCE.json").write_text(
+        json.dumps({"schema_version": 1, "artifacts": []}),
+        encoding="utf-8",
+    )
+    assert (
+        main(
+            [
+                "baselines",
+                "--output",
+                str(results),
+                "--figures",
+                str(tmp_path / "figures"),
+                "--quick",
+            ]
+        )
+        == 0
+    )
+    assert main(["audit", str(results), "--allow-unconverged"]) == 0
+
+
+def test_publication_commands_default_to_uniform_tempo() -> None:
+    parser = build_parser()
+    for command in ("n3-heat-grid", "error-map", "model-comparison"):
+        arguments = parser.parse_args([command])
+        assert arguments.exact_backend == "uniform_tempo"
+        explicit = parser.parse_args([command, "--exact-backend", "oqupy"])
+        assert explicit.exact_backend == "oqupy"
+
+
+def test_heat_valve_cli_defaults() -> None:
+    arguments = build_parser().parse_args(["heat-valve"])
+    assert arguments.output == Path("results/heat-valve")
+    assert arguments.cache == Path("results/cache/uniform_tempo")
+    assert arguments.figures == Path("figures/heat-valve")
+    assert not arguments.full
+
+
+def test_heat_valve_audit_command_accepts_a_valid_manifest(tmp_path) -> None:
+    manifest = valid_heat_valve_manifest()
+    (tmp_path / "heat_valve_manifest.json").write_text(
+        json.dumps(manifest),
+        encoding="utf-8",
+    )
+    assert main(["heat-valve-audit", str(tmp_path)]) == 0
diff --git a/tracks/mps/solutions/Ranger-123/tests/test_config.py b/tracks/mps/solutions/Ranger-123/tests/test_config.py
new file mode 100644
index 000000000..0a97a9e79
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/tests/test_config.py
@@ -0,0 +1,25 @@
+import pytest
+
+from floquet_if_manybody.config import ModelConfig, RunConfig
+
+
+def test_default_normalization_and_units():
+    cfg = RunConfig()
+    assert cfg.model.omega == 1.0
+    assert cfg.model.normalization == "bounded"
+    assert cfg.model.eta == 1 / cfg.model.n
+
+
+def test_normalizations():
+    assert ModelConfig(n=3, normalization="bounded").eta == pytest.approx(1 / 3)
+    assert ModelConfig(n=3, normalization="kac").eta == pytest.approx(1 / 3**0.5)
+    assert ModelConfig(n=3, normalization="collective").eta == 1
+
+
+def test_invalid_parameters_rejected():
+    with pytest.raises(ValueError, match="omega"):
+        ModelConfig(omega=0)
+
+
+def test_model_config_accepts_n4():
+    assert ModelConfig(n=4).n == 4
diff --git a/tracks/mps/solutions/Ranger-123/tests/test_convergence.py b/tracks/mps/solutions/Ranger-123/tests/test_convergence.py
new file mode 100644
index 000000000..c929bd0a4
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/tests/test_convergence.py
@@ -0,0 +1,35 @@
+import numpy as np
+import pytest
+
+from floquet_if_manybody.convergence import (
+    ConvergenceCache,
+    atomic_write_result,
+    curve_residual,
+    fingerprint,
+    state_residual,
+)
+
+
+def test_fingerprint_is_order_independent_and_commit_sensitive():
+    first = fingerprint({"alpha": 0.1, "dt": 0.2}, "abc")
+    second = fingerprint({"dt": 0.2, "alpha": 0.1}, "abc")
+    assert first == second
+    assert first != fingerprint({"alpha": 0.1, "dt": 0.2}, "def")
+
+
+def test_curve_and_state_residuals():
+    grid = np.linspace(0, 1, 11)
+    assert curve_residual(grid, grid, grid, grid) == 0
+    assert state_residual(np.eye(2), np.eye(2)) == 0
+    with pytest.raises(ValueError, match="grid"):
+        curve_residual(np.arange(3.0), np.ones(3), np.arange(4.0), np.ones(4))
+
+
+def test_cache_rejects_incomplete_or_wrong_key(tmp_path):
+    key = fingerprint({"x": 1}, "abc")
+    cache = ConvergenceCache(tmp_path)
+    cache.store(key, {"value": 3})
+    assert cache.load(key)["value"] == 3
+    atomic_write_result(cache.path_for(key), {"fingerprint": key, "complete": False})
+    with pytest.raises(ValueError, match="incomplete"):
+        cache.load(key)
diff --git a/tracks/mps/solutions/Ranger-123/tests/test_correlations.py b/tracks/mps/solutions/Ranger-123/tests/test_correlations.py
new file mode 100644
index 000000000..d82451e4a
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/tests/test_correlations.py
@@ -0,0 +1,26 @@
+import numpy as np
+from numpy.testing import assert_allclose
+
+from floquet_if_manybody.correlations import coherent_decomposition
+
+
+def test_single_cosine_has_one_coherent_harmonic():
+    steps = 128
+    omega = 1.7
+    amplitude = 0.6
+    period = 2 * np.pi / omega
+    times = np.arange(steps) * period / steps
+    delays = np.linspace(0, 3 * period, 301)
+    coherent, peaks = coherent_decomposition(amplitude * np.cos(omega * times), omega, delays)
+    assert len(peaks) == 1
+    assert peaks[0].harmonic == 1
+    assert_allclose(peaks[0].correlation_weight, amplitude**2 / 2, atol=1e-14)
+    assert_allclose(coherent, amplitude**2 / 2 * np.cos(omega * delays), atol=1e-14)
+
+
+def test_half_period_antisymmetry_removes_even_harmonics():
+    steps = 128
+    times = np.arange(steps) * 2 * np.pi / steps
+    signal = 0.4 * np.cos(times) + 0.1 * np.cos(3 * times)
+    _, peaks = coherent_decomposition(signal, 1.0, times)
+    assert {peak.harmonic for peak in peaks} == {1, 3}
diff --git a/tracks/mps/solutions/Ranger-123/tests/test_dark_channels.py b/tracks/mps/solutions/Ranger-123/tests/test_dark_channels.py
new file mode 100644
index 000000000..c355cb6a7
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/tests/test_dark_channels.py
@@ -0,0 +1,31 @@
+import numpy as np
+from numpy.testing import assert_allclose
+
+from floquet_if_manybody.dark_channels import (
+    dark_candidates,
+    floquet_matrix_elements,
+    harmonic_sum_rule,
+    period_variance,
+)
+from floquet_if_manybody.floquet import solve_floquet
+
+
+def test_static_system_has_only_zero_harmonic_matrix_elements():
+    hamiltonian = np.diag([-0.2, 0.3]).astype(complex)
+    operator = np.array([[0, 1], [1, 0]], dtype=complex)
+    solution = solve_floquet(lambda _time: hamiltonian, period=1.0, steps=64)
+    records = floquet_matrix_elements(solution, operator, harmonic_cutoff=2, threshold=1e-14)
+    bright = [record for record in records if record.weight > 1e-12]
+    assert {record.harmonic for record in bright} == {0}
+    assert_allclose(sorted(record.weight for record in bright), [1, 1], atol=1e-12)
+    assert harmonic_sum_rule(solution, operator, 2) < 1e-12
+
+
+def test_dark_candidates_and_variance():
+    hamiltonian = np.diag([-0.2, 0.3]).astype(complex)
+    operator = np.diag([1, -1]).astype(complex)
+    solution = solve_floquet(lambda _time: hamiltonian, period=1.0, steps=32)
+    records = floquet_matrix_elements(solution, operator, 1)
+    assert len(dark_candidates(records, 1e-8)) > 0
+    densities = np.repeat(np.eye(2, dtype=complex)[None, :, :] / 2, 8, axis=0)
+    assert_allclose(period_variance(densities, operator), 1)
diff --git a/tracks/mps/solutions/Ranger-123/tests/test_error_map.py b/tracks/mps/solutions/Ranger-123/tests/test_error_map.py
new file mode 100644
index 000000000..db950bcf6
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/tests/test_error_map.py
@@ -0,0 +1,99 @@
+from __future__ import annotations
+
+from copy import deepcopy
+
+import numpy as np
+import pytest
+
+from floquet_if_manybody.error_map import (
+    audit_grid_manifest,
+    build_error_record,
+    correlation_error,
+    heat_error,
+    trace_distance,
+)
+
+
+def _result(method: str) -> dict[str, object]:
+    return {
+        "method": method,
+        "converged": True,
+        "model_hash": "same",
+        "model": {"normalization": "bounded"},
+        "phase_state": {
+            "real": [[1.0, 0.0], [0.0, 0.0]],
+            "imag": [[0.0, 0.0], [0.0, 0.0]],
+        },
+        "correlation": {
+            "delay": [0.0, 1.0],
+            "connected": {"real": [1.0, 0.5], "imag": [0.0, 0.0]},
+        },
+        "frequency": [0.0, 1.0],
+        "continuous": [0.0, 1.0],
+        "evidence": [],
+    }
+
+
+def test_trace_distance_diagonal_example() -> None:
+    first = np.diag([0.75, 0.25]).astype(complex)
+    second = np.diag([0.5, 0.5]).astype(complex)
+    assert trace_distance(first, second) == pytest.approx(0.25)
+
+
+def test_identical_curves_have_zero_error() -> None:
+    grid = np.linspace(0, 1, 5)
+    curve = np.exp(-grid) + 1j * grid
+    assert correlation_error(grid, curve, grid, curve) == pytest.approx(0.0)
+    assert heat_error(grid, curve.real, grid, curve.real) == pytest.approx(0.0)
+
+
+@pytest.mark.parametrize("field", ["model_hash", "normalization", "frequency"])
+def test_build_record_rejects_incompatible_inputs(field: str) -> None:
+    exact = _result("pt_tempo_multitime")
+    markov = deepcopy(exact)
+    markov["method"] = "floquet_markov_qr"
+    if field == "model_hash":
+        markov["model_hash"] = "different"
+    elif field == "normalization":
+        markov["model"]["normalization"] = "kac"  # type: ignore[index]
+    else:
+        markov["frequency"] = [0.0, 2.0]
+    with pytest.raises(ValueError, match=field):
+        build_error_record(exact, markov)
+
+
+def test_build_record_rejects_unconverged_exact_input() -> None:
+    exact = _result("pt_tempo_multitime")
+    exact["converged"] = False
+    with pytest.raises(ValueError, match="converged"):
+        build_error_record(exact, _result("floquet_markov_qr"))
+
+
+@pytest.mark.parametrize(
+    "method",
+    ["pt_tempo_multitime", "uniform_tempo_floquet_multitime"],
+)
+def test_build_record_accepts_approved_process_tensor_methods(method: str) -> None:
+    record = build_error_record(_result(method), _result("floquet_markov_qr"))
+    assert record["status"] == "converged"
+    assert record["exact_method"] == method
+
+
+def test_grid_audit_accepts_explicit_resource_masks() -> None:
+    alphas = (0.025, 0.05, 0.1)
+    ratios = (0.75, 1.0, 1.25)
+    points = [
+        {
+            "alpha": alpha,
+            "drive_ratio": ratio,
+            "status": (
+                "resource_ceiling" if (alpha, ratio) == (0.1, 1.25) else "converged"
+            ),
+            "metrics": None if (alpha, ratio) == (0.1, 1.25) else {"heat": 0.1},
+        }
+        for alpha in alphas
+        for ratio in ratios
+    ]
+    audit = audit_grid_manifest({"points": points}, alphas, ratios)
+    assert audit["complete"]
+    assert audit["masked_points"] == 1
diff --git a/tracks/mps/solutions/Ranger-123/tests/test_fig3_validation.py b/tracks/mps/solutions/Ranger-123/tests/test_fig3_validation.py
new file mode 100644
index 000000000..0dd5b9955
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/tests/test_fig3_validation.py
@@ -0,0 +1,54 @@
+from __future__ import annotations
+
+import importlib.util
+from pathlib import Path
+
+import numpy as np
+
+
+def _module():
+    path = Path(__file__).parents[1] / "scripts" / "run_fig3_validation.py"
+    spec = importlib.util.spec_from_file_location("run_fig3_validation", path)
+    assert spec is not None and spec.loader is not None
+    module = importlib.util.module_from_spec(spec)
+    spec.loader.exec_module(module)
+    return module
+
+
+def test_reference_names_match_published_archive() -> None:
+    module = _module()
+    assert "ω_d_1.5" in module._reference_name(1.5)
+    assert module.REFERENCE_FREQUENCY.shape == (3000,)
+    assert np.isclose(module.REFERENCE_FREQUENCY[-1], 15.0)
+
+
+def test_comparison_metrics_separate_shape_and_amplitude() -> None:
+    module = _module()
+    reference = np.exp(-module.REFERENCE_FREQUENCY)
+    metrics = module.comparison_metrics(reference, 2 * reference)
+    assert np.isclose(metrics["continuous_relative_l1"], 0.5)
+    assert np.isclose(metrics["normalized_shape_relative_l1"], 0.0)
+    assert np.isclose(metrics["integrated_magnitude_ratio"], 2.0)
+
+
+def test_plot_summary_writes_both_publication_formats(tmp_path: Path) -> None:
+    module = _module()
+    curve = np.exp(-module.REFERENCE_FREQUENCY)
+    results = []
+    for drive_frequency in (1.0, 1.5, 2.0):
+        results.append(
+            {
+                "model": {"drive_frequency": drive_frequency},
+                "frequency": module.REFERENCE_FREQUENCY.tolist(),
+                "reference_continuous": curve.tolist(),
+                "continuous": curve.tolist(),
+                "delta_peaks": [
+                    {"frequency": drive_frequency, "harmonic": 1, "weight": 1.0}
+                ],
+                "metrics": {"normalized_shape_relative_l1": 0.0},
+            }
+        )
+    stem = tmp_path / "summary"
+    module.plot_summary(results, stem)
+    assert stem.with_suffix(".png").stat().st_size > 0
+    assert stem.with_suffix(".pdf").stat().st_size > 0
diff --git a/tracks/mps/solutions/Ranger-123/tests/test_finite_memory.py b/tracks/mps/solutions/Ranger-123/tests/test_finite_memory.py
new file mode 100644
index 000000000..b494a64b9
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/tests/test_finite_memory.py
@@ -0,0 +1,24 @@
+import numpy as np
+from numpy.testing import assert_allclose
+
+from floquet_if_manybody.backends.finite_memory import FiniteMemoryBackend
+from floquet_if_manybody.config import BathConfig
+
+
+def test_zero_bath_matches_unitary_evolution():
+    h = np.array([[0, 0.4], [0.4, 0]], dtype=complex)
+    coupling = np.diag([1, -1]).astype(complex)
+    rho0 = np.array([[1, 0], [0, 0]], dtype=complex)
+    dt = 0.05
+    result = FiniteMemoryBackend().run(
+        lambda _time: h, coupling, rho0, BathConfig(alpha=0), dt, 10, 2
+    )
+    unitary = expm_for_test(h, 10 * dt)
+    assert_allclose(result.density_matrices[-1], unitary @ rho0 @ unitary.conj().T, atol=1e-12)
+    assert result.diagnostics["trace_error"] < 1e-12
+
+
+def expm_for_test(hamiltonian, time):
+    from scipy.linalg import expm
+
+    return expm(-1j * hamiltonian * time)
diff --git a/tracks/mps/solutions/Ranger-123/tests/test_floquet.py b/tracks/mps/solutions/Ranger-123/tests/test_floquet.py
new file mode 100644
index 000000000..991fe5a96
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/tests/test_floquet.py
@@ -0,0 +1,30 @@
+import numpy as np
+from numpy.testing import assert_allclose
+from scipy.linalg import expm
+
+from floquet_if_manybody.floquet import solve_floquet
+
+
+def test_static_floquet_matches_matrix_exponential():
+    h = np.array([[0.2, 0.3], [0.3, -0.2]], dtype=complex)
+    period = 1.7
+    solution = solve_floquet(lambda _time: h, period, 32)
+    assert_allclose(solution.propagator, expm(-1j * h * period), atol=1e-13)
+    assert solution.unitarity_residual < 1e-13
+    assert solution.eigen_residual < 1e-12
+    assert np.all(solution.quasienergies >= -np.pi / period)
+    assert np.all(solution.quasienergies < np.pi / period)
+
+
+def test_midpoint_rule_converges_quadratically():
+    period = 2 * np.pi
+
+    def h(t):
+        return np.array([[0.4, 0.2 * np.cos(t)], [0.2 * np.cos(t), -0.4]])
+
+    reference = solve_floquet(h, period, 4096).propagator
+    errors = [
+        np.linalg.norm(solve_floquet(h, period, steps).propagator - reference)
+        for steps in (32, 64)
+    ]
+    assert errors[0] / errors[1] > 3.8
diff --git a/tracks/mps/solutions/Ranger-123/tests/test_floquet_markov.py b/tracks/mps/solutions/Ranger-123/tests/test_floquet_markov.py
new file mode 100644
index 000000000..4e0180ba1
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/tests/test_floquet_markov.py
@@ -0,0 +1,15 @@
+import numpy as np
+
+from floquet_if_manybody.backends.floquet_markov import FloquetMarkovBackend
+from floquet_if_manybody.config import BathConfig
+
+
+def test_markov_result_is_trace_preserving_and_labeled():
+    h = np.array([[0.5, 0.2], [0.2, -0.5]], dtype=complex)
+    s = np.diag([1, -1]).astype(complex)
+    result = FloquetMarkovBackend().run(
+        lambda _time: h, s, BathConfig(alpha=0.01), 2 * np.pi, 64, 2
+    )
+    assert result.method == "floquet_markov"
+    assert result.diagnostics["trace_error"] < 1e-12
+    assert result.diagnostics["minimum_population"] >= -1e-12
diff --git a/tracks/mps/solutions/Ranger-123/tests/test_heat_current.py b/tracks/mps/solutions/Ranger-123/tests/test_heat_current.py
new file mode 100644
index 000000000..5e05ae22f
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/tests/test_heat_current.py
@@ -0,0 +1,34 @@
+import numpy as np
+from numpy.testing import assert_allclose
+
+from floquet_if_manybody.config import BathConfig
+from floquet_if_manybody.correlations import CorrelationResult, DeltaCorrelationPeak
+from floquet_if_manybody.heat_current import heat_current_spectrum
+
+
+def test_coherent_delta_peak_is_not_smeared_into_continuum():
+    delays = np.linspace(0, 20, 2001)
+    weight = 0.18
+    frequency = 1.7
+    coherent = weight * np.cos(frequency * delays)
+    correlation = CorrelationResult(
+        delays,
+        coherent.astype(complex),
+        np.zeros_like(delays, dtype=complex),
+        coherent,
+        (DeltaCorrelationPeak(1, frequency, weight),),
+        "analytic_test",
+        {},
+    )
+    bath = BathConfig(alpha=0.05, cutoff=2.5)
+    result = heat_current_spectrum(correlation, bath, np.linspace(0, 4, 101))
+    assert_allclose(result.continuous, 0)
+    expected = (
+        np.pi
+        * bath.alpha
+        * frequency
+        * np.exp(-frequency / bath.cutoff)
+        * frequency
+        * weight
+    )
+    assert_allclose(result.delta_peaks[0].weight, expected)
diff --git a/tracks/mps/solutions/Ranger-123/tests/test_heat_valve.py b/tracks/mps/solutions/Ranger-123/tests/test_heat_valve.py
new file mode 100644
index 000000000..591ce4ddc
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/tests/test_heat_valve.py
@@ -0,0 +1,193 @@
+from __future__ import annotations
+
+from dataclasses import asdict
+from pathlib import Path
+
+import numpy as np
+import pytest
+from numpy.testing import assert_allclose
+from scipy.special import jn_zeros
+
+import floquet_if_manybody.heat_valve as heat_valve_module
+from floquet_if_manybody.backends.uniform_tempo import UniformTempoResult
+from floquet_if_manybody.convergence import ConvergenceCache
+from floquet_if_manybody.correlations import CorrelationResult
+from floquet_if_manybody.heat_valve import (
+    HeatValvePoint,
+    ValveNumerics,
+    build_heat_valve_manifest,
+    isolated_valve_scan,
+    prepare_heat_valve_point,
+    run_uniform_valve_point,
+)
+
+
+class FakePoleBackend:
+    def __init__(self, **_kwargs: object) -> None:
+        pass
+
+    def run_periodic(
+        self,
+        h0: np.ndarray,
+        coupling: np.ndarray,
+        model: object,
+        _bath: object,
+        controls: object,
+        *,
+        drive_operator: np.ndarray,
+    ) -> UniformTempoResult:
+        assert_allclose(drive_operator, 3 * coupling)
+        dimension = h0.shape[0]
+        period = model.period
+        dt = period / controls.steps_per_period
+        delays = np.arange(controls.delay_steps + 1) * dt
+        eigenvalues = np.array(
+            [1.0, 0.85, 0.75, 0.65, 0.55, 0.45, 0.4, 0.35],
+            dtype=complex,
+        )
+        residues = np.linspace(0.7, 0.1, 7).astype(complex)
+        connected = np.zeros(len(delays), dtype=complex)
+        for index, delay in enumerate(delays):
+            scaled = delay / period
+            if np.isclose(scaled, round(scaled), atol=1e-10):
+                order = round(scaled)
+                connected[index] = np.sum(residues * eigenvalues[1:] ** order)
+        correlation = CorrelationResult(
+            delays=delays,
+            total=connected,
+            connected=connected,
+            coherent=np.zeros(len(delays)),
+            delta_peaks=(),
+            method="uniform_tempo_floquet_multitime",
+            metadata={"dt": dt},
+        )
+        state = np.eye(dimension, dtype=complex) / dimension
+        return UniformTempoResult(
+            method="uniform_tempo_floquet_multitime",
+            floquet_state=state,
+            phase_states=np.repeat(
+                state[None, ...],
+                controls.phase_samples,
+                axis=0,
+            ),
+            correlation=correlation,
+            diagnostics={
+                "trace_error": 1e-12,
+                "hermiticity_error": 1e-12,
+                "minimum_density_eigenvalue": 1 / dimension,
+                "fixed_point_residual": 1e-12,
+                "floquet_transfer_residual": 1e-12,
+            },
+            metadata={
+                "dt": dt,
+                "period_steps": controls.steps_per_period,
+                "phase_samples": controls.phase_samples,
+                "bond_dimension": 2,
+                "tolerance": controls.tolerance,
+                "julia_version": "1.12.6",
+                "uniform_tempo_revision": "test",
+                "manifest_sha256": "a" * 64,
+                "process_tensor_cache_hit": 0,
+                "transfer_dimension": 48,
+                "pole_count": 8,
+            },
+            transfer_eigenvalues=eigenvalues,
+            transfer_eigenpair_residuals=np.full(8, 1e-12),
+        )
+
+
+def test_heat_valve_uses_common_physical_drive_for_all_sizes() -> None:
+    prepared = [
+        prepare_heat_valve_point(HeatValvePoint(n=n, xi=2.2))
+        for n in (1, 2, 3)
+    ]
+    assert_allclose(
+        [item.model.drive_amplitude for item in prepared],
+        [prepared[0].model.drive_frequency * 2.2 / 2] * 3,
+    )
+    assert_allclose(
+        [
+            np.linalg.norm(item.drive) / np.linalg.norm(item.coupling)
+            for item in prepared
+        ],
+        [1, 2, 3],
+    )
+
+
+def test_single_spin_high_frequency_gap_minimum_tracks_first_bessel_zero() -> None:
+    xis = np.linspace(2.2, 2.6, 41)
+    manifest = isolated_valve_scan(
+        HeatValvePoint(
+            n=1,
+            j=0.0,
+            drive_frequency=6.0,
+            xi=float(xi),
+            floquet_steps=360,
+        )
+        for xi in xis
+    )
+    minimum = min(manifest["points"], key=lambda item: item["cat_gap"])
+    assert abs(minimum["xi"] - jn_zeros(0, 1)[0]) <= xis[1] - xis[0]
+
+
+def test_interacting_scan_returns_resolved_cat_diagnostics() -> None:
+    manifest = isolated_valve_scan(
+        HeatValvePoint(n=n, xi=xi, drive_frequency=3.0, floquet_steps=180)
+        for n in (2, 3)
+        for xi in (2.2, 2.4, 2.6)
+    )
+    assert manifest["complete"]
+    assert len(manifest["points"]) == 6
+    for point in manifest["points"]:
+        assert point["cat_overlap"] >= 0.5
+        assert point["cat_gap"] >= 0
+        assert point["cat_brightness"] >= 0
+        assert point["unitarity_residual"] < 1e-10
+        assert point["floquet_eigen_residual"] < 1e-10
+
+
+def test_uniform_valve_point_records_poles_residues_and_fixed_controls(
+    tmp_path: Path,
+    monkeypatch: pytest.MonkeyPatch,
+) -> None:
+    monkeypatch.setattr(
+        heat_valve_module,
+        "UniformTempoBackend",
+        FakePoleBackend,
+    )
+    result = run_uniform_valve_point(
+        HeatValvePoint(n=3, xi=2.4, drive_frequency=3.0),
+        ValveNumerics(
+            steps_per_period=60,
+            tolerance=1e-6,
+            phase_samples=3,
+            delay_periods=12,
+            pole_count=8,
+        ),
+        ConvergenceCache(tmp_path),
+        source_revision="test",
+    )
+    assert result["model"]["drive_frequency"] == 3.0
+    assert result["bath"]["cutoff"] == 2.5
+    assert result["pole_fit"]["reconstruction_residual"] < 0.05
+    assert len(result["poles"]) == 7
+
+
+def test_manifest_selects_minimum_and_two_resolved_flanks() -> None:
+    records = []
+    for n in (1, 2, 3):
+        for xi, gap in ((2.0, 0.2), (2.2, 0.01), (2.4, 0.3)):
+            records.append(
+                {
+                    **asdict(HeatValvePoint(n=n, xi=xi)),
+                    "cat_overlap": 0.9,
+                    "cat_gap": gap,
+                }
+            )
+    manifest = build_heat_valve_manifest(
+        {"complete": True, "points": records}
+    )
+    assert not manifest["complete"]
+    assert [
+        point["xi"] for point in manifest["selected_points"]
+    ] == [2.0, 2.2, 2.4] * 3
diff --git a/tracks/mps/solutions/Ranger-123/tests/test_heat_valve_audit.py b/tracks/mps/solutions/Ranger-123/tests/test_heat_valve_audit.py
new file mode 100644
index 000000000..5f3fa24cd
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/tests/test_heat_valve_audit.py
@@ -0,0 +1,71 @@
+from __future__ import annotations
+
+from collections.abc import Callable
+from typing import Any
+
+import pytest
+from heat_valve_fixtures import valid_heat_valve_manifest
+
+from floquet_if_manybody.heat_valve_audit import audit_heat_valve_manifest
+
+
+@pytest.mark.parametrize(
+    ("mutation", "failure"),
+    [
+        (
+            lambda manifest: manifest["points"][0]["model"].update(
+                drive_frequency=2.9
+            ),
+            "fixed drive frequency",
+        ),
+        (
+            lambda manifest: manifest["points"][1]["pole_fit"].update(
+                reconstruction_residual=0.08
+            ),
+            "pole reconstruction",
+        ),
+        (
+            lambda manifest: manifest["points"][1].update(
+                integrated_absolute_heat=0.2
+            ),
+            "tenfold heat suppression",
+        ),
+        (
+            lambda manifest: manifest["points"][1].update(
+                visible_residue_weight=0.2
+            ),
+            "tenfold residue suppression",
+        ),
+        (
+            lambda manifest: manifest["points"][1]["poles"][0].update(
+                eigenpair_residual=1e-6
+            ),
+            "eigenpair residual",
+        ),
+        (
+            lambda manifest: manifest["points"][1]["poles"][0][
+                "eigenvalue"
+            ].update(abs=1.01),
+            "unit disk",
+        ),
+    ],
+)
+def test_audit_rejects_unsupported_dark_claim(
+    mutation: Callable[[dict[str, Any]], None],
+    failure: str,
+) -> None:
+    manifest = valid_heat_valve_manifest()
+    mutation(manifest)
+    audit = audit_heat_valve_manifest(manifest)
+    assert not audit.dark_channel_passed
+    assert any(failure in item for item in audit.failures)
+
+
+def test_audit_accepts_fixed_frequency_many_body_valve() -> None:
+    audit = audit_heat_valve_manifest(valid_heat_valve_manifest())
+    assert audit.complete
+    assert audit.dark_channel_passed
+    assert audit.many_body_amplification_passed
+    assert audit.markov_payoff_passed
+    assert audit.failures == ()
+    assert audit.metrics["heat_contrast_n3"] == 120.0
diff --git a/tracks/mps/solutions/Ranger-123/tests/test_influence.py b/tracks/mps/solutions/Ranger-123/tests/test_influence.py
new file mode 100644
index 000000000..ce7704b51
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/tests/test_influence.py
@@ -0,0 +1,18 @@
+import numpy as np
+from numpy.testing import assert_allclose
+
+from floquet_if_manybody.config import BathConfig
+from floquet_if_manybody.influence import discretize_influence
+
+
+def test_zero_coupling_has_zero_coefficients():
+    coefficients = discretize_influence(BathConfig(alpha=0), 0.1, 3)
+    assert_allclose(coefficients.values, 0, atol=1e-15)
+
+
+def test_small_cell_diagonal_limit():
+    bath = BathConfig(alpha=0.05, cutoff=2.5)
+    dt = 1e-3
+    coefficient = discretize_influence(bath, dt, 1).values[0]
+    assert_allclose(coefficient, 0.5 * bath.alpha * bath.cutoff**2 * dt**2, rtol=2e-3)
+    assert np.imag(coefficient) < 0
diff --git a/tracks/mps/solutions/Ranger-123/tests/test_model_comparison.py b/tracks/mps/solutions/Ranger-123/tests/test_model_comparison.py
new file mode 100644
index 000000000..2cf27a2b7
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/tests/test_model_comparison.py
@@ -0,0 +1,41 @@
+from __future__ import annotations
+
+import numpy as np
+from numpy.testing import assert_allclose
+
+from floquet_if_manybody.config import BathConfig
+from floquet_if_manybody.model_comparison import (
+    diagnostic_heat_rescaling,
+    model_variants,
+    variant_operators,
+)
+
+
+def test_variants_have_expected_coupling_norms() -> None:
+    variants = model_variants(n=3, j=0.5, bath=BathConfig(alpha=0.1, cutoff=2.5))
+    bounded = next(item for item in variants if item.name == "bounded_no_ct")
+    kac = next(item for item in variants if item.name == "kac_no_ct")
+    _, bounded_s = variant_operators(bounded)
+    _, kac_s = variant_operators(kac)
+    assert_allclose(np.linalg.norm(bounded_s, 2), 1.0)
+    assert_allclose(np.linalg.norm(kac_s, 2), np.sqrt(3))
+
+
+def test_counterterm_difference_is_explicit_s_squared() -> None:
+    bath = BathConfig(alpha=0.1, cutoff=2.5)
+    variants = model_variants(n=3, j=0.5, bath=bath)
+    no_ct = next(item for item in variants if item.name == "bounded_no_ct")
+    with_ct = next(item for item in variants if item.name == "bounded_ct")
+    h0, coupling = variant_operators(no_ct)
+    hct, _ = variant_operators(with_ct)
+    assert_allclose(hct - h0, bath.alpha * bath.cutoff * coupling @ coupling)
+    assert with_ct.metadata["counterterm_strength"] == 0.25
+    assert with_ct.metadata["normalization"] == "bounded"
+
+
+def test_diagnostic_rescaling_never_overwrites_raw_heat() -> None:
+    values = np.array([1.0, 2.0])
+    raw, diagnostic = diagnostic_heat_rescaling(values, eta=1 / 3)
+    assert_allclose(raw, values)
+    assert_allclose(diagnostic, 9 * values)
+    assert not np.shares_memory(raw, values)
diff --git a/tracks/mps/solutions/Ranger-123/tests/test_models.py b/tracks/mps/solutions/Ranger-123/tests/test_models.py
new file mode 100644
index 000000000..cd1bb7675
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/tests/test_models.py
@@ -0,0 +1,46 @@
+from numpy.testing import assert_allclose
+
+from floquet_if_manybody.config import ModelConfig
+from floquet_if_manybody.models import (
+    coupling_operator,
+    drive_operator,
+    ising_hamiltonian,
+)
+
+
+def test_n3_ising_diagonal_is_open_boundary():
+    cfg = ModelConfig(n=3, j=1, omega=1)
+    assert_allclose(
+        ising_hamiltonian(cfg).diagonal(),
+        [-2, 0, 2, 0, 0, 2, 0, -2],
+    )
+
+
+def test_counterterm_has_explicit_physical_coefficient():
+    bare = ModelConfig(n=2, counterterm_strength=0)
+    dressed = ModelConfig(n=2, counterterm=True, counterterm_strength=0.125)
+    s = coupling_operator(bare)
+    assert_allclose(
+        ising_hamiltonian(dressed) - ising_hamiltonian(bare),
+        0.125 * (s @ s),
+    )
+
+
+def test_per_spin_drive_is_independent_of_bath_normalization() -> None:
+    bounded = ModelConfig(
+        n=3,
+        normalization="bounded",
+        drive_normalization="per_spin",
+    )
+    kac = ModelConfig(
+        n=3,
+        normalization="kac",
+        drive_normalization="per_spin",
+    )
+    assert_allclose(drive_operator(bounded), drive_operator(kac))
+    assert_allclose(drive_operator(bounded), 3 * coupling_operator(bounded))
+
+
+def test_default_drive_operator_preserves_existing_semantics() -> None:
+    config = ModelConfig(n=3, normalization="bounded")
+    assert_allclose(drive_operator(config), coupling_operator(config))
diff --git a/tracks/mps/solutions/Ranger-123/tests/test_n2_heat.py b/tracks/mps/solutions/Ranger-123/tests/test_n2_heat.py
new file mode 100644
index 000000000..1248c564f
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/tests/test_n2_heat.py
@@ -0,0 +1,26 @@
+from __future__ import annotations
+
+from numpy.testing import assert_allclose
+
+from floquet_if_manybody.n2_heat import N2HeatPoint, prepare_n2_triplet
+
+
+def test_n2_triplet_preparation_tracks_exact_low_gap() -> None:
+    prepared = prepare_n2_triplet(N2HeatPoint(j=0.5))
+    assert prepared.dimension == 3
+    assert_allclose(prepared.bright_gap, (1.25) ** 0.5 - 0.5)
+    assert_allclose(prepared.model.drive_frequency, prepared.bright_gap)
+
+
+def test_n2_drive_ratio_and_counterterm_are_explicit() -> None:
+    prepared = prepare_n2_triplet(
+        N2HeatPoint(
+            j=0.5,
+            drive_ratio=1.25,
+            alpha=0.1,
+            cutoff=2.5,
+            counterterm=True,
+        )
+    )
+    assert_allclose(prepared.model.drive_frequency, 1.25 * prepared.bright_gap)
+    assert prepared.model.counterterm_strength == 0.25
diff --git a/tracks/mps/solutions/Ranger-123/tests/test_n3_heat.py b/tracks/mps/solutions/Ranger-123/tests/test_n3_heat.py
new file mode 100644
index 000000000..17bbc92a2
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/tests/test_n3_heat.py
@@ -0,0 +1,181 @@
+from __future__ import annotations
+
+import numpy as np
+from numpy.testing import assert_allclose
+
+import floquet_if_manybody.n3_heat as n3_heat_module
+from floquet_if_manybody.backends.uniform_tempo import UniformTempoResult
+from floquet_if_manybody.correlations import CorrelationResult
+from floquet_if_manybody.n3_heat import (
+    N3HeatPoint,
+    compare_sector_spectra,
+    prepare_n3_sector,
+    run_n3_heat_point,
+)
+
+
+def test_odd_point_is_j_independent_before_backend() -> None:
+    a = prepare_n3_sector(N3HeatPoint(j=0.25, sector="odd"))
+    b = prepare_n3_sector(N3HeatPoint(j=1.0, sector="odd"))
+    assert_allclose(a.h0, b.h0, atol=1e-13)
+    assert_allclose(a.coupling, b.coupling, atol=1e-13)
+    assert a.dimension == 2
+
+
+def test_default_drive_tracks_sector_bright_gap() -> None:
+    even = prepare_n3_sector(N3HeatPoint(j=0.5, sector="even"))
+    odd = prepare_n3_sector(N3HeatPoint(j=0.5, sector="odd"))
+    assert_allclose(even.bright_gap, 0.4450418679126287, rtol=1e-10)
+    assert_allclose(even.model.drive_frequency, even.bright_gap)
+    assert_allclose(odd.bright_gap, 1.0, atol=1e-13)
+    assert_allclose(odd.model.drive_frequency, 1.0, atol=1e-13)
+
+
+def test_n3_per_spin_drive_projection_differs_from_bounded_bath() -> None:
+    prepared = prepare_n3_sector(
+        N3HeatPoint(
+            j=0.5,
+            sector="even",
+            drive_normalization="per_spin",
+        )
+    )
+    assert_allclose(prepared.drive, 3 * prepared.coupling)
+
+
+def test_derived_drive_frequency_is_stable_at_cache_precision() -> None:
+    prepared = prepare_n3_sector(N3HeatPoint(j=0.5, sector="even"))
+    assert prepared.bright_gap == 0.44504186791263
+
+
+def test_drive_ratio_and_counterterm_are_explicit() -> None:
+    prepared = prepare_n3_sector(
+        N3HeatPoint(
+            j=0.5,
+            sector="even",
+            drive_ratio=1.25,
+            alpha=0.1,
+            cutoff=2.5,
+            counterterm=True,
+        )
+    )
+    assert_allclose(prepared.model.drive_frequency, 1.25 * prepared.bright_gap)
+    assert prepared.model.counterterm_strength == 0.25
+
+
+def test_phase_sample_count_must_divide_period_steps() -> None:
+    with np.testing.assert_raises_regex(ValueError, "phase_samples"):
+        N3HeatPoint(steps_per_period=12, phase_samples=5)
+
+
+def test_uniform_backend_controls_are_explicit() -> None:
+    point = N3HeatPoint(
+        backend="uniform_tempo",
+        steps_per_period=60,
+        phase_samples=3,
+        epsrel=1e-7,
+        uniform_auto_nc=False,
+        uniform_memory_cutoff=500,
+        uniform_low_rank_svd=True,
+        uniform_truncation="abs",
+        uniform_cap_rank=400,
+        uniform_max_rank=800,
+    )
+    assert point.backend == "uniform_tempo"
+    assert point.uniform_memory_cutoff == 500
+    assert point.uniform_truncation == "abs"
+
+
+def test_backend_label_is_validated() -> None:
+    with np.testing.assert_raises_regex(ValueError, "backend"):
+        N3HeatPoint(backend="unknown")  # type: ignore[arg-type]
+
+
+def test_uniform_backend_routes_through_existing_heat_transform(monkeypatch) -> None:
+    class FakeUniformBackend:
+        def __init__(self, **kwargs) -> None:
+            assert kwargs["tensor_cache_directory"] is None
+
+        def run_periodic(
+            self,
+            h0,
+            coupling,
+            model,
+            bath,
+            controls,
+            *,
+            drive_operator=None,
+        ):
+            assert h0.shape == (6, 6)
+            assert coupling.shape == (6, 6)
+            assert_allclose(drive_operator, coupling)
+            assert controls.steps_per_period == 4
+            assert controls.phase_samples == 2
+            delays = np.linspace(0.0, model.period, 5)
+            total = np.linspace(0.1, 0.01, 5).astype(complex)
+            correlation = CorrelationResult(
+                delays,
+                total,
+                total.copy(),
+                np.zeros(5),
+                (),
+                "uniform_tempo_floquet_multitime",
+                {"dt": model.period / 4},
+            )
+            return UniformTempoResult(
+                "uniform_tempo_floquet_multitime",
+                np.eye(6, dtype=complex) / 6,
+                np.repeat((np.eye(6, dtype=complex) / 6)[None, ...], 2, axis=0),
+                correlation,
+                {
+                    "trace_error": 1e-8,
+                    "hermiticity_error": 1e-8,
+                    "minimum_density_eigenvalue": 1 / 6,
+                    "fixed_point_residual": 1e-8,
+                    "floquet_transfer_residual": 1e-8,
+                },
+                {
+                    "dt": model.period / 4,
+                    "period_steps": 4,
+                    "phase_samples": 2,
+                    "bond_dimension": 3,
+                    "tolerance": controls.tolerance,
+                    "julia_version": "1.12.6",
+                    "uniform_tempo_revision": "b76a018",
+                    "manifest_sha256": "a" * 64,
+                },
+            )
+
+    monkeypatch.setattr(
+        n3_heat_module,
+        "UniformTempoBackend",
+        FakeUniformBackend,
+    )
+    result = run_n3_heat_point(
+        N3HeatPoint(
+            backend="uniform_tempo",
+            steps_per_period=4,
+            phase_samples=2,
+            delay_periods=1,
+            epsrel=1e-4,
+            frequency_points=9,
+        ),
+        commit="test",
+    )
+    assert result["converged"]
+    assert result["method"] == "uniform_tempo_floquet_multitime"
+    assert result["diagnostics"]["bond_dimension"] == 3
+    assert len(result["continuous"]) == 9
+
+
+def test_compare_sector_spectra_requires_matching_grids() -> None:
+    even = {
+        "frequency": [0.0, 1.0, 2.0],
+        "continuous": [0.0, 2.0, 0.0],
+    }
+    odd = {
+        "frequency": [0.0, 1.0, 2.0],
+        "continuous": [0.0, 1.0, 0.0],
+    }
+    comparison = compare_sector_spectra(even, odd)
+    assert comparison["maximum_absolute_difference"] == 1.0
+    assert np.isclose(comparison["normalized_l1_difference"], 1.0)
diff --git a/tracks/mps/solutions/Ranger-123/tests/test_operators.py b/tracks/mps/solutions/Ranger-123/tests/test_operators.py
new file mode 100644
index 000000000..fc3d90d3a
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/tests/test_operators.py
@@ -0,0 +1,17 @@
+import numpy as np
+from numpy.testing import assert_allclose
+
+from floquet_if_manybody.operators import collective_operator, pauli, site_operator
+
+
+def test_collective_z_eigenvalues():
+    s = collective_operator("z", n=2, eta=0.5)
+    assert_allclose(np.diag(s), [1, 0, 0, -1])
+
+
+def test_site_algebra():
+    x0 = site_operator("x", 0, 2)
+    y0 = site_operator("y", 0, 2)
+    z0 = site_operator("z", 0, 2)
+    assert_allclose(x0 @ y0, 1j * z0)
+    assert_allclose(pauli("x") @ pauli("x"), np.eye(2))
diff --git a/tracks/mps/solutions/Ranger-123/tests/test_paper_audit.py b/tracks/mps/solutions/Ranger-123/tests/test_paper_audit.py
new file mode 100644
index 000000000..3a7d74b08
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/tests/test_paper_audit.py
@@ -0,0 +1,176 @@
+from __future__ import annotations
+
+import json
+from pathlib import Path
+from typing import Any
+
+from floquet_if_manybody.paper_extension import audit_paper_results
+
+
+def _evidence() -> list[dict[str, Any]]:
+    common = {
+        "coarse_fingerprint": "a" * 64,
+        "refined_fingerprint": "b" * 64,
+        "state_residual": 1e-3,
+        "correlation_residual": 2e-3,
+        "heat_residual": 3e-3,
+        "passed": True,
+        "coarse_bond_dimension": 10,
+        "refined_bond_dimension": 12,
+        "coarse_phase_samples": 3,
+        "refined_phase_samples": 3,
+    }
+    return [
+        {
+            **common,
+            "parameter": "epsrel",
+            "coarse_value": 3e-7,
+            "refined_value": 1e-7,
+            "coarse_steps_per_period": 60,
+            "refined_steps_per_period": 60,
+            "coarse_tolerance": 3e-7,
+            "refined_tolerance": 1e-7,
+        },
+        {
+            **common,
+            "parameter": "epsrel",
+            "coarse_value": 3e-7,
+            "refined_value": 1e-7,
+            "coarse_steps_per_period": 90,
+            "refined_steps_per_period": 90,
+            "coarse_tolerance": 3e-7,
+            "refined_tolerance": 1e-7,
+        },
+        {
+            **common,
+            "parameter": "steps_per_period",
+            "coarse_value": 60,
+            "refined_value": 90,
+            "coarse_steps_per_period": 60,
+            "refined_steps_per_period": 90,
+            "coarse_tolerance": 1e-7,
+            "refined_tolerance": 1e-7,
+        },
+        {
+            **common,
+            "parameter": "phase_samples",
+            "coarse_value": 3,
+            "refined_value": 15,
+            "coarse_steps_per_period": 90,
+            "refined_steps_per_period": 90,
+            "coarse_tolerance": 1e-7,
+            "refined_tolerance": 1e-7,
+            "refined_phase_samples": 15,
+        },
+    ]
+
+
+def _diagnostics() -> dict[str, float]:
+    return {
+        "fixed_point_residual": 1e-5,
+        "trace_error": 1e-5,
+        "hermiticity_error": 1e-5,
+        "connected_tail_amplitude": 1e-3,
+        "minimum_density_eigenvalue": 0.0,
+    }
+
+
+def _write_manifests(directory: Path) -> None:
+    n3_points = [
+        {
+            "sector": sector,
+            "model": {"j": j},
+            "adaptive_status": "converged",
+            "adaptive_converged": True,
+            "diagnostics": _diagnostics(),
+            "evidence": _evidence(),
+        }
+        for sector in ("even", "odd")
+        for j in (0.25, 0.5, 1.0)
+    ]
+    error_points = [
+        {
+            "alpha": alpha,
+            "drive_ratio": ratio,
+            "status": "converged",
+            "metrics": {
+                "trace_distance": 0.1,
+                "correlation": 0.2,
+                "heat": 0.3,
+            },
+            "convergence_evidence": _evidence(),
+        }
+        for alpha in (0.025, 0.05, 0.1)
+        for ratio in (0.75, 1.0, 1.25)
+    ]
+    model_points = [
+        {
+            "variant": variant,
+            "adaptive_status": "converged",
+            "adaptive_converged": True,
+            "diagnostics": _diagnostics(),
+            "evidence": _evidence(),
+        }
+        for variant in ("bounded", "bounded_ct", "kac", "kac_ct")
+    ]
+    payloads = {
+        "n3_heat_manifest.json": {
+            "exact_backend": "uniform_tempo",
+            "converged": True,
+            "points": n3_points,
+            "odd_cross_j_relative_max_difference": 0.0,
+        },
+        "error_map_manifest.json": {
+            "exact_backend": "uniform_tempo",
+            "converged": True,
+            "points": error_points,
+        },
+        "model_comparison_manifest.json": {
+            "exact_backend": "uniform_tempo",
+            "complete": True,
+            "locally_complete": True,
+            "converged": True,
+            "points": model_points,
+        },
+    }
+    for name, payload in payloads.items():
+        (directory / name).write_text(json.dumps(payload), encoding="utf-8")
+
+
+def test_paper_audit_requires_nested_convergence_and_all_points(
+    tmp_path: Path,
+) -> None:
+    _write_manifests(tmp_path)
+    passed, failures = audit_paper_results(tmp_path)
+    assert passed
+    assert failures == []
+
+    path = tmp_path / "n3_heat_manifest.json"
+    payload = json.loads(path.read_text(encoding="utf-8"))
+    payload["points"][0]["evidence"] = payload["points"][0]["evidence"][1:]
+    path.write_text(json.dumps(payload), encoding="utf-8")
+    passed, failures = audit_paper_results(tmp_path)
+    assert not passed
+    assert any("both timestep grids" in failure for failure in failures)
+
+
+def test_paper_audit_accepts_explicit_kac_timestep_resource_ceiling(
+    tmp_path: Path,
+) -> None:
+    _write_manifests(tmp_path)
+    path = tmp_path / "model_comparison_manifest.json"
+    payload = json.loads(path.read_text(encoding="utf-8"))
+    payload["converged"] = False
+    for point in payload["points"]:
+        if not point["variant"].startswith("kac_"):
+            continue
+        point["adaptive_status"] = "resource_ceiling"
+        point["adaptive_converged"] = False
+        point["failed_parameter"] = "steps_per_period"
+        point["evidence"] = [
+            item for item in point["evidence"] if item["parameter"] == "epsrel"
+        ][:1]
+    path.write_text(json.dumps(payload), encoding="utf-8")
+    passed, failures = audit_paper_results(tmp_path)
+    assert passed
+    assert failures == []
diff --git a/tracks/mps/solutions/Ranger-123/tests/test_paper_extension.py b/tracks/mps/solutions/Ranger-123/tests/test_paper_extension.py
new file mode 100644
index 000000000..2824138d1
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/tests/test_paper_extension.py
@@ -0,0 +1,61 @@
+from __future__ import annotations
+
+from copy import deepcopy
+
+from floquet_if_manybody.n3_heat import N3HeatPoint, prepare_n3_sector
+from floquet_if_manybody.paper_extension import (
+    _odd_equivalent_payload,
+    n2_correlation_delay_periods,
+    uniform_error_schedule,
+    uniform_publication_schedule,
+)
+
+
+def test_odd_equivalent_payload_reuses_only_the_projected_model() -> None:
+    point = N3HeatPoint(j=0.25, sector="odd", backend="uniform_tempo")
+    prepared = prepare_n3_sector(point)
+    reference = {
+        "fingerprint": "a" * 64,
+        "source_commit": "test",
+        "point": {"j": 0.25},
+        "final_point": {
+            **point.__dict__,
+            "steps_per_period": 60,
+            "phase_samples": 3,
+        },
+        "model": {
+            "n": 3,
+            "j": 0.25,
+            "drive_frequency": prepared.model.drive_frequency,
+        },
+        "model_hash": "b" * 64,
+        "projected_model_hash": "c" * 64,
+        "bright_gap": prepared.bright_gap,
+        "continuous": [0.0, 1.0],
+        "adaptive_converged": True,
+    }
+    untouched = deepcopy(reference)
+    target = _odd_equivalent_payload(reference, 1.0)
+    assert reference == untouched
+    assert target["point"]["j"] == 1.0
+    assert target["final_point"]["j"] == 1.0
+    assert target["model"]["j"] == 1.0
+    assert target["continuous"] == reference["continuous"]
+    assert target["projected_model_hash"] == reference["projected_model_hash"]
+    assert target["numerical_reuse"]["h0_frobenius_residual"] < 1e-13
+    assert target["numerical_reuse"]["coupling_frobenius_residual"] < 1e-13
+
+
+def test_n2_correlation_window_grows_at_weak_coupling() -> None:
+    assert n2_correlation_delay_periods(0.1) == 4
+    assert n2_correlation_delay_periods(0.05) == 6
+    assert n2_correlation_delay_periods(0.025) == 12
+
+
+def test_n2_error_grid_has_a_deeper_compression_ladder() -> None:
+    publication = uniform_publication_schedule()
+    error = uniform_error_schedule()
+    assert error.steps_per_period == publication.steps_per_period
+    assert error.phase_samples == publication.phase_samples
+    assert error.tolerances[: len(publication.tolerances)] == publication.tolerances
+    assert error.tolerances[-1] < publication.tolerances[-1]
diff --git a/tracks/mps/solutions/Ranger-123/tests/test_paper_plotting.py b/tracks/mps/solutions/Ranger-123/tests/test_paper_plotting.py
new file mode 100644
index 000000000..72e1e1cea
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/tests/test_paper_plotting.py
@@ -0,0 +1,90 @@
+from __future__ import annotations
+
+from pathlib import Path
+
+from heat_valve_fixtures import valid_heat_valve_manifest
+
+from floquet_if_manybody.plotting import (
+    plot_dark_diagnostics,
+    plot_error_maps,
+    plot_heat_valve_hero,
+    plot_model_variants,
+    plot_n3_sector_heat,
+    plot_odd_sector_difference,
+)
+
+
+def _n3_manifest() -> dict[str, object]:
+    points = []
+    diagnostics = []
+    for sector in ("even", "odd"):
+        for j in (0.25, 0.5, 1.0):
+            points.append(
+                {
+                    "sector": sector,
+                    "adaptive_converged": True,
+                    "model": {"j": j},
+                    "frequency": [0.0, 1.0, 2.0],
+                    "continuous": [0.0, j, 0.0],
+                }
+            )
+            diagnostics.append(
+                {
+                    "sector": sector,
+                    "j": j,
+                    "integrated_continuous_heat": j,
+                    "period_variance": 0.5,
+                    "strongest_transitions": [
+                        {"source": 0, "target": 1, "weight": j}
+                    ],
+                }
+            )
+    return {"points": points, "dark_diagnostics": diagnostics}
+
+
+def test_all_paper_plots_render_pdf_and_png(tmp_path: Path) -> None:
+    n3 = _n3_manifest()
+    plot_n3_sector_heat(n3, tmp_path / "sector")
+    plot_odd_sector_difference(n3, tmp_path / "odd")
+    plot_dark_diagnostics(n3, tmp_path / "dark")
+    error = {
+        "points": [
+            {
+                "alpha": alpha,
+                "drive_ratio": ratio,
+                "status": "converged",
+                "metrics": {
+                    "trace_distance": 0.1,
+                    "correlation": 0.2,
+                    "heat": 0.3,
+                },
+            }
+            for alpha in (0.025, 0.05, 0.1)
+            for ratio in (0.75, 1.0, 1.25)
+        ]
+    }
+    plot_error_maps(error, tmp_path / "errors")
+    models = {
+        "points": [
+            {
+                "adaptive_converged": True,
+                "variant": name,
+                "frequency": [0.0, 1.0],
+                "continuous": [0.0, 1.0],
+                "continuous_eta_rescaled": [0.0, 2.0],
+            }
+            for name in ("bounded_no_ct", "bounded_ct", "kac_no_ct", "kac_ct")
+        ]
+    }
+    plot_model_variants(models, tmp_path / "models")
+    assert len(list(tmp_path.glob("*.pdf"))) == 5
+    assert len(list(tmp_path.glob("*.png"))) == 5
+
+
+def test_heat_valve_hero_writes_png_and_pdf(tmp_path: Path) -> None:
+    plot_heat_valve_hero(
+        valid_heat_valve_manifest(),
+        tmp_path / "heat_valve_hero",
+    )
+    assert (tmp_path / "heat_valve_hero.png").is_file()
+    assert (tmp_path / "heat_valve_hero.pdf").is_file()
diff --git a/tracks/mps/solutions/Ranger-123/tests/test_poles.py b/tracks/mps/solutions/Ranger-123/tests/test_poles.py
new file mode 100644
index 000000000..5470d5700
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/tests/test_poles.py
@@ -0,0 +1,111 @@
+from __future__ import annotations
+
+import numpy as np
+import pytest
+from numpy.testing import assert_allclose
+
+from floquet_if_manybody.poles import (
+    TransferPole,
+    fit_pole_residues,
+    match_transfer_poles,
+    transfer_poles,
+)
+
+
+def _poles(values: list[complex]) -> tuple[TransferPole, ...]:
+    return tuple(
+        TransferPole(
+            eigenvalue=value,
+            decay_rate=float(-np.log(abs(value))),
+            quasifrequency=float(np.angle(value)),
+            eigenpair_residual=1e-13,
+        )
+        for value in values
+    )
+
+
+def test_transfer_poles_convert_eigenvalues_to_rates() -> None:
+    period = 2.0
+    values = np.array([1.0, np.exp((-0.2 + 0.7j) * period)])
+    poles = transfer_poles(values, np.array([1e-13, 2e-13]), period)
+    assert len(poles) == 1
+    assert_allclose(poles[0].decay_rate, 0.2, atol=1e-12)
+    assert_allclose(poles[0].quasifrequency, 0.7, atol=1e-12)
+
+
+def test_transfer_poles_accept_resolved_approximate_steady_mode() -> None:
+    poles = transfer_poles(
+        np.array([0.9991 + 1e-15j, 0.8 + 0.1j]),
+        np.array([1e-13, 1e-13]),
+        period=1.0,
+    )
+    assert len(poles) == 1
+    assert poles[0].eigenvalue == 0.8 + 0.1j
+
+
+def test_fit_recovers_complex_residues() -> None:
+    period = 1.5
+    eigenvalues = np.array([0.8 * np.exp(0.2j), 0.55 * np.exp(-0.4j)])
+    residues = np.array([0.7 - 0.1j, -0.2 + 0.3j])
+    n = np.arange(16)
+    connected = sum(
+        residue * eigenvalue**n
+        for residue, eigenvalue in zip(residues, eigenvalues, strict=True)
+    )
+    fit = fit_pole_residues(
+        transfer_poles(
+            np.r_[1.0, eigenvalues],
+            np.full(3, 1e-13),
+            period,
+        ),
+        n * period,
+        connected,
+        period,
+        max_modes=2,
+    )
+    assert_allclose(
+        [item.residue for item in fit.residues],
+        residues,
+        atol=1e-10,
+    )
+    assert fit.reconstruction_residual < 1e-12
+
+
+def test_fit_uses_only_stroboscopic_delays() -> None:
+    poles = _poles([0.8 + 0.1j])
+    delays = np.arange(9) * 0.5
+    connected = np.full(9, 99 + 0j)
+    connected[::2] = (0.3 - 0.2j) * poles[0].eigenvalue ** np.arange(5)
+    fit = fit_pole_residues(
+        poles,
+        delays,
+        connected,
+        period=1.0,
+        max_modes=1,
+    )
+    assert_allclose(fit.residues[0].residue, 0.3 - 0.2j)
+    assert_allclose(fit.stroboscopic_delays, delays[::2])
+
+
+def test_fit_requires_an_overdetermined_stroboscopic_window() -> None:
+    with pytest.raises(ValueError, match="stroboscopic samples"):
+        fit_pole_residues(
+            _poles([0.8, 0.7]),
+            np.array([0.0, 1.0]),
+            np.array([1.0, 0.5], dtype=complex),
+            period=1.0,
+            max_modes=2,
+        )
+
+
+def test_mode_matching_follows_nearest_complex_poles() -> None:
+    previous = _poles([0.9 + 0.1j, 0.7 - 0.2j])
+    current = _poles([0.69 - 0.19j, 0.89 + 0.11j])
+    matched = match_transfer_poles(previous, current)
+    assert [item.current_index for item in matched] == [1, 0]
+
+
+def test_degenerate_matching_is_marked_ambiguous() -> None:
+    previous = _poles([0.8 + 0.1j, 0.8 + 0.1j])
+    current = _poles([0.8 + 0.1j, 0.8 + 0.1j])
+    assert all(item.ambiguous for item in match_transfer_poles(previous, current))
diff --git a/tracks/mps/solutions/Ranger-123/tests/test_pt_tempo.py b/tracks/mps/solutions/Ranger-123/tests/test_pt_tempo.py
new file mode 100644
index 000000000..4b5773760
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/tests/test_pt_tempo.py
@@ -0,0 +1,30 @@
+import numpy as np
+import pytest
+
+from floquet_if_manybody.backends.pt_tempo import PtTempoBackend
+from floquet_if_manybody.config import BathConfig
+
+oqupy = pytest.importorskip("oqupy")
+if np.lib.NumpyVersion(np.__version__) >= "2.0.0":
+    pytest.skip("OQuPy 0.5 requires NumPy <2", allow_module_level=True)
+
+
+def test_pt_tempo_short_run_is_labeled_and_trace_preserving():
+    h = np.array([[0, 0.5], [0.5, 0]], dtype=complex)
+    s = np.diag([1, -1]).astype(complex)
+    rho = np.array([[1, 0], [0, 0]], dtype=complex)
+    run = PtTempoBackend().run(
+        lambda _time: h,
+        s,
+        rho,
+        BathConfig(alpha=0.01),
+        dt=0.1,
+        steps=6,
+        memory_steps=2,
+        epsrel=1e-5,
+    )
+    assert run.result.method == "pt_tempo"
+    assert run.result.diagnostics["trace_error"] < 1e-3
+    assert run.result.metadata["spectral_density_convention"].startswith(
+        "OQuPy alpha divided"
+    )
diff --git a/tracks/mps/solutions/Ranger-123/tests/test_spectra_n2.py b/tracks/mps/solutions/Ranger-123/tests/test_spectra_n2.py
new file mode 100644
index 000000000..e0afc072f
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/tests/test_spectra_n2.py
@@ -0,0 +1,31 @@
+import numpy as np
+from numpy.testing import assert_allclose
+
+from floquet_if_manybody.config import ModelConfig
+from floquet_if_manybody.models import coupling_operator, ising_hamiltonian
+from floquet_if_manybody.spectra import diagonalize, transitions
+from floquet_if_manybody.symmetry import n2_sectors, project
+
+
+def test_n2_analytic_triplet_spectrum_and_weights():
+    _, triplet = n2_sectors()
+    omega = 1.0
+    for j in [0.0, 0.25, 0.5, 1.0, 2.0]:
+        cfg = ModelConfig(n=2, j=j, omega=omega)
+        spectrum = diagonalize(project(ising_hamiltonian(cfg), triplet))
+        e = np.sqrt(j**2 + omega**2)
+        assert_allclose(spectrum.energies, [-e, -j, e], atol=1e-12)
+        items = transitions(
+            spectrum, spectrum, project(coupling_operator(cfg), triplet), threshold=1e-10
+        )
+        from_ground = sorted(
+            [x for x in items if x.source == 0 and x.frequency > 0],
+            key=lambda x: x.frequency,
+        )
+        assert_allclose([x.frequency for x in from_ground], [e - j], atol=1e-12)
+        expected_low = 2 * cfg.eta**2 * (1 + j / e)
+        assert_allclose(from_ground[0].weight, expected_low, atol=1e-12)
+        high = [x for x in items if x.source == 1 and x.target == 2]
+        expected_high = 2 * cfg.eta**2 * (1 - j / e)
+        assert_allclose(high[0].frequency, e + j, atol=1e-12)
+        assert_allclose(high[0].weight, expected_high, atol=1e-12)
diff --git a/tracks/mps/solutions/Ranger-123/tests/test_spectra_n3.py b/tracks/mps/solutions/Ranger-123/tests/test_spectra_n3.py
new file mode 100644
index 000000000..4f57a89e4
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/tests/test_spectra_n3.py
@@ -0,0 +1,29 @@
+import numpy as np
+from numpy.testing import assert_allclose
+
+from floquet_if_manybody.config import ModelConfig
+from floquet_if_manybody.models import ising_hamiltonian
+from floquet_if_manybody.spectra import diagonalize
+from floquet_if_manybody.symmetry import n3_reflection_sectors, project
+
+
+def test_n3_odd_gap_is_single_spin_gap():
+    odd, _ = n3_reflection_sectors()
+    for j in [0, 0.5, 2.0]:
+        cfg = ModelConfig(n=3, j=j, omega=1)
+        energies = diagonalize(project(ising_hamiltonian(cfg), odd)).energies
+        assert_allclose(np.diff(energies), [1.0], atol=1e-12)
+
+
+def test_n3_cat_gap_asymptotic_coefficient():
+    _, even = n3_reflection_sectors()
+    ratios = []
+    for j in [4.0, 8.0, 16.0]:
+        cfg = ModelConfig(n=3, j=j, omega=1)
+        se = diagonalize(project(ising_hamiltonian(cfg), even))
+        # The cat partner has opposite global spin-flip parity inside the even
+        # reflection sector, so use the two lowest levels of this block.
+        gap = se.energies[1] - se.energies[0]
+        ratios.append(gap * 4 * j**2)
+    assert abs(ratios[-1] - 1) < abs(ratios[0] - 1)
+    np.testing.assert_allclose(ratios[-1], 1.0, rtol=0.02)
diff --git a/tracks/mps/solutions/Ranger-123/tests/test_symmetry_n2.py b/tracks/mps/solutions/Ranger-123/tests/test_symmetry_n2.py
new file mode 100644
index 000000000..65464d579
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/tests/test_symmetry_n2.py
@@ -0,0 +1,14 @@
+from numpy.testing import assert_allclose
+
+from floquet_if_manybody.config import ModelConfig
+from floquet_if_manybody.models import coupling_operator, ising_hamiltonian
+from floquet_if_manybody.symmetry import n2_sectors, project, sector_residual
+
+
+def test_n2_singlet_is_dark_and_invariant():
+    singlet, triplet = n2_sectors()
+    cfg = ModelConfig(n=2)
+    assert (singlet.dimension, triplet.dimension) == (1, 3)
+    assert_allclose(project(coupling_operator(cfg), singlet), 0, atol=1e-14)
+    assert sector_residual(ising_hamiltonian(cfg), singlet) < 1e-13
+    assert sector_residual(ising_hamiltonian(cfg), triplet) < 1e-13
diff --git a/tracks/mps/solutions/Ranger-123/tests/test_symmetry_n3.py b/tracks/mps/solutions/Ranger-123/tests/test_symmetry_n3.py
new file mode 100644
index 000000000..5d91d288b
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/tests/test_symmetry_n3.py
@@ -0,0 +1,15 @@
+from numpy.testing import assert_allclose
+
+from floquet_if_manybody.config import ModelConfig
+from floquet_if_manybody.models import ising_hamiltonian
+from floquet_if_manybody.symmetry import n3_reflection_sectors, project, sector_residual
+
+
+def test_n3_odd_sector_is_j_independent():
+    odd, even = n3_reflection_sectors()
+    h1 = project(ising_hamiltonian(ModelConfig(n=3, j=0.2)), odd)
+    h2 = project(ising_hamiltonian(ModelConfig(n=3, j=2.0)), odd)
+    assert_allclose(h1, h2)
+    assert (odd.dimension, even.dimension) == (2, 6)
+    assert sector_residual(ising_hamiltonian(ModelConfig(n=3)), odd) < 1e-13
+    assert sector_residual(ising_hamiltonian(ModelConfig(n=3)), even) < 1e-13
diff --git a/tracks/mps/solutions/Ranger-123/tests/test_symmetry_n4.py b/tracks/mps/solutions/Ranger-123/tests/test_symmetry_n4.py
new file mode 100644
index 000000000..937599ffb
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/tests/test_symmetry_n4.py
@@ -0,0 +1,21 @@
+import numpy as np
+
+from floquet_if_manybody.config import ModelConfig
+from floquet_if_manybody.models import coupling_operator, ising_hamiltonian
+from floquet_if_manybody.symmetry import n4_reflection_sectors, sector_residual
+
+
+def test_n4_reflection_dimensions_and_invariance() -> None:
+    odd, even = n4_reflection_sectors()
+    assert odd.dimension == 6
+    assert even.dimension == 10
+    model = ModelConfig(n=4, j=0.5)
+    h0 = ising_hamiltonian(model)
+    coupling = coupling_operator(model)
+    for sector in (odd, even):
+        assert sector_residual(h0, sector) < 1e-13
+        assert sector_residual(coupling, sector) < 1e-13
+        assert np.allclose(
+            sector.isometry.conj().T @ sector.isometry,
+            np.eye(sector.dimension),
+        )
diff --git a/tracks/mps/solutions/Ranger-123/tests/test_uniform_tempo_backend.py b/tracks/mps/solutions/Ranger-123/tests/test_uniform_tempo_backend.py
new file mode 100644
index 000000000..d5dd9ffb2
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/tests/test_uniform_tempo_backend.py
@@ -0,0 +1,284 @@
+from __future__ import annotations
+
+import json
+import sys
+from pathlib import Path
+
+import numpy as np
+import pytest
+from numpy.testing import assert_allclose
+
+from floquet_if_manybody.backends.uniform_tempo import (
+    UniformTempoBackend,
+    UniformTempoControls,
+    _encode_complex,
+    _tensor_cache_key,
+)
+from floquet_if_manybody.config import BathConfig, ModelConfig
+
+
+def _write_fake_runner(path: Path, payload: dict[str, object], exit_code: int = 0) -> None:
+    script = f"""\
+import json
+import pathlib
+import sys
+
+if {exit_code}:
+    print("synthetic Julia failure", file=sys.stderr)
+    raise SystemExit({exit_code})
+input_path, output_path = sys.argv[1:3]
+request = json.loads(pathlib.Path(input_path).read_text())
+pathlib.Path({str(Path("captured-request.json"))!r}).write_text(json.dumps(request))
+payload = {payload!r}
+payload["request_echo"] = request
+pathlib.Path(output_path).write_text(json.dumps(payload))
+"""
+    script = script.replace(
+        repr(str(Path("captured-request.json"))),
+        repr(str(path.parent / "captured-request.json")),
+    )
+    path.write_text(script, encoding="utf-8")
+
+
+def _valid_payload() -> dict[str, object]:
+    return {
+        "method": "uniform_tempo_floquet_multitime",
+        "dt": np.pi / 2,
+        "period_steps": 4,
+        "bond_dimension": 3,
+        "floquet_state": {
+            "real": [0.6, 0.0, 0.0, 0.4],
+            "imag": [0.0, 0.1, -0.1, 0.0],
+            "shape": [2, 2],
+        },
+        "phase_states": {
+            "real": [0.6, 0.0, 0.0, 0.4, 0.4, 0.0, 0.0, 0.6],
+            "imag": [0.0] * 8,
+            "shape": [2, 2, 2],
+        },
+        "one_point": [0.2, -0.2],
+        "phase_offsets": [0, 2],
+        "delay": [0.0, np.pi / 2, np.pi, 3 * np.pi / 2, 2 * np.pi],
+        "correlation": {
+            "real": [1.0, 0.5, 0.25, 0.125, 0.0625],
+            "imag": [0.0, -0.1, -0.05, -0.025, -0.0125],
+            "shape": [5],
+        },
+        "diagnostics": {
+            "trace_error": 1e-8,
+            "hermiticity_error": 1e-8,
+            "minimum_density_eigenvalue": 0.3,
+            "fixed_point_residual": 1e-7,
+            "floquet_transfer_residual": 1e-7,
+        },
+        "julia_version": "1.12.6",
+        "uniform_tempo_revision": "b76a018c32e5415989761d902b1b0e95f1a337da",
+        "manifest_sha256": "a" * 64,
+        "process_tensor_cache_hit": False,
+        "transfer_eigenvalues": {
+            "real": [],
+            "imag": [],
+            "shape": [0],
+        },
+        "transfer_eigenpair_residuals": [],
+        "transfer_dimension": 12,
+    }
+
+
+def _backend(tmp_path: Path, payload: dict[str, object]) -> UniformTempoBackend:
+    runner = tmp_path / "fake_runner.py"
+    _write_fake_runner(runner, payload)
+    return UniformTempoBackend(command_prefix=(sys.executable, str(runner)))
+
+
+def _model() -> ModelConfig:
+    return ModelConfig(
+        n=3,
+        j=0.5,
+        drive_amplitude=0.2,
+        drive_frequency=1.0,
+    )
+
+
+def test_valid_payload_round_trips_complex_arrays(tmp_path: Path) -> None:
+    backend = _backend(tmp_path, _valid_payload())
+    result = backend.run_periodic(
+        np.array([[0.0, 0.5], [0.5, 0.0]], dtype=complex),
+        np.diag([1.0, -1.0]).astype(complex),
+        _model(),
+        BathConfig(alpha=0.01, cutoff=2.5),
+        UniformTempoControls(
+            steps_per_period=4,
+            tolerance=1e-4,
+            phase_samples=2,
+            delay_periods=1,
+            auto_nc=False,
+            memory_cutoff=6,
+        ),
+    )
+    assert result.method == "uniform_tempo_floquet_multitime"
+    assert result.phase_states.shape == (2, 2, 2)
+    assert_allclose(result.floquet_state, [[0.6, -0.1j], [0.1j, 0.4]])
+    assert_allclose(
+        result.correlation.total,
+        [
+            1.0,
+            0.5 - 0.1j,
+            0.25 - 0.05j,
+            0.125 - 0.025j,
+            0.0625 - 0.0125j,
+        ],
+    )
+    assert_allclose(
+        result.correlation.total,
+        result.correlation.connected + result.correlation.coherent,
+    )
+    assert result.metadata["uniform_tempo_revision"].startswith("b76a018")
+    assert result.transfer_eigenvalues.size == 0
+
+
+def test_backend_round_trips_transfer_poles_and_independent_drive(
+    tmp_path: Path,
+) -> None:
+    payload = _valid_payload()
+    payload["transfer_eigenvalues"] = {
+        "real": [1.0, 0.8],
+        "imag": [0.0, 0.1],
+        "shape": [2],
+    }
+    payload["transfer_eigenpair_residuals"] = [1e-12, 2e-11]
+    backend = _backend(tmp_path, payload)
+    drive = 2 * np.diag([1.0, -1.0]).astype(complex)
+    result = backend.run_periodic(
+        np.array([[0.0, 0.5], [0.5, 0.0]], dtype=complex),
+        np.diag([1.0, -1.0]).astype(complex),
+        _model(),
+        BathConfig(alpha=0.01),
+        UniformTempoControls(4, 1e-4, 2, 1, pole_count=2),
+        drive_operator=drive,
+    )
+    assert_allclose(result.transfer_eigenvalues, [1.0, 0.8 + 0.1j])
+    assert_allclose(result.transfer_eigenpair_residuals, [1e-12, 2e-11])
+    request = json.loads((tmp_path / "captured-request.json").read_text())
+    assert request["drive"]["real"] == _encode_complex(drive)["real"]
+    assert request["controls"]["pole_count"] == 2
+
+
+@pytest.mark.parametrize(
+    ("field", "value", "message"),
+    [
+        ("transfer_eigenpair_residuals", [1e-12], "same length"),
+        ("transfer_eigenpair_residuals", [1e-12, -1.0], "nonnegative"),
+        (
+            "transfer_eigenvalues",
+            {"real": [1.0, "nan"], "imag": [0.0, 0.0], "shape": [2]},
+            "non-finite",
+        ),
+    ],
+)
+def test_invalid_transfer_pole_payload_is_rejected(
+    tmp_path: Path,
+    field: str,
+    value: object,
+    message: str,
+) -> None:
+    payload = _valid_payload()
+    payload["transfer_eigenvalues"] = {
+        "real": [1.0, 0.8],
+        "imag": [0.0, 0.1],
+        "shape": [2],
+    }
+    payload["transfer_eigenpair_residuals"] = [1e-12, 2e-11]
+    payload[field] = value
+    backend = _backend(tmp_path, payload)
+    with pytest.raises(ValueError, match=message):
+        backend.run_periodic(
+            np.eye(2, dtype=complex),
+            np.diag([1.0, -1.0]).astype(complex),
+            _model(),
+            BathConfig(alpha=0.01),
+            UniformTempoControls(4, 1e-4, 2, 1, pole_count=2),
+        )
+
+
+def test_nonzero_runner_exit_is_reported(tmp_path: Path) -> None:
+    runner = tmp_path / "failing.py"
+    _write_fake_runner(runner, {}, exit_code=7)
+    backend = UniformTempoBackend(command_prefix=(sys.executable, str(runner)))
+    with pytest.raises(RuntimeError, match="synthetic Julia failure"):
+        backend.run_periodic(
+            np.eye(2, dtype=complex),
+            np.diag([1.0, -1.0]).astype(complex),
+            _model(),
+            BathConfig(alpha=0.01),
+            UniformTempoControls(4, 1e-4, 2, 1),
+        )
+
+
+@pytest.mark.parametrize(
+    ("mutation", "message"),
+    [
+        (lambda payload: payload.pop("uniform_tempo_revision"), "provenance"),
+        (lambda payload: payload.update(method="wrong"), "method"),
+        (
+            lambda payload: payload["correlation"].update(real=[1.0, 0.5]),
+            "shape",
+        ),
+    ],
+)
+def test_malformed_payload_is_rejected(
+    tmp_path: Path, mutation, message: str
+) -> None:
+    payload = _valid_payload()
+    mutation(payload)
+    backend = _backend(tmp_path, payload)
+    with pytest.raises(ValueError, match=message):
+        backend.run_periodic(
+            np.eye(2, dtype=complex),
+            np.diag([1.0, -1.0]).astype(complex),
+            _model(),
+            BathConfig(alpha=0.01),
+            UniformTempoControls(4, 1e-4, 2, 1),
+        )
+
+
+def test_controls_require_commensurate_phase_sampling() -> None:
+    with pytest.raises(ValueError, match="phase_samples"):
+        UniformTempoControls(steps_per_period=6, tolerance=1e-5, phase_samples=4, delay_periods=1)
+
+
+def test_process_tensor_key_excludes_phase_and_delay_controls() -> None:
+    coupling = np.diag([1.0, -1.0]).astype(complex)
+    model = _model()
+    bath = BathConfig(alpha=0.01, cutoff=2.5)
+    coarse = UniformTempoControls(60, 3e-7, 3, 2)
+    denser_phase = UniformTempoControls(60, 3e-7, 15, 8)
+    assert _tensor_cache_key(coupling, model, bath, coarse) == _tensor_cache_key(
+        coupling,
+        model,
+        bath,
+        denser_phase,
+    )
+
+
+def test_backend_passes_content_addressed_tensor_cache(tmp_path: Path) -> None:
+    runner = tmp_path / "fake_runner.py"
+    _write_fake_runner(runner, _valid_payload())
+    backend = UniformTempoBackend(
+        command_prefix=(sys.executable, str(runner)),
+        tensor_cache_directory=tmp_path / "tensor-cache",
+    )
+    controls = UniformTempoControls(4, 1e-4, 2, 1)
+    backend.run_periodic(
+        np.array([[0.0, 0.5], [0.5, 0.0]], dtype=complex),
+        np.diag([1.0, -1.0]).astype(complex),
+        _model(),
+        BathConfig(alpha=0.01, cutoff=2.5),
+        controls,
+    )
+    request = json.loads((tmp_path / "captured-request.json").read_text())
+    cache_key = request["controls"]["process_tensor_cache_key"]
+    assert len(cache_key) == 64
+    assert request["controls"]["process_tensor_cache_path"].endswith(
+        f"{cache_key}.jls"
+    )
diff --git a/tracks/mps/solutions/Ranger-123/tests/test_uniform_tempo_environment.py b/tracks/mps/solutions/Ranger-123/tests/test_uniform_tempo_environment.py
new file mode 100644
index 000000000..c5054ad64
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/tests/test_uniform_tempo_environment.py
@@ -0,0 +1,37 @@
+import shutil
+import subprocess
+import tomllib
+from pathlib import Path
+
+import pytest
+
+PROJECT_ROOT = Path(__file__).resolve().parents[1]
+JULIA_PROJECT = PROJECT_ROOT / "julia" / "Project.toml"
+
+
+def test_julia_project_declares_required_dependencies() -> None:
+    project = tomllib.loads(JULIA_PROJECT.read_text(encoding="utf-8"))
+    assert {"UniformTEMPO", "OrdinaryDiffEq", "JSON3", "KrylovKit"} <= project[
+        "deps"
+    ].keys()
+    assert project["compat"]["julia"] == "1.12"
+
+
+def test_julia_runner_rejects_missing_input(tmp_path: Path) -> None:
+    julia = shutil.which("julia")
+    if julia is None:
+        pytest.skip("Julia is not installed")
+    completed = subprocess.run(
+        [
+            julia,
+            f"--project={PROJECT_ROOT / 'julia'}",
+            str(PROJECT_ROOT / "julia" / "run_uniform_tempo.jl"),
+            str(tmp_path / "missing.json"),
+            str(tmp_path / "out.json"),
+        ],
+        capture_output=True,
+        text=True,
+        check=False,
+    )
+    assert completed.returncode != 0
+    assert "input" in completed.stderr.lower()
diff --git a/tracks/mps/solutions/Ranger-123/uv.lock b/tracks/mps/solutions/Ranger-123/uv.lock
new file mode 100644
index 000000000..adfea015e
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/uv.lock
@@ -0,0 +1,1013 @@
+version = 1
+revision = 3
+requires-python = ">=3.11"
+resolution-markers = [
+    "python_full_version >= '3.15'",
+    "python_full_version >= '3.12' and python_full_version < '3.15'",
+    "python_full_version < '3.12'",
+]
+
+[[package]]
+name = "ast-serialize"
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diff --git a/tracks/mps/solutions/Ranger-123/validation/ARTIFACT_PROVENANCE.json b/tracks/mps/solutions/Ranger-123/validation/ARTIFACT_PROVENANCE.json
new file mode 100644
index 000000000..7f5afed3c
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/validation/ARTIFACT_PROVENANCE.json
@@ -0,0 +1,58 @@
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diff --git a/tracks/mps/solutions/Ranger-123/validation/fig3_transversal_summary.json b/tracks/mps/solutions/Ranger-123/validation/fig3_transversal_summary.json
new file mode 100644
index 000000000..c97b8e175
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/validation/fig3_transversal_summary.json
@@ -0,0 +1,41 @@
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diff --git a/tracks/mps/solutions/Ranger-123/validation/fig3_transversal_wd2.json b/tracks/mps/solutions/Ranger-123/validation/fig3_transversal_wd2.json
new file mode 100644
index 000000000..f8e1a5a22
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/validation/fig3_transversal_wd2.json
@@ -0,0 +1,39 @@
+{
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diff --git a/tracks/mps/solutions/Ranger-123/validation/n3_same_model_error_map.json b/tracks/mps/solutions/Ranger-123/validation/n3_same_model_error_map.json
new file mode 100644
index 000000000..d80b87f96
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/validation/n3_same_model_error_map.json
@@ -0,0 +1,19 @@
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diff --git a/tracks/mps/solutions/Ranger-123/validation/n4_pilot.json b/tracks/mps/solutions/Ranger-123/validation/n4_pilot.json
new file mode 100644
index 000000000..a7e922af5
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/validation/n4_pilot.json
@@ -0,0 +1,49 @@
+{
+  "method": "n4_uniform_tempo_convergence_pilot",
+  "complete": true,
+  "converged_points": 2,
+  "model_scope": "same N=4 Hamiltonian and bath at J/Omega=0.25, resolved by reflection sector",
+  "points": [
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+  "note": "Raw trace-norm diagnostics can exceed one slightly because the accepted UniformTEMPO density matrices retain small negative eigenvalues within the preregistered -0.005 gate.",
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+}
diff --git a/tracks/mps/solutions/Ranger-123/validation/uniform_tempo_oqupy_crosscheck.json b/tracks/mps/solutions/Ranger-123/validation/uniform_tempo_oqupy_crosscheck.json
new file mode 100644
index 000000000..dc155588d
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/validation/uniform_tempo_oqupy_crosscheck.json
@@ -0,0 +1,17 @@
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+}
\ No newline at end of file
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new file mode 100644
index 000000000..8dbdb4f19
--- /dev/null
+++ b/tracks/mps/solutions/Ranger-123/validation/uniform_tempo_single_spin.json
@@ -0,0 +1,884 @@
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+    "counterterm_strength": 0.0,
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+    "drive_frequency": 1.0,
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+  "phase_state": {
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+  },
+  "uniform_tempo_revision": "b76a018c32e5415989761d902b1b0e95f1a337da"
+}
\ No newline at end of file