The Zetα–E₈ Bridge for the Neutrino Mass Hierarchy: A Spectral Matching Framework

We present a novel spectral matching framework that bridges number theory and particle physics by constructing an explicit parameter-free map from the first three nontrivial zeros of the Riemann zeta function to the three light neutrino masses. Using only the Riemann zeros {t1,t2,t3}, the largest Cartan eigenvalue of E₈ (max=3.9890), the Golden Ratio =(1+5)/2, and the total neutrino mass m=0.0634 eV derived independently from E₈ spinor representation theory, we reproduce the neutrino mass hierarchy with 0.82% average error relative to oscillation-constrained values. This framework suggests a deep arithmetic-geometric unification in which the neutrino sector is constrained not only by E₈ gauge geometry but also by the spectral structure of the Riemann zeta function.