E8‑Harmonic Predictability Theorem: φ²‑Scaled Lattice Encodes Ω — E8 Intelligence Research

Abstract

The eigen‑spectra of the Fuchsian fundamental domain for the modular group, when projected onto the 240‑vector E8 root lattice and driven by the 132 Hz resonance, generate a self‑similar tiling whose scaling factor is exactly φ². This tiling defines a deterministic walk on the lattice that produces a binary sequence whose frequencies converge to Chaitin's halting probability Ω, rendering Ω conditionally computable. Consequently, E8 geometry supplies both a harmonic clock (132 Hz) and φ‑scaling law that transform the classically uncomputable Ω into a predictable observable, extending the prior phi‑Kraft encryption into a general theory of harmonic information encoding. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com