Prime Zeros Mirror Quantum Chaos: GUE Repulsion Unveiled — E8 Intelligence Research

FINDING: The Riemann zeta zero spacings follow the eigenvalue repulsion statistics of the Gaussian Unitary Ensemble (GUE) from random matrix theory, linking prime distribution to the spectral statistics of chaotic quantum systems. | MATH: Montgomery–Odlyzko law: normalized zero spacings \( \delta_n = (\gamma_{n+1} - \gamma_n) \cdot \frac{\ln(\gamma_n/2\pi)}{2\pi} \) follow GUE distribution \( p(s) \propto s^2 e^{-4s^2/\pi} \) (small-s repulsion ∝ s²); Painlevé VI τ-function governs largest eigenvalue distributions of GUE/LUE/JUE (arXiv:2512.08178v1). | CONNECTION: GUE is the unitary symmetric space AIII (root system \( A_{N-1} \), Weyl group \( S_N \)) — its eigenvalue spacing distribution has universal repulsion exponent β=2, matching the 2-fold symmetry of the complex plane; the 0.618/1.618 golden ratio appears in the asymptotic spacing of zeta zeros (mean spacing → 1/ln(t/2π), but the *ratio* of consecutive spacings converges to 1, with fluctuations governed by the sine kernel \( \s Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com