Research audit: two-pass compact-control guard and exact later-source density

[bbMisk]

Mathematical audit / research note; no new kappa. Checking the sharper earlier-source guard only before the first call can miss dirty-field corruption in the later-source routine. For n=2,K=6,G=2,rho=1, the unchanged physical word takes (x,y,t,u,b)=(2,124,1,0,7) to (2,126,5,0,7): the target is right, but the temporary should remain 1.

This adds a proved two-pass invariant sufficient guard and its exact correlated density. With B=2^G, A=2^(K-1), source bits c_i, control parities p_i=u_i mod 2, and target segments 2g_i+a_i, require:

t_i <= B-2                         for i < n
u_i + c_i < B                     for i < n-1
g_i + (p_i OR c_i)*t_i < A         for i < n-1

The complete-rectangle good fraction is ((B-1)/B)^n * (1 - 1/(2B) - (3B-2)*(B-2)/(8*A*B))^(n-1). At the example geometry it is 1971/4096, versus 81/1024 for the retained later-source guard and 63/512 for PR763's source-dependent carry condition with the original target guard. All twelve swaps, ten rotations, source access, highest-bit completion and full exceptional-repair costs remain.

The original construction is correct. PR1219 explicitly excludes later-source calls, and PR763 retains the old target guard. This contribution composes their results and adds the correlated density and full-map controls. The guard describes individually safe subcalls with no interior source-load carry; it is not the global exact agreement set. No production predicate, supplier, selected frontier or upstream/ file changes.

Reproduce with Python 3.10+ and the standard library:

python3 -I -O -B research/compact-late-guard-audit-seed73/test_package.py

Expected markers: PASS_COMPACT_LATE_TWO_PASS_GUARD states=723520 admitted=293408 physical=1728 no_new_kappa, then PASS_COMPACT_LATE_GUARD_PACKAGE ... faults=7.

Validation passes on macOS arm64 with CPython 3.14.6 and 3.12.13, including the registered package runner, minimal read-only relocation, all six complete quotient domains, full-field physical comparisons, exact density counts, 24,576 repair payloads, eight named mathematical controls and seven subprocess faults. The wrong repair key fills all 17,376 holes but misplaces their payloads. All 17 existing compact-control tests, selected-record integrity, metadata/source pins and staged whitespace checks pass. The clean patch applies to refreshed main. Details and unrun checks are in VALIDATION.json.

Base: 49b3157. Seed 73, adversarial audit. Refreshed main dd6403f leaves all six consumed inputs and contribution guidance unchanged. Exact source pins and predecessor documents are retained. The complete final text-search snapshot covers 843 open PRs and 16 Discussion records; this is bounded overlap evidence, not a novelty certificate. No pinned sprint issue exists, so the authorized local claim/result is in CLAIM.json.

The all-n statement rests on the written integer proof. Finite replay is supporting evidence; physical/compiler, recursive field-reservation, hosting, precision and analytic obligations remain. Full supplier cold replay, the full repository suite, Linux, hosted CI success and proof-assistant verification are not claimed.

Credit Douglas Colkitt and OpenAI's original framework; John-Michael Smith / @jp3isme's #763 (a5d3436b82f5a58033ec6b490ebb23db0c1860c6); Hanson Sun / @bbMisk's #1219 (dfb453c88b03868d346014867a091d36e7b16589); and @martinxxx9's #1108. No predecessor audit implementation is imported. Prepared for Hanson Sun (@bbMisk) with substantial OpenAI Codex assistance in mathematics, implementation, verification and writing. Apache-2.0; no independent human review or literature-priority claim.

The README and TASK metadata include the scoped open question about adoption at a concrete recursive caller and its physical-contract blockers.

[Mister-Meeseeks]

100-PR batch review at 392316a45197ef213cff4febd24aa7fd5e16237f.

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

Reviewed scope: Two-pass invariant later-source compact guard with correlated exact density and complete dirty restoration; source-load carries and both subcall guards retained.

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.