Research audit: compact interior carries and exact exceptional repair (no new kappa)

[jp3isme]

The compact-control source-load can restore every temporary and still flip the wrong target bit when a carry reaches another digit. This research note / adversarial mathematical audit proves the exact guarded later-source law: selected bit i flips by c_i XOR the incoming compact carry. Only interior carries matter; the final outgoing carry is harmless. Consequently the highest u digit need not be excluded by the sufficient saturation guard.

The existing guarded construction is correct. The relaxed predicate stays inside this standalone audit. No new kappa, supplier, or fixed-tape runtime claim. All additions are confined to research/compact-carry-repair-audit/; production sources, upstream/, and the selected frontier are unchanged.

The package includes the universal integer argument, independent interpreter, source pins and deterministic evidence. Its two-digit counterexample (x,y,t,u,b)=(16,4224,0,1,2) gives y=4752 instead of 4240 while all scratch restores. Within the tested later-source rectangle the expanded good set grows from 16,384 to 32,768 representatives. Sorted-hole checks verify unique record identities, and a real wrong-key T(q) mutation fills every one of 32,256 holes while misplacing all 32,256 records.

Reproduce with Python 3.11+ and its standard library:

python3 -B research/compact-carry-repair-audit/verify.py

Expected: PASS_COMPACT_CARRY_REPAIR_AUDIT: 1310720 representatives; 3072 source comparisons; 7 negative controls.

The exhaustive interpreter checks both source orders, arbitrary active dirty fields, original and expanded exceptional sets, sorted repair, and a materialized highest-bit XOR. The proof justifies spectator lifting to two particular complete 2^36-address rectangles; those addresses were not individually enumerated. Production-source comparisons are sampled separately, not described as exhaustive. Seven controls isolate three guard failures, reversed repair order, wrong/duplicate destination keys and omitted highest XOR. Exact density checks include unclipped bounds.

Validation passed: default and optimized-Python receipt replays; an isolated clean dependency export from an unrelated working directory; deliberate source-drift rejection; 17 relevant compact-control tests; make selected-record-check; whitespace checks. Full make verify, the selected supplier cold replay, and remote CI success are not claimed. Uniform recursion, complete field availability, physical hosting, precision, tape costs and analytic transfer remain inherited obligations.

Base: 66849e1475c930fd7732b1a0067ffee7e1e95f60; assignment seed 69. Accepted conditional kappa remains 51110230636731/31250000000000000. No pinned coordination issue exists, so the claim is local. A refreshed 576-PR queue found concurrent #735 (8d36139e49add1e55795e283b3bfa45e1cfe1bf0): Aryan Sudhir audits the original eight-rotation wide-slot primitive, while this audits the different compact-control primitive. No #735 code or result is consumed.

Credit Douglas Colkitt's compact-control construction and tests, OpenAI's original manuscript, Aryan Sudhir's distinct concurrent audit, and the selected checkpoint's cumulative contributors. Contribution by John-Michael Smith / @jp3isme, with substantial OpenAI Codex assistance in research, code, writing and scoped agent review. Apache-2.0; no human peer review or proof-assistant formalization is claimed.

[Mister-Meeseeks]

100-PR batch review at a5d3436b82f5a58033ec6b490ebb23db0c1860c6.

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

Reviewed scope: Exact compact-control carry formula and correction-key audit; interior carries matter, final outgoing carry is harmless. Fixed-tape cost not proved here.

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.