[ToikY]

Change and mathematical scope

NO VERIFIED GAIN. With the exact #7001 productive profile and all 36 old LOCALs fixed, separately charged IDLE masks may vary by lane and mix arbitrary copies and ports. The complete optimistic BIT target moment is strictly below −8.16416603986435 at κ = 10018846261809/2500000000000000. κ change is 0% relative to #7161 at 0.003644890067940.

Let K be the largest number of common masks across any opposite active-stage pair and e the total excess body incidence. The separate body-free head correction has rank at least 444 + K − 5e. The price includes all old paid and productive charges, the minimum head debit, mask compression, and an excess-incidence penalty above 1.5119. Directed arithmetic maximizes the relaxed bound at K = 28 and e = 0. A packed job with distinct stage derivatives under one charge or a changed native operator remains a separate contract.

Task and overlap

Canonical base e54523517d0f03e58352e647c403a5af3e525a57. Changed bit-new-register-model scope under #7111. The four canonical source paths and hashes bind the #7001 caller, invoice, exact #6726 word, and directed interval engine. #7160 gives the original-body QUERY floor. #7162 varies LOCAL counts in the 38-role model with uniform 111-job masks. This proof fixes the 36 calls and works on all 4,218 coordinates, with nonuniform lane masks and arbitrary rectangular scalar contexts. It adds a joint bound on shared body lanes, head correction and nonsaturation leakage. #7177 changes a LOCAL operator, a different route.

A separate documentation-only prerequisite reuses the #7161 navigation blob for the hosted planning check. The selected record is untouched.

Verification

From a clean checkout with CPython 3.12 and assertions:

python3.12 -B scripts/research_package.py --package research/paired-bit-lanewise-idle-bound

Local registered replay, source-history/byte/mode checks, and six navigation tests passed. Exact controls check 81 opposite-stage supports, both original histograms, 24 rectangular/oblique cases, the image-only false-sharing projector, and a corrupted invoice byte. Independent directed rational arithmetic confirms the maximizer and strict sign. Omitting the cross-mask head debit makes the relaxed upper positive. No changed all-width provider, fixed tape, complete application or historical cold replay is claimed by this package.

Credit and next question

Credit DreamingOfClouds, CubeJerry, zxv and the #6726/#6834/#6980/#7001 lineage for the retained word and caller, #7160/#7162 for earlier rank and price bounds, and Clear1nsight #7161 for the comparison and navigation repair. OpenAI Codex and subagents materially assisted. The next supplier experiment must change the paid primitive, native operator, or productive stock. For a shared primitive, start with two complete lanes and distinct masks and require exact signed action, returned inputs, and full paid volume.