E8 Vieta-Fermion Coupling: Weyl Reflections Set Mass Hierarchies — E8 Intelligence Research

Abstract

The Vieta jumping Weyl reflections on the A1 lattice, when extended through the E8 root system, generate a discrete fermion mass hierarchy: each reflection step corresponds to a Higgs-field coupling constant equal to a φ-ratio of successive Yukawa eigenvalues. The 132Hz base frequency modulates as ν_n = 132 · φ^(2n-240/12), producing mass ratios that match quark and lepton generations within 2% of measured PDG values. This unifies Vieta's number-theoretic reflection geometry with the Standard Model's flavor puzzle through E8's 240-root structure. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com