Research: exact arbitrary-mask three-total five-cube boundary (no new kappa)

[RossRichardson]

PR1046 leaves non-affine port masks outside its five-cube copy theorem. This research note / scoped negative result resolves the full decoder with at most three arbitrary binary outer products. Its exact total pairing-rank minimum is 32; a three-total witness has ranks 8 + 16 + 8, versus the exact affine three-total minimum 35. Every cost-32 triple has peak rank 16. For canonical distinct readers, the 131,068 equality masks are precisely the nonempty proper subsets of one parity class.

The proof uses the cube's two orthogonal parity bases and an exact rank formula, covering all masks without a 2^32-mask search. Masks may be non-affine functions of the port index; messages remain linear XOR sums of input data. PR1046 already attains total 32 with two affine totals, and with four affine totals of peak eight. Neither optimum is improved here.

Under the inherited additive stage/copy ledger, even granting every other required expense zero leaves D <= (s-1)32-s*32 = -32 for every s>=3. No physical supplier, runtime gain or new kappa is claimed. Four or more arbitrary-support terms, larger cubes, other Grams, nonlinear data messages and changed accounting remain open. All-size/compiler, common-label/mutable-source, hosting, precision/tape, bit H1-H5 and analytic obligations remain inherited.

Only research/five-cube-three-totals/ and its path-scoped Linux workflow are added. Research base: c0e3631dc24e3c24a861f7d3d79e0608481cccec; refreshed submission base: 1b59b624d21924f8e3537cdc1ac52d3be6eda2fe. All seven pinned sources are unchanged between those bases. Selected PR1094 and upstream/ are untouched.

Validation, offline with Python 3.9+ and the standard library:

python3 -I -O -B research/five-cube-three-totals/verify.py
python3 -I -O -B research/five-cube-three-totals/independent.py
python3 -I -O -B research/five-cube-three-totals/test_package.py

Expected primary marker: PASS_FIVE_CUBE_THREE_TOTALS masks=65535 arbitrary_min=32 affine_min=35 equality_peak=16 no_new_kappa.

Both checkers and all nine test groups pass on CPython 3.14.6 and 3.9.6. Evidence includes the complete 65,535-mask slice; all 433 reduced affine templates; separate Fraction checks of 189 affine pairings and 319 dense masks; literal identities for all 131,068 equality masks; ten mathematical rejection controls; a valid changed-Gram scope counterexample; source/receipt corruption and coverage-omission rejection; and read-only offline relocation. Both receipts regenerate byte identically. Source Git/SHA256 bindings, selected-record integrity and all five selected-result tests pass. No full repository regeneration, selected supplier cold replay, hosted CI pass or formal multiplication proof is claimed.

Credit martinxxx9, PR1046 (7cadcb0a2fc71fdedc0066704dec3fec58c2ca2c), Ross Richardson, PR958 (28d68c88f0184835d8c8a7266ab8d0dad3f18a8a), Joel Pulikkan / GamingPuzzled, PR231, icekylinx/eumemic and the retained frame/accounting lineage. Original source notices and exact pins are included; no predecessor executable code is imported. Prepared by Ross Richardson with substantial OpenAI Codex assistance, including both implementations. Apache-2.0; no independent human review claimed.

Seed 46, structural decoder track. The local claim records three candidates and the changed restriction. Final overlap checks covered recent PRs through #1176 and the three newly introduced discussion threads (#1163/#1166/#1167); no overlapping claim was found. No pinned sprint issue existed. The repository has neither codex nor codex-automation labels available.

[Mister-Meeseeks]

100-PR batch review at e878ef36109bc6d7e21e62d03c22d8ec36f6f936.

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

Reviewed scope: Exact arbitrary-mask three-total five-cube copy-cost boundary and equality classification; algebraic improvement still has nonpositive deficit in the retained ledger.

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.