DONE: sharp COPY power floor for row-masked P112 basis switches

[RossRichardson]

DONE / HANDOFF — sharp COPY power floor for arbitrary row-masked two-coordinate basis switches

Artifact: #1747
Exact verified/published head: bde435d
Package: research/p112-row-mask-basis-switch

Established: for all 28 P112 coordinate pairs, every fixed A in GL(2,C), and every subset S of the 112 source rows, keep coordinate sources outside S and use A-dual sources inside S. The complete separate COPY rank sum is at least 64 and the COPY power bill is at least 8*8^theta for every 0<theta<=1. The empty mask attains both bounds. This is a written universal proof with exact finite premises, not an enumeration of 2^112 masks.

The new step is a balanced common-independent-set certificate: sixteen units per case, eight independent projected-label columns in each old/new group. Route a unit by its row mask, then use the chord bound. All 308 certificates (28 pairs x 11 complete complex support strata) pass separate projection and Euclidean-full-column/set-elimination implementations. An exact rank 10 augmented-source fixture shows two independent source directions outside col(X).

Validation: registered Python 3.12 replay; 42 exact endpoint fixtures/526848 entries; 17472 Gaussian support controls; ten primary and three separate controls; five regression groups; optimized Python 3.14; deterministic certificate regeneration; source/receipt corruption and read-only relocated checks. Both checkers pass from a read-only Git export of the exact committed head. Selected-record integrity passes separately. No hosted-CI pass is presumed.

Boundary: one common mask and one fixed basis are essential to this proof. Original arbitrary four-ray source corrections remain open. No physical dirty-workspace restoration, native/hosting admission, full selected cold replay, precision/tape/analytic transfer, Lean/human proof review or new kappa. The original 5% physical construction gate was not met. Selected and frozen sources are unchanged.

Next: fix sum/difference readers and try source supports not representable as one common mask of the dual basis; bill all four terms. Alternatively classify one explicit 3x3 basis family and seek balanced 24-unit certificates. Neither extension is claimed here.

Credit Mihir Srivastava/PR845, woklerx/PR998, Philipp/mightyOil/PR1197, DreamingOfClouds/PR717/446, GamingPuzzled/PR620, Denis/PR1689 and the full lineage retained in the README. PR1689's complementary Walsh-mask family is distinct. Final overlap 08:28–08:30 UTC: 421 open PRs, 379 Discussion records, complete pagination/no warnings, plus local notes and ledger; no novelty guarantee.

Prepared for Ross Richardson with substantial OpenAI Codex assistance in research, both algorithms, tests and prose. Apache-2.0. No subagents or independent human review. CLAIM RELEASED.

Original claim and bounded scope refinement

CLAIM — arbitrary row-masked GL(2,C) basis switching on P112

Scope checkpoint (08:18 UTC): one bounded narrowing from wholly arbitrary sources to a common arbitrary row mask, while allowing any invertible complex two-coordinate basis. For every coordinate pair p<q, A in GL(2,C), and subset S of all 112 source rows, take the old coordinate sources outside S and the A-dual sources inside S. Both added reader totals are paid separately.

Preliminary finding: 308 exact balanced common-independent-set certificates (28 pairs times 11 support strata) give the sharp COPY floor 64 and power bill at least 8*8^theta for all 0<theta<=1. Each certificate has sixteen units, independent in both old/new projected-label representations with eight per group. The argument covers every mask, not only binary character cuts. Separate replay and proof-boundary checks are in progress.

This is a COPY-component obstruction, not an arbitrary-source theorem, physical supplier, 5% construction-gate success or new kappa. The original four-ray arbitrary-source case stays open. Package: research/p112-row-mask-basis-switch. Claim expiry unchanged: 2026-10-14 10:15 UTC.

Pivot overlap refreshed at 08:15–08:17 UTC: 418 open PRs and 371 Discussion records, complete pagination, plus local packages/ledger. PR1689 uses complementary Walsh masks with arbitrary real reader coefficients; this uses one arbitrary common mask and the exact dual basis for arbitrary complex coefficients. Neither contains the other. No novelty guarantee.

Prepared for Ross Richardson with substantial OpenAI Codex assistance.

Original claim and provenance

CLAIM — fixed four-ray P112 decoder with arbitrary source columns

Question: retain the eight coordinate readers and add x_p+x_q and x_p-x_q, for p<q in 0..7, with arbitrary complex source columns. Can this coupled rank-two subfamily lower the separate COPY bill below 64? I will derive the exact binary support-subspace feasibility problem and seek a sharp floor or a counterexample. Ordinary transpose and all-pairs equality are required.

Base: 0b1cccf; selected PR1094 unchanged. Predecessors: Mihir Srivastava PR845 geometry/single-lift theorem, woklerx PR998 complex extension, Philipp/mightyOil PR1197 coupled rank-two opening. PR1689 restricts both source totals to masked Walsh columns; this question fixes the added reader directions and permits arbitrary sources. PR1327 changes both factors and is a different parity-lift family.

Method/domain: exact binary subspace geometry and coefficient-support feasibility for four reader rays {e_p,e_q,e_p+e_q,e_p-e_q}. Additional physical overhead is optimistically free; this is a copy-cost side result, not a completed supplier or the original 5% physical construction gate. At most 25 minutes before one bounded narrowing or handoff; final quarter for independent implementation/controls.

Expected artifact: scoped proof/checker or precise handoff, package research/p112-four-ray-sources. Revision-3 task complex-rank-shape-decoder; one OS draw b753af53242f8a79a9032531c8f15c54, scope changed explicitly. Initial fresh overlap covered 415 open PRs and 365 Discussion records with complete pagination, plus local packages/ledger; no novelty guarantee.

Claim expires: 2026-10-14 10:15 UTC. Prepared for Ross Richardson with substantial OpenAI Codex assistance. No new kappa is presumed.