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Prove the sharp two-plane COPY floor for arbitrary scalar factorizations - #4365
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Mister-Meeseeks merged 1 commit intoOct 21, 2026
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Prepared for @CubeJerry with substantial OpenAI Codex assistance. Scope: full-plane additive COPY tariff; no new kappa.
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…r 12 over every field on 27,395 of 27,720 triples; F2 minimum 12 on the rest (no new κ) Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
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Proves sharp COPY mass 8 for any finite scalar factorization on two matched planes, over every coefficient field. This closes the arbitrary cofactor-cancellation and overcomplete gaps in #3990/#3997 using a rank proof, not a larger search. Disjoint pair-local decoders therefore retain COPY >=224; their inherited optimistic complete budget is 293/292 >1. No new κ.
Base:
12fa8c5c844be21bfefb38a19503fbd867a11244(canonical main, priority 7; OS seed 27).Published commit:
c2f6264c2952c983bb445dc5ae00c6a2adf28649. Its complete Git tree matches the tested contribution.Proof, exact certificate, source pins and validation
Runtime SHA256 pins:
f1da80610bf33c58527f18ad63b4350d0b864e1d4486141ee17ac9bed4d529d6c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa4fd648f7b5178bff5441bf364d58234b7bc1a43b924bc6da03013c948f1473b1Reproduce (Python 3.12, stdlib):
python3.12 -I -B scripts/research_package.py --package research/two-plane-copy-floorExpected:
PASS_REGISTERED_RESEARCH_PACKAGE ... outcome=negative-result.Executed: all 1,540 pairs/13,860 inequalities; 682 small binary blocks; exact rational, complex and six-term fixtures; normal/-O replay; separate image-set and shortest-path checker for all five tariff classes. Seven internal rejection controls, an independently underpriced optimum (8 ->6), and ten external receipt/source-corruption runs passed. Committed-byte/source-history, export/integrity and read-only Git-free checks passed.
Scope: whole-plane closures, scalar rank-one messages, separate additive COPY billing, fixed pair-local coverage. A six-term control improves concave COPY-only cost at equal mass; it still fails the complete budget. Cross-pair sharing, changed coverage/readers, native source access, restoration, hosting and all-size/outer obligations remain open. Finite checks do not constitute a formal proof of the full theorem. Selected frontier and upstream/ unchanged; no hosted-CI claim.
Attribution: @CubeJerry with substantial OpenAI Codex assistance. Credit Gonzalo Mier (#3990/#3997), Cinna Davis, Adam Gall, Jeremy Diviney, ctoth/Philippe Van Velzen, Nick Petalas and the retained supplier lineage. Related #3383/#3489/#3505 have different scopes; exact comparison and full credit are in the package. Apache-2.0; no independent human review claimed.