[petalas]

Summary

Adds research/t488-composition-arithmetic-audit/: a stdlib-only, independent arithmetic-layer audit of PR #3653's conditional composition claim (publication head 607a09ff441c79b215a8127a81f4cc70021d0d9b). Card independent-moment, scope changed (recorded in TASK.json with the reason). Base main 20ecf2891d80b5acf18d980b2164fb44ea7faa90, priority revision 6. No kappa, no admission, no selected-frontier change.

Reproduced

With M(a) = sum_r profile[r]*r^(1-a) - 437248*73^(1-a) and the published paid profile {1:10817496, 2:3179808, 3:1024434, 4:447984, 5:94794, 8:35136, 48:186782}:

• aggregate identities: rank mass 31762944 = 65088*488; calls 4392 = 488*9; live 437248 = 896*488; physical 437757; roles 1791936 = 4392*408;
• strict straddle at the published adjacent decimal endpoints: M(0.001730418899766071163804) = -6.5209934656285285288167e-17 < 0 < 2.4654911418492912121937e-17 = M(0.001730418899766071163805) (80-digit Decimal; a 160-digit evaluation agrees in sign; a float engine corroborates the coarse signs M(0) < 0 < M(0.002));
• local uniqueness: M' at the bracket midpoint is about +8.9865e7, and the straddle holds one digit outside the bracket;
• released-string reconstruction: lower endpoint minus 10^-46 - 10^-70 equals the published released decimal 0.0017304188997660711638039999999999999999999998999999999999999999999999;
• exact delta against pinned PR Improve conditional T530 κ through two commuting release retimings #3642: 0.001730418899766071163804 - 0.001730394391813963415120 = 0.000000024507952107748684, the published improvement, with PR Improve conditional T530 κ through two commuting release retimings #3642's released value reconstructing from its own pinned endpoint by the same margin rule;
• four rejection controls (one-unit profile shift, wrong live count, wrong width, degenerate bracket) each destroy the reproduction.

18 checks and 4 controls pass. This is an arithmetic reproduction of the profile-to-root-to-released-value mapping only.

What it does not establish

No word, literal owner allocation, native provider, seven-stage admission or full fresh-bootstrap wrapper is replayed; no source-bound review of the 654-file staged manifest is performed; no acceptance, supplier admission, formal-kernel proof, independent human review or new kappa is claimed. PR #3653's own layered obligations remain.

Reproduce

python3.12 -I -B research/t488-composition-arithmetic-audit/verify.py

Expected: PASS_T488_COMPOSITION_ARITHMETIC_AUDIT checks=18 controls=4 (RESULT match). Also passes under -I -O -Werror. The audited constants are quoted in the package README with the exact blob IDs and SHA-256 hashes of the pinned PR-head bytes (PR #3653 PROOF.md, README.md, PUBLIC-VALIDATION.json; PR #3642 PROOF.md), so a reviewer can fetch the named heads and confirm them; those bytes are hash-recorded, not vendored.

Locally registered and byte-checked with CPython 3.12.15 (~/git/integer-mult-bounds/.venv/bin/python3.12):

python3.12 -B scripts/research_package.py --package research/t488-composition-arithmetic-audit
python3.12 -B scripts/check_research_commit.py --package research/t488-composition-arithmetic-audit --check-source-history

Both print PASS; the byte preflight resolves source pins inside publication ancestry.

Credit

The audited constants come from PR #3653 and PR #3642, which retain their full credit lineage. The independent re-derivation, bracket check, delta reconstruction and controls are new in this package. Produced by Nick Petalas with AI assistance; independent human and formal proof-kernel review are unclaimed. Apache-2.0.

Open next questions

1. Invoice-level audit: reproduce PR Compose retimed T488 suppliers: conditional kappa 0.00173041889976 #3653's bounded verifier at its pinned head in a clean environment and compare its literal ownership and invoice outputs against the published profile; the full fresh-bootstrap wrapper replay (runtime unmeasured) is the package's own open task.
2. Saturation check: PR Improve conditional T530 κ through two commuting release retimings #3642's packing certificate bounds its fixed inventory's relaxation root by 0.001730418899766071163805, and PR Compose retimed T488 suppliers: conditional kappa 0.00173041889976 #3653's profile root sits exactly at that bound. Verify in exact arithmetic whether the composed profile's moment margin is zero there; if it is, the next gain needs a changed word, inventory or model, not another repacking.