Add exact rank-one center-difference sharing mechanism

[1337isnot1337]

Summary

• Add an exact local construction for two same-frame bilinear centers F and F+H when H has rank one: route the rank(F) atoms to both dirty output panels, then evaluate the correction once. If each center separately has rank r, the paired map has rank at most r+1 rather than 2r in the common-frame bilinear-rank model.
• Give the concrete F2^2 instance with exact joint rank 3 versus separate ranks 2+2. The output-slice flattening has rank 3, certifying minimality; an exhaustive replay checks all 1,024 dirty input, target and scratch states, with correction and fanout negative controls.
• Add an exact selected-profile sensitivity screen. Even if all 72 candidate pairs were eligible and all other overhead were zero, the fixed-word a cap is [50198000463/15625000000000, 3212672029633/10^15], below 1/99. No selected occurrence, supplier change or new kappa is claimed.

The construction counts bilinear rank-one atoms and their output coefficient vectors. Frame changes, copies, precision, hosting and restoration are not priced at a real supplier occurrence.

Reproduction

python3.12 -B scripts/research_package.py --package research/rank1-center-delta-seeddfc2

On the author’s host, Python 3.12 is unavailable. The package verifier and metadata check passed under Python 3.14.7; the registered Python 3.12 replay remains for CI/reviewer confirmation.

Base: 0b1cccf86e2f5132ed286a26ef0a681a495740ea. Selected-record SHA-256: 10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32. Exact live inputs and provenance pins are in SOURCES.json.

Related work: #1708 identical-center fanout, #1748 reverse shared-center phase, and #1791 selected-profile pricing. This package adds the explicitly charged rank-one difference case; it does not claim an eligible selected occurrence. The scoped claim and handoff are in Discussion #1166 comment 18922942.

Prepared with substantial OpenAI Codex assistance; no independent human review is claimed.

[Mister-Meeseeks]

Batch review at e495653a48e46f4b5cd177d8cd890b7a01e404dc.

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

Reviewed scope: Explicit paired two-bit bilinear maps have joint rank3 versus separate2+2, proved by output-slice flattening and a matching three-atom circuit; all1024 dirty states pass. All72 selected-pair scenario remains hypothetical and misses1/99 even optimistically.

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.