Prove generic output-bank mixing cannot lower connector map calls

[RossRichardson]

Output-bank mixing is an explicit gap in the generic one-connector exclusions. This package proves it cannot lower the labelled map-call bill: every universally correct word using arbitrary scalar GL mixing and any finite dirty output-only bank has an ordinary word with the same B timeline and no more calls of each A_i. The theorem even grants arbitrary physical reader ports. Fixed port-independent complete prices therefore have the same optimum with or without mixing.

The five-source/all-31-mask minimum remains 74 complete A/B calls, and the credited heterogeneous fixture remains 182. These numerical optima are inherited; the contribution is the all-parameter erasure argument and constructive checker. No new kappa or selected-supplier adoption is claimed.

Scope: independently variable arbitrary exact F2 readers, a word independent of map entries/data, immutable sources, one connector excluded from bank mixing, all dirty helpers restored, and output observation only at batch exit. A shared-reader counterexample and a valid three-readout identity show why reader isolation and transfer through erasure are necessary. Port-dependent routing and complete physical runtime are not dominated by this proof.

Evidence in research/generic-output-mixing-erasure/:

• Written proof for every M, L>=1 and finite R>=n; no formal-kernel claim.
• Forward/inverse normalized coefficient check and independently implemented noncommutative full-state/suffix-routing oracle, covering every dirty column.
• Two separate 945-pairing enumerators, all 168 GL(3,2) frames in the stated fixture, all 19,531 short words in the stated five-letter alphabet, and exhaustive 2x2 matrix scope controls.
• Seven behavioral test groups: actual detector removal, helper-only defects, source/receipt/fixture corruption, missing evidence, normal/optimized unchanged relocation and explicit no-overwrite generation.

Verified locally on CPython 3.12.12:

python3.12 -I -B scripts/research_package.py --package research/generic-output-mixing-erasure
make selected-record-check
git diff --cached --check

The registered replay passes; independent normal/optimized receipts agree. The selected-record check is source integrity, not its full cold replay. Hosted CI is separate and not claimed successful.

Original source base c676548106012571fefa1dce0ec16f1bcfe11dce; integrated main e112d71c8d7bb32435debcc54df932593dd8223a with all scoped inputs unchanged. Result head a86b65e648f5b004f4aa68b3ed2c7975e8ca0163. Selector nonce, full source/selected hashes, predecessor heads, scope refinement and structured next question are in TASK/SOURCES. Final overlap paginated 328 open PRs and 691 Discussion records without warnings (18:08–18:10 UTC); this is not an exhaustive novelty proof. Claim: #2043.

Credit Ross Richardson's #943/#934 and dirty-commutator/fanout lineage; Adam Gall #1915; Arham Garg #1945; Cinna Davis #1770; and 1337isnot1337's common-A broadcast #1707. Substantial OpenAI Codex assistance, including separate recursive-interface and exact-verification specialists. Apache-2.0; predecessor inputs/notices and the selected frontier are unchanged.