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Research audit: literal binary spectra and moment-preserving corruption control (no new kappa) - #812
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The spectrum audit (#812) pins scripts/experiments/single_intersection.py by whole-file SHA-256 at its pre-#778 digest. #778 (f015b04) rewrote only minor_rows, which the audit never calls (it imports spectral_parity_bound, byte-identical), and the old and new minor_rows agree on all 41 audit cases. With the pin bypassed, a fresh certificate equals the committed RESULT.json in every field. Refresh the pin in SOURCE.json and regenerate RESULT.json with the audit's own --write (one line). This makes the `tests` group of Verify research artifacts pass again on main.
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The historical single-intersection screen checks two integer spectral moments, but those checks can miss a wrong modular characteristic polynomial. This research audit adds an independent exact calculation from literal subset-intersection matrices. No new kappa is claimed.
All 41 cases with
4 <= h <= 10,2 <= k <= min(4, floor(h/2)), and0 <= j < kmatch the claimed binary polynomial and rank lower bound. The largest matrix has order 210. The bound is strict in 21 cases, so the evidence preserves the distinction between a lower bound and a binary diagonalization.The useful negative control is a two-edge switch at
(h,k,j)=(7,3,0): it preserves every row degree, integer trace 35 and squared trace 175, but changes the characteristic polynomial. The independent audit rejects it. A complementary-subset nilpotent example and a wrong odd-multiplicity control document the other failure boundaries.Reproduce from the repository root with standard-library Python:
Expected:
PASS_LITERAL_BINARY_SPECTRAL_AUDIT,completed_cases: 41. The command checks pinned source bytes, recomputes every case and both rejection controls, and compares the complete result with the committed certificate. The README gives the matrix-similarity argument, polynomial recurrence, exact domain, stopping rule, dependencies and limits.Validation passed on Python 3.14.6: 559 tests in 85 isolated repository modules and all 20 historical patch checks, 10 focused tests normally and under
-O, standalone audit under-Sand-O, selected-record integrity, and mypy on both new Python files. The determinant engine is compared with direct Leibniz expansion on all 512 binary 3-by-3 matrices and 48 seeded matrices of orders 4,5,6; ranks are checked independently by exhaustive kernel enumeration. Fullmake verify, the selected supplier cold replay and Lean were not rerun for this isolated audit.Exact base:
66849e1475c930fd7732b1a0067ffee7e1e95f60. OS-random assignment seed 65, adversarial mathematical audit. Three narrow candidates and the local claim are retained inSOURCE.json; no pinned sprint coordination issue existed. Final overlap metadata was refreshed through PR #811. #778 (merramil, headf015b04c74801fa330f818d178e809c760fb5469) checks large orbit Gram packing in the same family; this adds the distinct modular characteristic-polynomial obligation and moment-preserving corruption control, without importing its code.Credit Douglas R. Colkitt's historical screen and the Johnson-spectrum sources cited in the README. Contribution by Lucas Steinmetz (
ljste), with substantial OpenAI Codex assistance, under the repository's Apache-2.0 license. This is finite verification evidence, not a formal proof of the all-size spectral formula or multiplication theorem. The selected frontier, inherited construction assumptions andupstream/are unchanged.