DONE: PR4100 arbitrary-source compact caller and explicit repair inverse

[kumagi]

DONE — PR #4169, exact head 835c3563ee7ede8ceaf329ede7372e50f7823136.

The scoped PR4100 caller audit is complete. For every admissible field width and target count, Boolean control functions omitting all active targets and borrowed controls make the compact macro agree with the ideal switches on the stated good set. The explicit reverse word computes the inverse on every dirty address, including inactive high digits and reevaluation of controls at current inverse states. Applying PR763’s existing total-repair theorem then restores exact payloads.

The distinction from predecessor evidence is a caller-specific arbitrary-function proof and direct inverse-key evaluation instead of an exhaustive inverse table. The all-target condition matters: on the guarded input (4,0,1040), the own-target-only mutant returns (5,0,1041) instead of (4,0,1040). This is a counterexample to a weakened premise, not a defect in the stated PR4100 caller.

Evidence: 77,824 complete parameter/function states with both inverse compositions and source comparisons; 1,024 larger sampled states; all 4,096 addresses through ten actual CRT caller layers with 29,440 exceptional visits; five semantic controls. Registered normal and optimized CPython3.12.13 replays agree. Committed-byte/source-history preflight, Git-free optimized export replay, unchanged-input checks and source-corruption rejection pass. Hosted CI is not represented as passed by this report.

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

Final refresh: canonical main remains 12fa8c5c844be21bfefb38a19503fbd867a11244, priority revision7. Complete pagination at 2026-10-20 07:21–07:24 UTC covered291 open PRs and2690 Discussion records, with no matching competing caller audit found. The existing mixed-provider admission handoff is a separate scope.

Limits/handoff: no selected-frontier change or new kappa. Reservoir availability, last-K boundary operations, ordinary-callee correctness, control generation, tape/head-return/sort costs, precision and remaining complex/Gaussian interfaces remain separate. A useful next task is one actual reservoir/shuttle cost audit, or a sequential implementation of one direct inverse-key calculation with all current-state controls and erasure charged. No independent human review, formal proof-assistant result or complete multiplication theorem acceptance is claimed.

Credit Cinna Davis/PR4100; John-Michael Smith (@jp3isme)/PR763 for the existing carry and generic repair theorem; Douglas Colkitt/OpenAI for the underlying construction. New work by Hiroki KUMAZAKI (@kumagi), with substantial OpenAI Codex assistance. Scope released.

{
  "schema": "integer-mult-coordination/v1",
  "kind": "DONE",
  "task": "uniform-transfer-audit",
  "scope": "PR4100 arbitrary-source compact caller, explicit reverse-word key evaluation and exact sparse repair",
  "base": "12fa8c5c844be21bfefb38a19503fbd867a11244",
  "expiry": null,
  "artifact": "https://github.com/CrocSwap/integer-mult-bounds/pull/4169"
}