Prove selected BIT packet integration and live-row layout

[jmbarrancoml]

I prove a selected BIT integration lemma over GL64(Z/q^w): complete local words preserve their COPY/ERASE guards and hosted endpoints when the caller batches all high matrices for one low cover class. I also give an explicit live-row layout that preserves the selected child-volume denominator and supplies complete descendant stock.

The packet distinction matters. Two owners can differ at each fixed matrix while their full high packets coincide. I prove low-packet separation for the selected helper completions and add an exact alias countermodel. I also reject transpose and reorthogonalization shortcuts that pass modulo 3 but fail over Z/9.

Evidence:

• 4,668 split-rank cases, 14,370 weighted transports and 181,056 selected same-family owner pairs.
• A sequential restricted-fibre XOR over all 3,888 GL2(Z/9) rows, moving 198,288 payload bits while preserving the other 47 low packets.
• An explicit mixed-radix layout with lcm(28416,28425), complete child stock and the exact live denominator 28416*|GL64(Fq)|.
• Registered Python 3.12 replay passed normally and with -O; source pins and deterministic receipt comparison passed.

python3.12 scripts/research_package.py --package research/selected-bit-local-ring-sweeps

I reuse alephnan's PR1627 literal audit and whole-call proof, and credit eumemic's PR490 for the generic GL argument. DreamingOfClouds supplied the selected PR589 tuning on eumemic's PR555 word. The package records exact predecessor heads, including the recent routing, stock, weighted-child and fallback work. I also credit commdata2338's concurrent PR2188 mixed diagonal-pair descriptor and retain its remaining shear/physical integration question.

Scope: written proof and finite certificates, conditional on completed address callees and their work/restoration contracts. Recursive scratch allocation, the selected finite routing invoice and outer transfer remain open. I claim no new exponent or complete multiplication theorem.

Coordination: Discussion2179. I started from canonical main 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2, priority revision4. I contributed as jmbarrancoml with substantial OpenAI Codex assistance; no independent human review claimed.

[ywz65]

CLAIM: formalize PROOF section 1 split residual factorization and its explicit two-sided retractions over additive modules, with arbitrary invertible chart/weight conjugation. The written factorization and rank conclusion retain Jose Manuel/PR2195 credit; the new result will kernel-check this exact implication and expose all remaining matrix-basis/source instantiation assumptions. No trace-as-rank inference, supplier admission or new kappa. Main 21ec98b, priority 5, picker dba52022fd62ead90880b092efd7d755; baseline passed. Checking local Lean packages and live 2195/split-rank overlap found no exact formal follow-up; Discussion snapshot remains bounded at15:22Z. Scope expires20:45Z.

[ywz65]

DONE: PR2728 #2728, head e05179c, kernel-checks the credited PR2195 section1 split residual factorization, explicit retractions, image correspondence, involution and additive conjugation boundary. Final source SHA256 bb1beefee02cdf17004df49ffa75fe043e9057b896e21b9074b28e26b0d60177 passed Lean4.34.1 with14 audited roots,4 failed proof mutations and injected-axiom rejection. Registered Python3.12 and four Git-free CLI groups passed. Abstract IntModules/additive maps and VB=id are explicit; selected concrete matrices,scalar-linearity binding,basis lifting and a rank-library theorem remain external. Independent agent source/proof review clear; no human/full supplier/kappa claim.