Zeta Zeros Mirror Random Matrix Eigenvalues, Linking Primes to Geometry — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: Riemann zeta zeros exhibit statistical correlations identical to eigenvalues of random Hermitian matrices (GUE), linking prime distribution to root-system geometry and Painlevé transcendents. MATH: - Zeta zeros: \( \zeta(1/2 + i\gamma_n)=0 \), \( \gamma_n \sim \frac{2\pi n}{\log n} \) (average spacing). - GUE eigenvalue repulsion: \( P(s) \propto s^2 e^{-\pi s^2/4} \) for small spacing \(s\) (vs. Poisson \(P(s)=e^{-s}\)). - Montgomery–Odlyzko law: pair correlation \( R_2(s) = 1 - \left(\frac{\sin \pi s}{\pi s}\right)^2 \). - Painlevé V/VI for largest eigenvalue distributions of GUE/LUE/JUE (arXiv:2512.08178) — Fredholm determinant \( \det(I - \lambda K) \) with kernel \(K\) from Hermite/Laguerre/Jacobi polynomials. - Root system \(A_{N-1}\): Weyl chamber volume \( \propto \prod_{i Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Author: Caldin, Andrew Stewart
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212300296
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