Research: quadratic five-cube copy floor and sharp rank-cap tradeoff (no new kappa)

[bbMisk]

PR1046 leaves nonlinear masks outside its affine five-cube decoder theorem. This scoped structural negative result covers every common code span_F2{1, parity, h} with Boolean degree(h) <= 2, allowing any finite number of binary rank-one terms. All 16,383 augmented codes have exact minimum pairing-rank sum 32. In the 16,368 genuinely quadratic codes, imposing rank at most 15 on every term raises the total to at least 34 or makes the factorization impossible. A 13 + 13 + 8 witness attains 34 in a 60-code orbit.

The certificate covers all 64 cube-isometry orbits, 3,136 ordered rational term ranks and every state of each 512-state coefficient graph. Edge potentials certify lower bounds without trusting the shortest-path search; attaining words are checked on all 1,024 port pairs. The separate checker imports no generator code: it uses polynomial substitutions, rational elimination and direct binary-span/edge checks. Zero-cost and redundant terms are included. Under the inherited additive stage ledger, even granting all other work zero expense leaves deficit at most -32. No physical supplier or new kappa is claimed.

Reproduce with Python 3.10+ and the standard library:

python3 -I -O -B research/five-cube-quadratic-code-seed44/test_package.py

Expected: six test groups pass (Ran 6 tests, OK). Validation includes complete regeneration, a separate full checker, semantic corruption controls, changed-source rejection, occupied-output preservation and standalone optimized reproduction. The selected-record check and all 25 selected-record regressions pass. Exact execution evidence, source pins, proof and task card are in the package. Hosted CI and the full selected-supplier cold replay are not claimed.

Base: 1b59b624d21924f8e3537cdc1ac52d3be6eda2fe; OS seed 44, structural decoder track. Only research/five-cube-quadratic-code-seed44/ is added. Both factors must stay in the same three-dimensional code; different codes, multiple extra masks, higher degrees, other Grams and changed copying/stage accounting remain outside scope. All physical/compiler, hosting, precision/tape and analytic obligations remain inherited.

Credit Martin Rv / @martinxxx9's PR1046, Ross Richardson's PR958 and adjacent PR1177, Joel Pulikkan / GamingPuzzled's PR231, and the retained frame/accounting lineage. PR1177 treats at most three arbitrary masks; its canonical three-total family contains the displayed rank-34 witness. The new contribution certifies every finite term count in the stated quadratic codes. Final overlap inspection covered 823 open PRs through #1214 and active discussions. No pending implementation or theorem is imported.

Prepared by Hanson Sun (@bbMisk) with substantial OpenAI Codex assistance in research, proof, implementation, verification and writing. Both implementations are AI-assisted; no independent human review or formal multiplication-theorem verification is claimed. Apache-2.0.

[Mister-Meeseeks]

100-PR batch review at c6fe323581d3803a080b000b263a07edf2b00b54.

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

Reviewed scope: All16383 common quadratic-augmented five-cube codes: copy cost32 for arbitrary finite term counts, with rank≤15 cost≥34 on genuinely quadratic codes. Complete symmetry transports and512-state potential certificates; fixed additive ledger only.

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.