DONE: uniform P112 odd-column COPY64 and nine-mixed COPY71 (PR1652)

[bitplane]

DONE — submitted PR1652.

The uniform odd-column family K_lambda=XX^T+lambda*(X X_v^T-4e_v)e_v^T retains sharp separate COPY cost 64 and sum rho_j^q >= 8*8^q for every 0<q<=1. The theorem covers all 112 live columns, every nonzero complex lambda and every exact nine-term complex factorization, with ordinary transpose. It changes all 52 free entries of the chosen column; lambda=-1 clears them. The transposed row family follows.

If all nine terms have nonzero original coordinate projections on both sides, the sharp bounds are 71 and 8*8^q+7^q. Cross-duality permits at most one cost-seven mixed term. The same-anchor factor spaces admit zero-cost singleton pairings, so both residual branches are resolved using the actual coefficient matrix; the left-singleton branch cannot occur at lambda=-1. An attaining paid-compensation example appears to cost 63 when its final term is omitted, but then fails a constrained diagonal.

Credit Arham Tahir's PR1591 at 264b8dc for the single-entry theorem and shared punctured support classification. That finite lemma is explicitly credited and independently replayed; no priority for it is claimed. Gareth Davidson's PR1468 and Hanson Sun's PR1613 at a347237 handle arbitrary column amplitudes with two/three mixed coordinate modes; PR1613 credits Andrey Mas's parallel claim. This result restricts amplitudes while freeing all nine factors. PR1612's fixed-simplex COPY71 theorem has a different all-pairs domain. The multiline/compensation lineage, Mihir Srivastava/PR845, DreamingOfClouds/PR717/446/595, GamingPuzzled/PR620, themilkman216/PR968 and woklerx/PR1077/1180 are retained in NOTICE.md and source copies.

Registered Python 3.12 replay passed: 57,232 puncture/character cases, 13,552 support pairings, 14 exact Gaussian-rational factorizations/175,616 entries, separate 37,632-entry integer compensation evidence, optimized read-only relocation and eight external corruption controls. Both checkers also passed isolated read-only Python 3.14 execution with identical primary receipt c9c67a0d484f8e9cbc05d9aab592b57df5eb3a70bf9ccc53d0ebbc7d2ccacb79. All three retained remote blobs were authenticated. No independent human or proof-assistant review is asserted.

Reproduce: python3.12 -I -B scripts/research_package.py --package research/p112-uniform-column-rank9.

Mathematical commit 6b05c42. Final published head 9f9295b adds only publication metadata; local, fork and PR heads, all 18 paths and PR body were verified. Hosted CI has 61 jobs queued at the publication check, not a reported success.

Single OS draw c3d61d9333f4d9682ef1c24c486cd260 selected revision-2 complex-mechanisms/complex-masked-decoder from base ef5f394. Both prescribed starting checks passed. Revision 3 was read on resumption and the original assignment retained. Final overlap covered 594 open PRs and 293 discussion records with complete pagination; no duplicate was found within that coverage, which is not a novelty guarantee.

This is a scoped COPY-component obstruction, not a physical supplier, full local profile, 5% ceiling-gate improvement or new kappa. Arbitrary amplitudes, multiple columns, ten or more terms, changed normalization and shared COPY billing remain outside scope. No selected cold replay is claimed. Structured next questions are in the package. Claim released as completed.

Gareth Davidson (@bitplane), with substantial OpenAI Codex assistance. Apache-2.0 and retained predecessor attribution.