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Prove sharp stability of the P104 support relaxation (no new κ) - #6287
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Prepared for @CubeJerry with coordinated OpenAI Codex assistance. Credit Nick Petalas PR6275, DreamingOfClouds PR6170, Matarener PR6267, Ali Romman PR5599 and the retained P104 lineage. No new kappa.
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For any unit-diagonal matrix over any field, let s=m-2(n-r), with m ordered off-diagonal nonzeros. Deleting at most 2s matching row/column indices leaves singleton ones and reciprocal rank-one pairs; factor two is sharp. A mask-compatible P104 rank-56/support-97 example requires two deletions. New beyond #6275: quantitative stability, with a separate deterministic proof rather than its random-order argument.
Base: 2485805.
#6275 comparison: 681c547. Source hashes: SOURCES.json.
Reproduce (Python 3.12, stdlib):
Expected:
PASS_REGISTERED_RESEARCH_PACKAGE.Executed: complete F2 matrices through n=4, F3 through n=3, 21,700 sparse n=5 binary matrices, 112 weighted cases; independent exhaustive 531,441 F3 n=4 matrices and 729 kernel-count rank checks. P104 witness passes six prime fields. Fourteen controls reject forged certificates, altered source and invalid field/input conditions. Normal/-O, source/history/modes, export and unchanged read-only Git-free replay pass. Fixed exhaustive domains; no random seed. The written proof establishes the universal statement, not failed search.
No new κ. Only the matrix relaxation: physical geometry, restoration and complete paid/productive accounting remain open. No physical 3597 lower bound, supplier admission or discharged framework assumption.
By @CubeJerry with substantial OpenAI Codex assistance: worker C, independent induction reviewer, worker B census/review and lead. Credit Nick Petalas (#6275), DreamingOfClouds (#6170), Matarener (#6267), Ali Romman (#5599) and retained lineage. No human/proof-kernel acceptance.
Proof, exact pins, controls and limitations: https://github.com/CubeJerry/integer-mult-bounds/tree/0f5560f3aebb2cf09640c9df1ab6d87a3be9395c/research/p104-support-independent-audit
Complete remote Git tree matches the tested contribution.