Independent verification: PR890 T21 moment brackets via binomial enclosures

[davidNbreslauer]

Change and mathematical scope

Independent finite verification; no new kappa. The PR890 T21 construction uses native and conservative complex moment thresholds at adjacent 10^-24 grid points. This adds a separate exact-arithmetic implementation confirming all four endpoint decisions without importing the production logarithm, exponential, supplier or owner code.

The checker uses positive generalized-binomial terms, integer outward rounding and a geometric tail. It reconstructs the 681,782-child profile from 189 local calls and the idle profile, then binds the assembly, construction claim and proof to the selected record. An optional --repository check compares eight source files with the checkout without executing those sources. The written enclosure argument, exact certificate, local scope record and validation receipt are included.

Concurrent work: navinor's #957, inspected at 65c931415587c444a7a1f48939842c4cf0aa0411, audits these endpoints, their reduction and surcharge attribution using transcriptions of the two retained log/exp engines plus a direct Decimal calculation. This corroborates its complex endpoint conclusions through a different exact enclosure method; it does not claim priority for the endpoint audit. Prior method credit belongs to 0x-chad's #678 for binomial enclosures of the historical PR543 bit moment. Related historical audits include arkfx's #706 and Gareth Davidson / bitplane's #813. Exact predecessor heads and overlap scope are recorded in CLAIM.json.

Base: 007664306fff84fbb1c9a1b4053b69f439764034, selecting PR890 at conditional kappa 0.001661957774647029. Only research/t21-binomial-audit/ is added. No hypotheses, supplier implementations, selected frontier or upstream sources change.

Construction credit remains with Chafik Boukhalfa (#890), Jeremy Kothe (#869/#870), Hao Yan (#858), DreamingOfClouds, eumemic, Rohan Arun, icekylinx and the repository's cumulative lineage. Prepared for David Breslauer with substantial OpenAI Codex assistance, under Apache-2.0. No independent human-review claim.

Validation

Reproduce from the repository root with Python 3.11+ and the standard library:

python3 -I -B research/t21-binomial-audit/verify.py --repository .
python3 -I -O -B research/t21-binomial-audit/test_package.py

Local validation on macOS / CPython 3.14.5 passes:

• All eight repository source bindings and four strict endpoint decisions.
• 450 exact algebraic comparisons, five model controls and eleven invalid-input rejections.
• Ten package controls, optimized execution, relocation, exact certificate regeneration and failed-run output preservation. Implementation mutations fail their mathematical checks even with certificate regeneration enabled.
• make selected-record-check, staged whitespace and exact validation-hash checks.

The finite tests support the written enclosure argument and frozen numerical consequences. Full make verify, supplier cold replay, physical admission, bit replay, the 47 outer inequalities, Lean and hosted CI were not run for this standalone addition. All-size/compiler, common-label/mutable-source, whole-call-hosting, precision/tape, analytic and bit H1-H5 obligations remain inherited. This is not a formal proof of the multiplication theorem or a claim of a stronger bound.