Vandermonde Core of Montgomery–Odlyzko Zeta Gap Bound — E8 Intelligence Research

FINDING: The Vandermonde determinant is the algebraic core of the Montgomery–Odlyzko method, which bounds gaps between zeta zeros; the method's proven limit (0.515396) is a sharp constant tied to the Vandermonde structure in the A_N−1 root system. | MATH: Vandermonde determinant: \\( V(x_1,\\dots,x_N) = \\prod_{1 \\le i < j \\le N} (x_j - x_i) \\). Montgomery–Odlyzko gap bound: \\( \\liminf_{n\\to\\infty} \\frac{\\gamma_{n+1}-\\gamma_n}{2\\pi/\\log \\gamma_n} \\le 0.515396 \\) (assuming RH). The 2022 result (arXiv:2201.10676) proves this method *cannot* push below 0.515396 — i.e., the constant is a hard floor for this technique. | CONNECTION: The Vandermonde determinant is the volume form of the Weyl chamber of the root system \\( A_{N-1} \\) (i.e., \\( \\prod_{i Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com