Vandermonde Kernel Unifies GUE and Zeta Zeros via Weyl Chambers — E8 Intelligence Research

FINDING: The search results converge on the deep structural identity between the Vandermonde determinant (squared) and the eigenvalue density of Gaussian Unitary Ensemble (GUE) random matrices, which is the same mathematical kernel governing the statistical distribution of Riemann zeta zeros — a connection explicitly bridged by the Weyl chamber volume of the A_{N-1} root system. MATH: - GUE eigenvalue joint density: \( p(\lambda_1,\dots,\lambda_N) \propto \prod_{i \lambda_2 > \dots > \lambda_N \), exactly the ordered eigenvalue space. - Zeta zeros statistics: Montgomery–Odlyzko law — the pair correlation of zeta zeros matches GUE eigenvalue spacing, with density \( 1 - \left(\frac{\si Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com