Scoped negative result: tensor E8 basis mixing cannot lower 72^d copy rank

[Mister-Meeseeks]

Scoped negative result; no new kappa. For the fixed full-E8 binary decoder matrix B, arbitrary minimal factorizations of B tensor-powered d have copied-information rank sum exactly 72^d. This includes nonsymmetric, nonseparable changes of total basis across tensor factors. A written tensor-support lemma proves the all-depth statement; finite replay supplies its exact depth-one premise and controls.

The existing depth-one floor belongs to GamingPuzzled (#620) and Chi Zhao (#631). This contribution extends it to arbitrary minimal tensor factorizations. It also covers overcomplete decompositions when both factors stay in the tensor code. The physical interpretation explicitly inherits DreamingOfClouds' #446 per-total copy-tree model; the review ledger marks that predecessor unreviewed. Changing the decoder matrix, unrestricted overcomplete factors, punctures and interacting delivery programs remain outside scope.

Only five files under research/tensor-e8-copy-floor/ are added: proof and handoff, standard-library verifier, exact certificate, source pins and the local sprint claim. upstream/, the selected frontier and existing generators are unchanged.

Reproduce

python3 -B research/tensor-e8-copy-floor/verify.py

Expected: PASS_TENSOR_E8_COPY_FLOOR: 511 exact base minors; 162 tensor supports; 8 negative controls; cost 72^d.

• All 511 nonzero base reader supports have committed nonzero integer determinants. Root coordinates and all 14,400 base binary pairings bind to the pinned Direct delivery with 504 helpers for conditional κ = 0.001517760977820331 #531 prototype.
• A seed-43 depth-two basis mixture checks all 207,360,000 binary matrix entries by complete bit-packed row equality and 162 full-rank support minors modulo three. This is a finite control, not the universal proof.
• Eight mathematical negative controls include a single-root puncture, a factor outside the code, a degenerate physical pairing and a missing inverse-transpose update. Source-hash and receipt-tamper packaging controls also reject.
• Python 3.14.6 (normal, optimized and isolated) and 3.13.0 reproduce the same receipt. A separate implementation regenerated affine planes and rechecked all 511 determinants without importing the verifier. Selected-record integrity and staged whitespace passed.
• The repository-wide suite and selected supplier cold replay were not repeated because only the new research package changes. No hosted CI or proof-assistant pass is claimed.

Pins, overlap and attribution

Exact base: 66849e1475c930fd7732b1a0067ffee7e1e95f60. Assignment seed 43, structural decoder research. No pinned coordination issue existed; the local claim records the result and its source link. All dependency and source pins are in SOURCES.json.

The overlap refresh covered 581 open PRs. Russell Seligmann's new #757 concerns the actual punctured P111 fixtures, whereas this result concerns full-unit tensor powers; its source-order correction is credited. #647/#682 concern a different complex RAM provider and are not ruled out. #669/#703/#715/#717 have different geometry or factorization scopes. Main and the selected conditional kappa 51110230636731/31250000000000000 were unchanged.

Credits include #446/#620/#631, icekylinx's #531 prototype, eumemic's #543 selected bit supplier, the #622/#623/#626 construction lineage, and the predecessor notices cited in the note. Prepared for Douglas R. Colkitt and submitted as @Mister-Meeseeks with substantial OpenAI Codex assistance in mathematics, implementation, verification and writing. Apache-2.0; no independent human review claimed.

[Mister-Meeseeks]

100-PR batch review at d8eaa3db32f76111b39db9b930f347ef30118a28.

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

Reviewed scope: Tensor full-E8 code support lemma gives copied-rank 72^d for minimal factors or code-constrained overcomplete factors; arbitrary overcomplete decoders remain open.

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.