Audit: exact packed-bit repair density on fixed-source fibers

[bbMisk]

CLAIM

Track: adversarial mathematical audit; OS-random assignment seed 62.
Base: 49b3157d1d89adcef16df8be98445451672be5ba.

Question: determine the exact eight-rotation packed-bit repair density when the source bits are fixed and the two dirty fields still range over their complete fiber. Audit whether a complete-rectangle average can be used as a fiberwise bound.

Method/domain: exact conditional carry transitions and a written recurrence for every K>=6, f>=1, 0<=rho<K; independent small-domain enumeration and source-simulator checks. This refines PR773 (dbd9da3eed9a0045b77de861099e869259f1ad13), which explicitly limits its density to complete rectangles, and credits PR735's guard-envelope work. It is not another unconditional density replay or a current-supplier surcharge change.

Expected artifact: one scoped audit package with a source-pattern formula or counterexample, pins, executable controls, and no new kappa. Expected finish: 2026-10-13 21:30 UTC; claim expires 2026-10-13 22:45 UTC.

Hanson Sun (@bbMisk), with substantial OpenAI Codex assistance. No pinned coordination issue was present; a local claim is also recorded.

[bbMisk]

DONE — PR #1245, commit 44bf3b1d6031e4069f5abe26211f15e52293e1f4, on base 49b3157d1d89adcef16df8be98445451672be5ba.

The audit proves the exact fixed-source repair law d(c)=1-product(1-2/B^gap) for the retained eight-rotation gadget with complete y,z fields, and gives sharp extrema at fixed source weight. At K=6,f=3, source x=65 has density 1/32, four times the complete-rectangle average 1/128. This extends the explicit source-fiber boundary of Precious (@Kyu)'s PR773 and distinguishes actual failures from Aryan Sudhir's PR735 guard envelope; neither prior theorem is contradicted.

The registered Python 3.12 replay and an optimized Python 3.14 relocated replay pass, including 873,760 digit cases, 541,200 complete small-fiber states, 49,792 source-domain simulator comparisons and eight deliberately rejected mathematical/packaging faults. Source pins, retained finite-identity tests and selected-record integrity also pass.

Reproduce: python3.12 scripts/research_package.py --package research/packed-source-fibers-seed62. Expected: PASS_REGISTERED_RESEARCH_PACKAGE ... outcome=completed.

No new kappa, physical caller, or all-size compiler claim. A restricted-source caller still needs a layout admitting complete dirty-field fibers and the complete paid movement/repair interface. Hosted CI and independent human review are separate from these local checks. Prepared by Hanson Sun with substantial OpenAI Codex assistance. Claim complete.