Scoped negative result: affine seven-cube copy floor 128 and peak tradeoff

[bbMisk]

Change and mathematical scope

Adds one scoped structural negative result in research/seven-cube-affine-seed43/. On the smallest seven-port cube with the explicit cubic Walsh Gram, every finite affine binary factorization of the full decoder has copied-rank sum at least 128. Two terms attain 64+64; four attain 32+32+32+32.

The sharp peak rank is 30, attained by an eight-term word of total cost 240. The minimum peak among total-cost-128 decoders is 32, so the sum and peak optima cannot be attained together. The exact total optimum under peak cap 30 remains open; 240 is an upper bound only.

Even granting every other required expense zero cost, the inherited additive stage ledger gives D <= (s-1)*128 - s*128 = -128 for every s>=3. This excludes positive saving in that stated model. No new kappa, physical supplier, selected-frontier change, or full multiplication theorem is claimed. Non-affine masks, masked identities, different Grams, additional ports and retained information across stages are outside scope.

Task and overlap

OS-random seed 43, structural decoder track. Exact base: 64039f1bd3b6a523b96083fd858ad040a75e3030. The selected PR1094 result and its actual construction/review were followed; complex remains binding, with PR589 on the bit side. Exact source blobs and SHA256 pins are in SOURCES.json.

TASK.json declares the catalogue card complex-masked-decoder changed to the donor's seven-port binary/cubic geometry question. This changes the five-cube geometry rather than rerunning its closed search. Nearest predecessors PR1046, PR1177, PR1222, and PR1482 concern the five-cube. The pending packages are overlap context, not theorem premises.

The final complete scan covered 713 open PRs and 218 discussion records, finding only this local package for the seven-cube terms. This is bounded overlap evidence, not a novelty guarantee. Main was refreshed to 680967accfd4311f3241dc154e1f434869747b43; all three live source blobs and the selected kappa are unchanged, with no package-path collision. No pinned sprint issue existed, so the donor's local-claim fallback was used.

Validation

python3.12 -I -B scripts/research_package.py --package research/seven-cube-affine-seed43
python3.12 -I -B research/seven-cube-affine-seed43/test_package.py

Both pass locally on Python 3.12.13. The primary checker uses the intersection polynomial, exact integer elimination and subset syndromes. The separate checker imports no generator/predecessor code and uses Walsh features, Fraction elimination and binary RREF.

Coverage: 65,025 ordered affine pairs in 127 exact rank orbits; 566,275 reduced source assignments; all 64 coefficient equations per assignment in the second checker; 49,152 literal witness entries per implementation. The written rank/diagonal reduction covers arbitrary finite term counts; the finite census is not represented as formal verification of the multiplication theorem.

Ten semantic/proof-boundary controls pass. Both implementations reject rank underclaims, an omitted orbit, an omitted assignment, an omitted witness term and source corruption (10 intended rejections), and both pass optimized read-only relocation. Metadata/source-pin validation and verify_selected_result.py pass. Full selected cold replay, native/global supplier admission, physical/hosting/precision/analytic adoption, proof-assistant checking and independent human review are unrun. Hosted CI is separate.

Credit

Joel Pulikkan / GamingPuzzled (PR231); Ross Richardson (PR958); martinxxx9 (PR1046); icekylinx/eumemic; and the retained DreamingOfClouds, Jacob Sussman and Zhihao Chen copy/frame lineage. Exact attribution and source pins are in the package.

Prepared by Hanson Sun (@bbMisk) with substantial OpenAI Codex assistance in mathematics, both implementations, verification and writing. The second implementation is by the same AI-assisted author, not independent human review. Apache-2.0.

Open next questions

The README and TASK.json describe one unclaimed next question: a fully priced arbitrary-dirty two-stage interface that retains a displayed coded total and changes the additive s*C charge. No such physical interface is provided, and a rank-table optimization alone cannot remove this negative deficit.

[Mister-Meeseeks]

Batch review at ecaca2048a0f18dbc315513c023415eacce2216d.

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

Reviewed scope: Complete affine seven-cube rank orbits, reduced factorization cases and diagonal relaxations prove COPY128 for any term count, with separate sharp peak30 and cost128/peak32 witnesses. Cap30 total optimum is not claimed, and the inherited additive ledger remains nonpositive.

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.