Scoped negative result: fixed P112 24-row boundary retains COPY64

[bbMisk]

Change and mathematical scope

Scoped negative result with a written proof and exact finite premises; no new supplier or kappa. PR #1375 leaves its first free-compatible 24-row span-loss boundary open. This package proves that this exact boundary still has sharp whole-decoder COPY cost 64, for arbitrary complex correction amplitudes (including zeros), arbitrary singleton amplitude, and every GL(3,C) mixing with the two specified coordinate modes.

The replacement ranks either include two ranks at least eight, or are all at least seven. Thus their separate power bill is at least 2*8^q for every 0<q<=1. The cancellation-aligned example changes (8,8,0) into (7,8,7): reducing one term raises the whole bill to 70. Omitting its compensation fails a constrained entry. Identity mixing attains 64, including a rank-nine masked completion.

Only research/p112-boundary24-seed39/ is added. Larger rectangles, other supports, more mixed modes, shared-copy billing and physical realization remain outside scope. No full child histogram, moment improvement, all-size compiler, precision/hosting invoice or multiplication theorem is claimed.

Task and overlap

• Base: bce54fb3f895cbe5cd4c0eb477c3afeed100190f; contribution: 4bcc49e3f4041018b0607da46a87d8928a6e0fd0.
• OS-random seed 39, complex-supplier track. Task complex-masked-decoder, scope refined to the fixed PR1375 boundary. The initial aligned-amplitude question extends to arbitrary amplitudes on the same support through the proof, not a larger search.
• Predecessor PR Research: COPY floor 64 for two-coordinate P112 mixing with small free rectangles (no new kappa) #1375: 4a533aff2a7a87c9b36e077a31774b332a7f64bd. Its support cap 23 does not cover the full named boundary. Its theorem is not assumed: all new finite premises are recomputed.
• PR Scoped obstruction: one free P112 rectangle cannot improve one coordinate COPY #1331: f08b698cc2bd74e2425486728a008e531fc35f0e, the one-coordinate predecessor and two-coordinate handoff. Discussion CLAIM: sharp copy floor for all rank-nine factorizations of a single odd-entry P112 completion #1360 concerns all nine factors of a singleton-by-singleton completion; this package treats a 24-by-one correction with two original modes mixed.
• Claim. The final recorded overlap scan completely paginated 788 open PRs and 146 discussion records without warnings. Another agent listed this boundary as a candidate but chose a different investigation.
• Refreshed main 410026dc5513b87db92ae98571d1d5984c69a983 preserves all four source pins; the patch applies cleanly. Selected frontier and frozen sources are unchanged.

Validation

Python 3.12.13, standard library only:

python3.12 -B scripts/research_package.py --package research/p112-boundary24-seed39

Expected: PASS_REGISTERED_RESEARCH_PACKAGE research/p112-boundary24-seed39 outcome=negative-result.

The primary implementation checks 655 exact support pairings, 9 Gaussian-rational full matrix fixtures (112,896 entries) and 9 controls. A separate implementation imports neither primary nor predecessor code, rebuilds Euclidean E8 geometry, rechecks every finite premise with set-based binary elimination, and checks 25,088 integer identities, two nonzero rank-nine minors and 6 controls.

The registered replay, both optimized-mode checkers, read-only relocated replay, five external corrupted-source/receipt rejection runs, 20 repository workflow tests, selected-record integrity and whitespace check pass. The scoped quantified argument is written in the README; finite replay is not formal verification. Native/Lean builds, hosted CI and the full selected-supplier cold replay were not run locally.

Credit

Credit commdata2338 / PR1375 for the explicit boundary and question; Arham Tahir / PR1331 for the earlier handoff; Mihir Srivastava / PR845 for the pinned geometry; DreamingOfClouds / PR717 and PR446/595 for the framework; themilkman216 / PR968 for the pairing-cost model; Joel Pulikkan / GamingPuzzled / PR620 for COPY64; and woklerx / PR1077 for the orientation check.

Prepared for Hanson Sun / bbMisk with substantial OpenAI Codex assistance in mathematics, code, verification and writing. Both implementations have the same AI-assisted author; no independent human review is claimed. Apache-2.0.

Open next questions

The package README identifies two bounded extensions: another maximal free rectangle, or three original modes on this U. First compute the relevant survivor/pure-correction pairings and coupled power bill. The present singleton case split and two-mode geometry do not settle either question.

[Mister-Meeseeks]

100-PR batch review at 4bcc49e3f4041018b0607da46a87d8928a6e0fd0.

Merged to main, preserving the original contributor commits and package attribution.

Reviewed scope: Fixed P112 two-coordinate, one-column correction theorem covers arbitrary GL3 complex mixing and all nonzero amplitudes, including compensation. Exact finite rank premises pass; separate COPY cost cannot improve in this class, not arbitrary decoder geometry.

The pinned scoped command passed; the batch ledger contains its command, input hashes, environment and log. This incorporates the research/tooling contribution and does not change the selected κ or discharge the inherited multiplication-theorem assumptions.

Batch review, attribution and evidence. Thank you for the contribution.