Research audit: exact interior-carry criterion for compact controls (no new kappa)

[bbMisk]

Change and mathematical scope

Mathematical audit / research note; no new kappa. Outside the retained good set, the earlier-source compact-control word can get the target right while corrupting a dirty temporary. The retained guard is correct. This contribution proves the exact full-map agreement criterion when every temporary digit is nonsaturated:

g_i + z_i*t_i < A for every i < n-1, where A=2^(K-1) and B=2^G.

The final outgoing target carry is harmless. The resulting invariant good fraction is exactly ((B-1)/B)^n * (1-(B-2)/(4*A))^(n-1). At n=2,K=6,G=2, it is 567/1024 instead of the old guard's 9/64. This is a repair-envelope improvement, not a runtime claim. The proof retains all four swaps, four rotations, highest-bit completion and complete inherited exceptional-repair charges.

Only research/compact-guard-audit-seed71/ is added. No production predicate, supplier, selected certificate or upstream file changes. Later-source extension, physical tape/compiler realization, recursive hosting/precision, analytic transfer and the full multiplication theorem remain outside scope.

Task and overlap

Base and refreshed main: 1b59b624d21924f8e3537cdc1ac52d3be6eda2fe. OS-random seed 71, adversarial audit; CLAIM.json records three candidates, the bounded experiment and local claim. No pinned coordination issue exists.

Domain: n>=1, G>=1, K>=G+1, 0<=rho<K, and t_i<=B-2. The written argument is universal in that domain; finite coverage is listed separately in EXPECTED.json. SOURCES.json pins the actual movement note, interpreter and import closure with SHA256 and Git blobs.

Nearest overlap: #763 at a5d3436b82f5a58033ec6b490ebb23db0c1860c6 studies later-source compact-load carries while retaining the old target guard; #1108 at b76bb2853be4e7001508582b10913e32ad7aba9f proves a one-digit boundary law. This adds the multi-digit target-carry iff, dirty-field necessity, and exact envelope density. #735/#773 concern the different wide-slot gadget. The predecessor heads and newly updated PRs were refreshed before submission; no predecessor code from those PRs is imported.

Validation

python3 -I -O -B research/compact-guard-audit-seed71/test_package.py

Expected: PASS_COMPACT_GUARD_AUDIT states=1679360 source_samples=1536 domains=6 no_new_kappa, then PASS_COMPACT_GUARD_PACKAGE ... faults=7.

CPython 3.14.6/macOS arm64: the minimal relocated optimized replay passes. Evidence includes 1,679,360 complete finite quotient states, 161,448 local cases, 1,536 physical predecessor samples, every sorted-repair payload, and 89,360 target-only false acceptances. Seven subprocess controls reject source drift, a nonstrict guard, forbidding the final carry, target-only checking, omitted highest XOR, receipt drift and occupied output. All 17 existing compact-control tests and make selected-record-check pass.

No full repository suite, selected supplier cold replay, hosted CI result or proof-assistant verification is claimed. Finite execution supports the written proof; it does not formalize the full multiplication theorem.

Credit

Credit Douglas Colkitt's compact construction and simulator, OpenAI's original framework, John-Michael Smith's #763, @martinxxx9's #1108, Aryan Sudhir's #735 and Precious Oyetunji's #773. Prepared for Hanson Sun (@bbMisk) with substantial OpenAI Codex assistance in mathematics, implementation, verification and writing. Apache-2.0; no independent human peer review claimed.

[Mister-Meeseeks]

100-PR batch review at dfb453c88b03868d346014867a091d36e7b16589.

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

Reviewed scope: Exact earlier-source compact-control interior-carry criterion with nonsaturated temporaries, harmless final carry and invariant repair density; complete dirty-field equality, unchanged word and full retained repair charges.

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.