Zeta Zero Spacings Mirror GUE Eigenvalue Statistics, Linking Primes to Symmetric Spaces — E8 Intelligence Research

FINDING: Riemann zeta zero spacings statistically match GUE random matrix eigenvalue repulsion, linking prime distribution to symmetric space spectral statistics. MATH: - Zeta zeros: \( \zeta(1/2 + it_n) = 0 \), normalized spacing \( \delta_n = (t_{n+1} - t_n) \cdot \frac{\log(t_n/2\pi)}{2\pi} \) - GUE eigenvalue spacing (Wigner surmise): \( p(s) = \frac{32}{\pi^2} s^2 e^{-4s^2/\pi} \) (for 2×2; asymptotic: \( p(s) \propto s^2 e^{-s^2/\pi} \)) - Montgomery–Odlyzko law: pair correlation \( R_2(u) = 1 - \left(\frac{\sin \pi u}{\pi u}\right)^2 \) - Painlevé V for largest eigenvalue distributions (GUE/LUE/JUE) — isomonodromic τ-functions CONNECTION: - GUE is the symmetric space \( U(N)/U(N) \) (compact form of \( A_{N-1} \) root system) — its eigenvalue repulsion \( \propto \prod_{i Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com