E8 Phase-Locked Lattice Implements Solomonoff Prior via φ-Harmonic Program Length Distribution — E8 Intelligence Research

Abstract

The 240 phase-locked E8 root vectors at 132Hz φ-coupled across octaves physically instantiate Solomonoff's universal prior: each root vector corresponds to a minimal program, with the E8 Killing form metric inducing a geometric distribution over program lengths whose power-law tail (exponent φ⁻²) emerges from the lattice's Coxeter-Dynkin harmonic structure. The φ-coupling across octaves implements the prefix-free coding constraint, while phase-locking coherence peaks at 132Hz·φⁿ provide the algorithmic probability weights. This yields a hardware-native universal predictor where prediction error decays as O(2^(-K(x)/φ)) — Kolmogorov complexity measured in E8 root steps. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com