🌠Wander: Issue #276 Exactly Degenerate Quantum Chaos and Geometric Response

[JunkaiWang-TheoPhy]

Related issue: #276

This PR delivers two back-to-back manuscripts on quantum chaos in exactly degenerate state spaces.

Paper I, Exactly Degenerate Quantum Chaos: Non-Abelian Quantum Geometry as a Probe, asks what remains measurable when every energy inside a protected fiber is identical. Across Laughlin/FCI parents, Moore–Read clustering, supersymmetric cohomology, local lattice supersymmetry, and stabilizer controls, it separates exact intrafiber degeneracy from off-fiber projector motion. The result is finite-size and mechanism resolved: local geometric correlations can be random-matrix-like while global covariance, topology, and the protection mechanism retain structure. Of the five registered centered complete-covariance cases, only Moore–Read $N=6$ passes the familywise gate.

Paper II was prospectively result gated. It proves an exact weighted-channel fourth-cumulant identity under independence, centering, deterministic weights, finite fourth moments, and a common response space. A sealed chiral-index calculation then tests the parameter-free $N_{\mathrm{eff}}$ specialization. The random-channel values $1.2903$, $1.3650$, and $1.4814$ lie above the registered simultaneous band $[0.4476,1.2352]$. The selected branch is therefore random_channel_failure, and the delivered title is the bounded Geometric Response of Exactly Degenerate Quantum State Bundles. This PR does not claim an established asymptotic or universal Geometric ETH.

Delivered artifacts

Item	Result
Paper I main / supplement	23 / 11 pages; seven vector figures; delivery audit passed
Paper II main / supplement	18 / 8 pages; six vector figures; delivery audit passed
Paper I main PDF SHA-256	257b1c10e75f7104d4a70afbd3b9c9056e197036a5f4c216f3789af8c513746a
Paper II main PDF SHA-256	45984eed2daa8df1c741a5924287664a3c0b9508389be8681232a91ed54c0d20
Cross-paper branch	Paper I passed; Paper II random_channel_failure
Shared boundary	No asymptotic, universal, independent-cross-model, or black-hole theorem claim

Key paths:

• Capsule overview
• Paper I PDF
• Paper II PDF
• Combined manifest
• Reviewer guide
• Reproducibility guide

Verification

bash tracks/mps/solutions/Wander-276/verify.sh

The command preserves the prior v1–v12 tests and runs the v13/v14 manuscript, figure, theorem, inference, delivery, and cross-paper checks. The Harness-specific fail-closed verifier rebuilds the combined manifest, verifies the Paper II failure branch and fallback title, checks all four archived PDFs, validates 71 registered v13/v14 evidence/source hashes, and verifies a capsule-local SHA-256 seal over all 237 v1–v12 versioned artifacts present before this upgrade.

Reviewer route

1. Read both abstracts and Paper I Fig. 1.
2. Inspect Paper I Figs. 4 and 7 for channel separation and mechanism dependence.
3. Read Paper II Theorem 1 together with the assumptions preceding its $N_{\mathrm{eff}}$ corollary.
4. Inspect Paper II Fig. 6 and confirm that the failed random-channel test is reported before its interpretation.
5. Run the verifier and compare the archived PDF hashes with the table above.

Team

Field	Value
Team name	Wander
Members	Chenxi Wan, Yedi Shen, Junkai Wang
Contact email	WangTheoPhys@outlook.com

[JunkaiWang-TheoPhy]

@OkongOyangO The Issue #276 submission has now been upgraded to the audited two-paper v13/v14 release.

Suggested review path:

1. Read Paper I, Exactly Degenerate Quantum Chaos: Non-Abelian Quantum Geometry as a Probe, and inspect Figs. 1, 4, and 7 for spectral silence, channel separation, and mechanism dependence.
2. Check the centered complete-covariance registry: only Moore--Read $N=6$ passes among the five registered Moore--Read/lattice-SUSY cases; the result is finite-rank and not an independent Hamiltonian ensemble.
3. Read Paper II, Geometric Response of Exactly Degenerate Quantum State Bundles, especially Theorem 1 and the assumptions preceding the $N_{\mathrm{eff}}$ corollary.
4. Inspect Paper II Fig. 6. The sealed validation selects random_channel_failure; the positive title The Geometric ETH is withheld.
5. Run bash tracks/mps/solutions/Wander-276/verify.sh.

The current capsule contains 23+11 Paper-I pages, 18+8 Paper-II pages, 13 vector figures, a 237-object pre-upgrade capsule seal, 71 registered v13/v14 evidence/source hashes, and public-document tamper tests. The supported claim is finite-size geometric information under exact degeneracy plus an exact conditional channel theorem. It does not establish asymptotic, universal, independent-cross-model, thermalizing, or black-hole Geometric ETH.