High-Precision Numerical Lower Bound for Maximal Bipartite Two-Qudit Stabilizer Rényi Entropy $M_2$ at $d=5$: Saturating the Knipfer Conjecture - RJW

This repository provides an independently verified, high-precision numerical lower bound for the maximum bipartite two-qudit stabilizer Rényi entropy ($M_2$) at prime dimension $d=5$ (ququints). Knipfer, Beigi, Gross, and Nezami (arXiv:2607.07197, July 2026) established an analytical maximum for two-qutrit systems and provided numerical evidence for a conjectured formula bounding $M_2$ across prime dimensions. This submission provides the tightest known independent numerical lower bound to support that $d=5$ conjecture, saturating the hypothesized limit of $\ln(625/49)$ to within a gap of $-2.1885 \times 10^{-14}$. This package documents a massive tightening of the numerical gap—representing an improvement factor of over 507,000 from the baseline search—achieved entirely on a single personal workstation. The $M_2$ evaluation is rigorously confirmed at 120 decimal places using arbitrary-precision arithmetic (mpmath). Included in this release are the exact 25-dimensional unit vector state components (to 18 significant figures), the fully self-contained Python verification script requiring zero proprietary dependencies, and the deterministic audit certificates generated by an independent, localized AI fleet. This artifact operates strictly as a high-precision numerical lower bound, demonstrating that extreme "magic" (nonstabilizerness) and quantum-scale mathematical closure can be achieved, refined, and audited without the use of cryogenic quantum hardware or distributed cloud clusters.Authors Note: Thanks for reading. Just thought i would push this a little deeper. My AI agents did great. Not bad on a gaming computer. Thanks for reading. RJW