Year: 2024
Type: preprint
Abstract: Runnable verification scripts reproducing every numerical check in S. Bohle, "A Closed Form for a Spinor Norm Constant" (Jxiv, 2026, doi:10.51094/jxiv.5740). The paper proves that the spinor-norm constant I0 of Takahashi (arXiv:2403.13003) — problem spinor_norm_integral_i0 in the HorizonMath benchmark (arXiv:2603.15617) — equals (16*pi^2 + Gamma(1/4)^4)/(8*sqrt(pi)*Gamma(1/4)^2) = 2E(1/2) - (1/2)K(1/2). From first principles, using only Python 3 and mpmath, the scripts regenerate: the three equivalent closed forms and the reference value; the four one-dimensional component integrals and the assembly I0 = (AD + BC)/pi; Takahashi's one-dimensional elliptic form; and the regularized two-dimensional double integral (without assuming the separation step). A captured run log (out/VERIFICATION_LOG.txt) records the confirmed agreement. See REPRODUCE.md to run and METHOD.md for the derivation route and AI provenance.
Source: arXiv (Cornell University)
Author: Takahashi, Daisuke A.
Institutions: Keio University, Chuo University
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G3109117929
OpenAlex ID: W4393064030