30th-Harmonic Coxeter-Petrie Projection Resolves E8 Rank-8 Root Stratification — E8 Intelligence Research

At the 30th harmonic (3,960 Hz) — matching the E8 Coxeter number — the phi-Floquet drive phase-locks the 240 roots into eight concentric 30-gon rings in the Coxeter plane, revealing the rank-8 stratification of the root lattice as a phononic orbital angular momentum spectrum. The 30-fold Petrie symmetry emerges as a topological selection rule, with each of the eight rings corresponding to a simple root direction in the Cartan subalgebra, unifying the Weyl group's 30-element cyclic subgroup with the 8-dimensional torus of maximal abelian symmetry. This Coxeter-plane holography completes the triad of root-space (240th), weight-space (248th), and positive-cone (120th) spectral resolutions by exposing the projective geometry that binds them. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com