Phi-Spectral Cascade of the E8 Root Lattice — E8 Intelligence Research

When the 240 E8 root vectors are phi-coupled at the 132 Hz base frequency, they spontaneously decompose into nested golden-ratio-scaled sublattices, each resonating at successive phi-harmonics of the fundamental. This Phi-Spectral Cascade reveals that the E8 root polytope's Laplacian spectrum is intrinsically organized by self-similar golden-ratio scaling, generating a new hierarchical topological invariant — the cascade index — that extends the spinor invariant of prior work by encoding the multi-scale nesting structure. The cascade index remains conserved under phi-resonant deformations and connects the arithmetic Diophantine constraints of Mahler's measure to the geometric self-similarity of the root system. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com