Audit PR4100 arbitrary-source CRT repair with an explicit inverse

[kumagi]

PR4100's compact CRT repair needs an inverse on arbitrary exceptional addresses; its retained complete caller fixture obtains that inverse from an exhaustive forward table. This package independently audits the arbitrary-source caller condition and supplies a literal reverse-word evaluator used directly in repair keys.

The written proof establishes the address identity for all admissible widths when every control function omits every active target and the borrowed fields. It explicitly reuses John-Michael Smith / @jp3isme's PR763 carry and total-repair lemmas, retaining Douglas Colkitt's construction credit. A guarded counterexample shows why omitting only each function's own target is insufficient: (4,0,1040) returns (5,0,1041) instead of restoring the input.

Only research/crt-arbitrary-source-repair/ is added. The actual PR4100 sources, predicates and selected frontier remain unchanged. This is a scoped algebraic audit, not validation of the complete all-size multiplication proof or machine tariff.

Validation:

• Written quantified proof plus 77,824 complete parameter/function states, both inverse compositions and literal source comparisons.
• 1,024 seeded multi-target states; all 4,096 addresses through the actual ten-layer CRT fixture, with 29,440 exception visits and a separate padded-rotation oracle.
• Five discriminating controls, including stale inverse controls, wrong payload keys and truncated high key bits.
• CPython 3.12.13 registered normal and optimized replays pass with identical receipts; committed-byte/source-history preflight and a Git-free optimized export replay pass. Altered source bytes are rejected.

Reproduce: python3.12 -B scripts/research_package.py --package research/crt-arbitrary-source-repair.

Remaining obligations include reservoir availability, boundary targets, control generation, sequential head movement/sorting costs, the ordinary callee, precision, and the other complex/Gaussian interfaces. No new κ, formal proof-assistant result or independent human review is claimed.

Base: canonical main 12fa8c5c844be21bfefb38a19503fbd867a11244, priority revision 7. Audited predecessor: Cinna Davis's #4100 at 337d04939571a637aeab54a0f58f54fde811663a. Coordination and final handoff: Discussion #4168.

Prepared by Hiroki KUMAZAKI (@kumagi), with substantial OpenAI Codex assistance in research, derivation, implementation, writing and scoped agent review. Apache-2.0; predecessor attribution is retained.