A Rigorous Computer-Assisted Positivity Certificate for the Localized Weil Quadratic Form up to a = (1/2) log 5
Year: 2026
Type: preprint
Abstract: This preprint presents an author-claimed computer-assisted proof of strict positivity of the closed localized Weil quadratic form for 0 < a <= (1/2) log 5. The proof combines an exact cutoff-free Fourier representation with rigorous 1024-bit Arb/python-flint interval arithmetic. At the endpoint a = (1/2) log 5, the certificate verifies the required finite spectral bounds in both parity sectors, high-frequency coercivity, finite-to-infinite coupling estimates, cancellation-preserving control of the infinite tail, and positivity of the final Schur complements. Positivity for smaller support parameters follows from support monotonicity of the closed localized form. The numerical certificate was completed in one uninterrupted run and was subsequently reproduced ball-for-ball in a separate execution environment using the same hash-verified source code and Python-FLINT wheel. Additional independent computational audits checked representative matrix entries from the defining Weil functional, the exact prime-power shift norms, the high-frequency formula, the Lerch-transcendent tail identity, and the packet-tail bounds. The archive contains the manuscript, source files, authoritative certificate driver, original and independently reproduced certificate records, verification reports, execution-environment information, reproduction instructions, and SHA-256 checksums. This is a finite-support result. It does not establish positivity for a > (1/2) log 5, does not provide a lower bound uniform in the support parameter, does not prove global Weil positivity, and does not prove the Riemann hypothesis. Independent human specialist review and ordinary peer review remain pending. AI assistance disclosure: AI systems were used under the author’s direction for computational experimentation, code development, literature organization, drafting, source comparison, and adversarial review. Mathematical statements and certified numerical values were not accepted solely on the basis of AI-generated output. They are tied to explicit derivations, reproducible source code, rigorous interval certificates, hash-verified execution records, and independent computational checks. The author assumes responsibility for the final manuscript, its claims, and the deposited materials.
Author: Roberto Carlo Angelone
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204077431
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