Two-coordinate COPY floor for arbitrary one-column free corrections

[bitplane]

DONE — PR1468

For all 28 P112 coordinate pairs and 112 singleton sites, arbitrary complex free corrections supported on any subset of the site's 52 odd neighbors retain the sharp complete COPY floor 64 after all GL(3,C) mixing with the two original terms. Six original terms stay fixed; transposition covers one-row corrections. For every 0<q<=1, the three replacement ranks satisfy sum r_j^q >= 2*8^q, giving complete power floor 8*8^q. Identity mixing attains both bounds for every allowed correction.

The proof uses complete odd-neighborhood survivor spans and the coupled inverse-factor identity. The pure nonsingleton factor retains its actual charge. The lower envelopes are (8,8,0), (6,6,6) or (6,6,4). The 24-row example has ranks (7,8,7): the former per-child rank-eight premise fails, while the complete bill still cannot improve.

Evidence: two geometry representations agree on 140 support strata, 71,540 character evaluations, 15,680 even-neighbor slices, 15,680 singleton erasures and 700 pairings. Thirteen Gaussian-rational full nine-term fixtures check 163,072 scalar entries and every proof branch. Registered Python 3.12 replay and seven semantic test groups pass. A separate read-only isolated optimized Python 3.14 replay gives the identical receipt 6d621ea5ffffc4079cc50a8bf4a0e4d83305ec48ce78b7d95e844da97a4c0627, with every runtime file unchanged. Source/receipt corruption and mathematical failure controls pass.

Attribution: commdata2338/PR1375 supplies the small-rectangle result, erasure method and 24-row support. Cinna Davis/PR1373 supplies the three-active branch at (4,6); Arham Tahir/PR1331 supplies the earlier handoff. The final refresh found Hanson Sun/bbMisk's PR1432, which already proves the fixed 24-row case and the same (7,8,7) example, and PR1460, an independent arbitrary-rectangle compensation bound at (4,6). Both are credited at exact heads in the package. This is an independently derived all-pair one-column proof and certificate; no pending theorem or code is imported. The newer two-column claim in Discussion1316 and all-nine-factor singleton claim1360 are distinguished. Credit PR845/Mihir Srivastava, DreamingOfClouds/PR717/446/595, GamingPuzzled/PR620, themilkman216/PR968 and woklerx/PR1077/1180.

Scope: a separate COPY screen at unchanged width, normalization and multiplicity, granting all added overhead zero. This package does not cover general two-sided rectangles, more mixed coordinates, other punctures or shared COPY billing. No physical word, frame/restoration schedule, owner/hosting admission, native run, selected cold replay, precision/tape, all-size compiler or analytic transfer was established. Written proof, not proof-assistant checked. No new supplier or kappa.

One OS draw 149d7583c4efedede03fc432c003699f selected complex-mechanisms / complex-masked-decoder, scope key 2a6f2c726b78f9ae7d26, priority revision 2. Required starting example passed. Research and refreshed main base: 410026dc5513b87db92ae98571d1d5984c69a983; both live inputs unchanged. Mathematical commit: 725cc996905139e6ba81053c78e248eb2e29608f. Final head: 5e2d8ec8ebff17c85e813ef1bd6f06312c1fe16a. Complete overlap snapshot: 824 open PRs and 159 discussion records, no pagination warnings. Package: research/p112-column-correction-floor/, 14 files.

Handoff: investigate exact frame-preserving transport of PR1460's arbitrary-rectangle proof between pairs before repeating searches. More than two mixed coordinates needs a new support classification and coupled-factor power bound. Reproduce with python3 -I -B scripts/research_package.py --package research/p112-column-correction-floor.

Prepared for Gareth Davidson (@bitplane) with substantial OpenAI Codex assistance; Apache-2.0. No subagents or independent human review. Claim complete; hosted CI and maintainer review remain separate from passing local checks.