Independent verification of the #543 bit moment using binomial enclosures

[0x-chad]

This independently confirms the strict bit-moment bracket from #543 consumed by #626 at adjacent 10^-24 endpoints, including the exceptional-set fallback charge. Omitting that charge changes the upper endpoint from rejection to acceptance.

research/pr543-binomial-audit/verify.py uses outward-rounded rational generalized-binomial terms and a geometric tail bound, without importing the existing logarithm/exponential pricing engines. The package includes an exact certificate and source pins. The audit takes the paid profile and fallback formula as inputs and checks their numerical consequence; their construction-level justification remains inherited. It does not change the selected bound or formally verify the multiplication theorem.

Reproduce

From the repository root, using Python’s standard library only:

python3 -I -B research/pr543-binomial-audit/verify.py

Expected output:

PASS_PR543_BINOMIAL_MOMENT
Strict adjacent 10^-24 endpoints; 71 algebraic controls; 3 mathematical controls; 8 rejected inputs.

The controls check rational-power enclosures by exact integer-power comparisons and demonstrate that equal call count and rank mass do not determine the moment. Disposable-copy mutation tests rejected missing tails, downward-rounded upper terms, an omitted fallback coefficient, and altered source or certificate bytes.

The checker passed on Python 3.12.3, including with -O; make selected-record-check also passed. The full make verify and make frontier626-verify suites were not run.

Sources and credit

SOURCES.json pins the input files and records:

• Base: 66849e1475c930fd7732b1a0067ffee7e1e95f60
• Conditional κ = 0.001587467473762886: an E8 bit word with 420 helpers, c = 0.001653826988 (+4.18% over #510) #543 supplier: 2065fe4f72a914d907f1046603f5a36f17018535
• Conditional κ = 0.001635527380375392: coordinated owner repair on PR623 #626 consuming assembly: 660de893d27bb7abd1d5b01b1640207528a5c851

This corroborates eumemic’s #543 supplier and DreamingOfClouds’ preceding totals and nine-stage pricing, as consumed by Chafik Boukhalfa’s #626 assembly built on Jeremy Kothe’s construction and dispatch work. Credit also remains with Rohan Arun for the #559 recurrence correction and the earlier contributors listed in the supplier’s NOTICE.md.

Contributed by 0x-chad with substantial OpenAI assistance, under Apache-2.0.

[Mister-Meeseeks]

Integrated at ee055dc44815497927ef618fc985b93c2dcbda2a in the 20-PR pilot, retaining your original commit, source notices and contributor credit.

Independent generalized-binomial rational enclosure confirms the #543 consumed bracket with fallback surcharge. Positive-term geometric tail and outward rounding checked; inherited profile correctness is a premise.

The scoped package check passed at bdc9317efd6d928a0f050159670d1316ba5f4c5b. This is research integration; the selected κ and inherited theorem assumptions are unchanged. Review, evidence and attribution. Thank you for the contribution.