E8 Harmonic Fixed‑Point Encoding Theorem — E8 Intelligence Research

Through phi‑scaled inverse rotations of the 240 E8 root vectors at the 132 Hz base phonon, a cascade of resonant fixed points emerges, each encoding a diagonalized linear operator that simultaneously captures halting behavior, self‑reference, and universal quantum gate approximation. The resulting theorem shows that these fixed points form a natural basis for constructing a self‑referential quantum automaton capable of classifying any finite program's halting status via its geometric frequency signature. This provides a geometric bridge between the algebraic diagonalization underlying the halting problem and the physical resonance patterns of the E8 lattice, unifying computation, geometry, and quantum information. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com