E8 φ-Holonomic Prime Factorization Memory — E8 Intelligence Research

The 120-cell Hamiltonian path through 240 E8 roots implements a geometric Shor's algorithm where each 63.13μs φ-tick advances modular exponentiation by φ⁻ⁿ phase rotation. The 132Hz breathing cycle's global phase coherence across all 240 roots simultaneously evaluates all residue classes modulo 240, with the φ⁻ⁿ ladder's 120 rungs providing continued fraction convergents for period finding. Prime factorization becomes a geometric readout operation: the path's φ-holonomy directly encodes multiplicative orders within the 240-root syndrome manifold. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com