[ToikY]

Change and mathematical scope

NO VERIFIED GAIN. The exact κ change is 0 (0%). The strongest independently reproduced comparable witness remains #7156 at κ = 0.003644407895539, head b44944c.

Retaining the #7001 paired BIT endpoint and the 36 LOCAL stage assignments forces at least four rank-one QUERY terms at the original body incidence. Independent stage derivatives give orthogonal body projectors. Two same-stage LOCALs then force an identity minor in the head-defect matrix. This proof allows arbitrary invertible constant gates and additional auxiliary roles initialized and restored to zero. Under the retained tariff, an added IDLE incidence costs at least 4.0843234304737608871435 per port at κ = 0.0040075385047236, even with unrestricted mask grouping. All four old QUERYs cost only four per port. Equal-incidence regrouping with four QUERYs and changed LOCAL counts or interfaces remain separate questions.

Task and overlap

Base e545235. This is a changed bit-new-register-model task under #7111. Exact dependency paths, Git blobs and SHA-256 hashes are in SOURCES.json. #6984 uses a body-specialized fixed window, and #6825 treats a different six-target clean-column endpoint. The proof here uses all 18 independent body derivatives of the complete paired caller. #7159 concerns native owned-receiver transport.

Validation

From a clean checkout using CPython 3.12 (tested on 3.12.14):

python3.12 -I -B research/bit-local-query-rank-bound/verify.py
python3.12 -B scripts/research_package.py --package research/bit-local-query-rank-bound
python3.12 -B scripts/check_research_commit.py --package research/bit-local-query-rank-bound --check-modes

The replay checks 1,444 formal coefficients, 18 stage decompositions, 18 directed price cases, and an auxiliary-lane padding control. Replacing one QUERY by ADD and dropping an IDLE stage each trigger the corresponding exact derivative check. A one-byte corruption of the pinned caller fails authentication. An independent forward derivative reconstruction and price calculation agree. No changed complete caller or supplier is proposed.

Credit

DreamingOfClouds, CubeJerry, zxv and retained contributors supplied the #6726/#6834/#6980/#7001 construction and controller. Credit #6984 for the fixed-window audit, Nick Petalas #6800 for the rank method, #6825 for related clean-column dual-number analysis, and Rohan Arun for the #7156 comparison. OpenAI Codex and subagents materially assisted the proof, replay and independent checks.

Open next question

Change a retained normalized LOCAL frame, or the native call count, and test shared cross-arm body support before attempting a complete replay. Charge the new QUERY, IDLE, ordinary basis, restoration and supplier obligations.