Research: batch common-factor product shears with dirty restoration

[CubeJerry]

Change and mathematical scope

Independent output shears y_i += A_i B x can share B's computation and restoration while preserving entirely dirty workspace. This research package emits the literal batch, proves its exact noncommutative identity and a sharp 2k+2 query minimum in the specified one-connector star model, and prices all child/inverse calls, storage, source access, routing, arithmetic, dispatch and precision.

The seed-58 fixture uses 246 primitive factor-shear calls instead of 680 for separate balanced binary products, with four dirty arrays in either schedule. This is a scoped recursive-interface construction; no new κ, instantiated supplier or general circuit optimum is claimed. Rounded leaves have exact restoration with a separately bounded output error.

Only research/dirty-fanout-batch/ is added. Base: f567884aeb8851b6e794af1184119a3bfbe1e631. PR628 is pinned at 0768f97d06c623b8211e651543c66135796b62bf; original source/proof/notice bytes are retained. The accepted #799/#589 frontier is unchanged. The local claim records track seed, candidate selection and the original overlap checks. Before submission, upstream main was refreshed (unchanged at the base above), the latest 100 open PRs were checked through #888, and targeted all-state searches covered fanout, common-factor and multiple-output work. This contribution batches distinct output shears sharing B; #822 concerns dirty connector reuse, #840 native dyadic pairs, and #793 scalar coefficient batching. No duplicate of this scoped multi-output construction was identified. No sprint coordination issue was found. CLAIM.md preserves the original completion-time network/access history; API access was subsequently restored for this submission. Credit and substantial OpenAI Codex assistance are disclosed in NOTICE.md.

Validation

python3 -I -O -B research/dirty-fanout-batch/verify.py
python3 -I -O -B research/dirty-fanout-batch/test_package.py

Expected: PASS_DIRTY_FANOUT_BATCH and PASS_PACKAGE.

• 128 free-word cases, 384 weighted-price cases, 795 dense cases across three schedules and inverses, 27 rounded-grid cases and one rational noncommuting case.
• All 9,331 shorter two-output star words reject; the general lower bound is proved separately.
• 15 algebraic/admission controls, plus six package-corruption controls and standalone relocation.
• Normal/optimized Python 3.12.14 runs agree; retained files match fetched Git objects; selected-record integrity and all five existing selected-record tests pass.

No cold supplier replay, repository-wide artifact regeneration, hosted CI or full theorem formalization is claimed. Physical supplier integration and all inherited all-size/analytic obligations remain open.

[Mister-Meeseeks]

100-PR batch review at e2021d1c9e06948528cbc0a8fd7079b671da981d.

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

Reviewed scope: Dirty fanout batch and restricted star-query minimum, charging connector restoration; no native supplier implementation.

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.