Research audit: 286-to-160-bit prefix estimate for pinned #626 (no new kappa)

[Brodee042]

The pinned #626 invoice multiplies growth allowances across all eight interleaved replica controllers. A maximum-family-norm induction instead charges the largest individual replica count, reducing its sufficient global-prefix estimate from 286 to 160 bits:
101 + 37 + 72 + 72 + 4 → 101 + 37 + 18 + 4.

Status: conditional mathematical audit / research note; no new kappa. The physical helper endpoint may be a nonidentity unitary within its own family. The proof retains the inherited 101-bit local-prefix envelope and does not permit uncharged cross-family mixing. The production reserve remains 512, and only research/replica-prefix-audit/ is added.

The research base is 66849e1, where #626 was selected. Before submission, upstream advanced to 7ee02b7 and selected #741, with kappa 1661202643272239/1000000000000000000. This submission explicitly audits historical #626; no 160-bit estimate for #741 is claimed. All 17 pinned input files remain byte-identical at that newer main.

Reproduce with Python 3.10+ and the standard library:

python -I -O -B research/replica-prefix-audit/verify.py

Expected:
PASS_REPLICA_PREFIX_AUDIT calls=72 owner_roles=35424 prefix_bits=286->160 retained_payload=512 no_new_kappa.

Validation completed:

• 72 call bindings, 240 scheduled replica events and 35,424 helper roles.
• 12 schedule/ownership rejection controls; eight exact signed dirty-helper gadgets; six interleavings, 24 boundaries and 384 exact norm comparisons; six mathematical adverse controls.
• All five package tests pass, including relocation, optimized Python, source/receipt corruption, equivalent gzip repackaging and overwrite protection.
• The selected-record integrity check passes at the pinned base. Clean patch application reproduces the committed tree; a fresh extracted offline bundle passes optimized replay. The published Git tree matches the checked local tree.

The selected generated global template is not committed in its receipt directory. Source bindings therefore use the retained parent template, pinned substitution/emitter/audit source, selected plan/owners and frozen receipts; this is not a fresh cold replay. Native supplier arithmetic and all-size compiler, common-label/mutable-basis, hosting, normalization, precision, tape/exact recovery and analytic obligations remain inherited. Full make verify, cold supplier rebuild, Lean, second-platform testing and remote CI were not run locally. Finite models are corroboration, not proof-assistant verification.

OS-random seed 72, adversarial audit track. The local claim records three candidates, narrow scope, stopping rule and completed coverage; no pinned sprint issue existed. The initial full scan covered 621 open PRs, followed by refreshed titles/bodies through #811. No duplicate 286-to-160 result was identified; this is not a literature-priority claim.

Credit eumemic's #496 for the foundational maximum-stream norm and unitary-helper argument; this contribution adds per-replica counters for #626. Credit Chafik Boukhalfa / chafreaky, Jeremy Kothe / jeremykothe2, and the retained construction lineage. Related #675/#696/#734/#783 work is distinguished in NOTICE.md.

Prepared by Brody Arbon (@Brodee042) with substantial OpenAI Codex assistance, including separate scoped AI proof/source reviews. No independent human review is claimed. Apache-2.0. Nothing is merged or selected-frontier-modified

[Mister-Meeseeks]

100-PR batch review at 6b832a6ba4dce8dd6e2fb0897dd4543364b932f8.

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

Reviewed scope: Conditional replica-local precision accounting for historical #626: sufficient prefix allowance 286 to 160 bits; production allocation unchanged.

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.