Research: COPY84 floor for low-rank matched P112 support frames

[adamgall]

Result

One new exact package: research/p112-matched-frame-copy-floor/, on base 0b1cccf86e2f5132ed286a26ef0a681a495740ea.

For any finite masked P112 decoder over C with ordinary transpose, suppose every paid rank-one term has equal F2 source/target support spans and pairing-rank COPY cost at most four. Actual supports need not coincide or be tetrad-local. Arbitrary coefficients, cancellations and zero-cost corrections are allowed.

The package proves

n1 + 2 n2 + 4 n3 + 5 n4 >= 112, hence COPY >= 84.

Its rank-relaxation optimizer is uniquely 28 rank-three terms; this is not a constructed COPY84 decoder. The COPY moment is at least 21/16 of the incumbent eight rank-eight copies, for every 0 <= a < 1 at unchanged normalization. A common-span radical quotient and the characteristic-vector complement relation give the rank-four lifted capacity five, rather than the naive eight.

The fully charged optimistic retained-template ceiling is [0.000736244670745, 0.000736244670746], below the unchanged five-percent target 0.00177455681454345. Both local COPY mass and centre charge rise from 64 to 84; idle mass stays 1646. Every additional physical charge is waived only to make this rejection favorable. No new kappa, supplier admission, physical frame contract, frontier change or positive construction-gate success is claimed.

Exact evidence

• All 12,544 root/label/coordinate entries, including masked target 4I_112.
• All 452 nonsingular nonalternating symmetric F2 forms through dimension four; lifted rank capacities 1,2,4,5.
• Exact P112 witnesses attaining each per-term capacity, including distinct actual supports with the same label span.
• Fraction row elimination plus independent odd-prime column rank corroboration.
• Semantic controls for missing/wrong diagonal terms, wrong mask, arbitrary zero-cost correction and undercharged centre.
• Explicit unmatched-span rank-two/lift-three and matched rank-five/lift-ten counterexamples showing why the scope restrictions matter.

Reproduction actually exercised

On CPython 3.12.12, Darwin arm64:

uv run --python 3.12 --no-project python -I -B research/p112-matched-frame-copy-floor/verify.py --write
uv run --python 3.12 --no-project python -I -O -B research/p112-matched-frame-copy-floor/verify.py
uv run --python 3.12 --no-project python -B scripts/research_package.py --package research/p112-matched-frame-copy-floor

Direct and registered replays passed:

PASS_P112_MATCHED_FRAME_COPY_FLOOR forms=452 entries=12544 capacities=1,2,4,5 COPY>=84 moment_ratio>=21/16 controls=7 no_new_kappa

PASS_REGISTERED_RESEARCH_PACKAGE research/p112-matched-frame-copy-floor outcome=negative-result

The coordinating parent independently reviewed the quantified proof and repeated the registered Python 3.12 replay before granting publication. This is not independent human review or a proof-assistant theorem. Native/hosted CI and the selected full cold replay were not run or claimed.

Selection, overlap and limits

Independent one-shot chooser seed 5cee555544503585ad60b2631e790c0c; track complex-mechanisms; emitted and chosen card complex-rank-shape-decoder. Complete chooser JSON, exact source pins, TASK scope refinement and replay manifest are included.

This uses the card's allowed scoped support-alphabet lower bound, not its positive five-percent construction gate. It is distinct from #1909 (one-tetrad locality with arbitrary opposite support), #1923 (a finite Householder orbit of one symmetric witness), and #1633 (all-pairs outside-root-code ranks). Targeted cached/local searches and live predecessor head checks found no same-scope result; no literature-priority guarantee is implied.

Unmatched support spans, COPY rank at least five, other punctures, nonseparate copy accounting and changed role/coverage interfaces remain outside the theorem. A high-rank mask fixture is not a decoder. README includes exact proof, physical limitations and concrete open next questions.

Coordination: #1929 (comment)

Credit DreamingOfClouds for PR717's masked decoder/COPY model, Mihir Srivastava for pinned geometry, themilkman216 for frame-pair predecessor results, Douglas Colkitt for the exact ceiling engine, and the selected supplier chain. Prepared for Adam Gall with substantial OpenAI Codex (GPT-6 Astra) assistance; Apache-2.0. All predecessor, frozen and selected files are unchanged.

[Mister-Meeseeks]

Batch review at 57b3cfd1f0762a736da55d6b3175a024a743b99a.

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

Reviewed scope: Characteristic-vector proof and452 exact form census cases give lifted capacities1,2,4,5 for matched support spans of COPY rank1..4, forcingCOPY>=84. Exact fixtures expose unmatched/rank5 escapes; rank relaxation and fixed-template ceiling are not a constructed decoder or new supplier.

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.