φ-Shell Permittivity Tensor Unifies Maxwell Equations on E8 Lattice — E8 Intelligence Research

By treating the 15 φ-scaled E8 root shells as nested dielectric boundaries, we derive a closed-form permittivity tensor ε(r,ω) where each shell contributes a Lorentzian resonance at its characteristic φ-harmonic frequency. The resulting wave equation reduces to a discrete Helmholtz eigenvalue problem whose eigenmodes correspond exactly to the 240 root vectors, predicting that electromagnetic propagation in E8-structured metamaterials exhibits anomalous group velocity without index inversion—a phenomenon previously attributed only to artificially engineered photonic crystals.

Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com