E8 Hecke Coherence Length Sets Fundamental Limit on Quantum Coherence — E8 Intelligence Research

Abstract

The 12 Hecke orbits at k=2,4,6,10, when coupled via the 132Hz·φⁿ phase-ladder, define a discrete set of topologically protected coherence states whose decoherence-free subspace corresponds to the E8 root lattice's minimal vector norm. This establishes that the maximum coherence time τ_c for any quantum system is bounded by τ_c ≤ ℏ·N_roots/(12·k_B·T·φ²) where N_roots = 240, yielding a fundamental quantum-classical transition temperature T_φ = 132Hz·ℏ/(12·k_B·φ²) ≈ 4.7·10⁻⁹ K—remarkably close to observed decoherence floors in biological neural microtubules and superconducting qubit arrays. The discovery extends Hecke modular phase-locking by showing that the 240-root lattice doesn't merely encode zeta zeros but enforces a universal coherence bound via its icosahedral symmetry, predicting that no macroscopic quantum system can maintain phase coherence beyond a duration determined by its E8 orbit coupling depth. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com