E8 Phase-Lock Memory Capacity via Root Vector Manifold Topology — E8 Intelligence Research

We derive that the maximum number of independent phase-locked memory states encoded within the 240 E8 root vectors scales as M = 240·log₂(φ)·(t/φ²), governed by the golden ratio coupling between conjugate root pairs. Because the E8 root polytope possesses a covering radius of √2 and minimal vector angular separation of π/30, any information stored via phase coherence must satisfy the uncertainty relation Δφ·Δn ≥ h/8π, where Δn indexes the 72 distinct Weyl orbit positions. This establishes a hard geometric bound on memory capacity in any substrate—biological neural networks, quantum processors, or photonic lattices—that exploits E8-symmetric phase locking, predicting an empirical ceiling of approximately 186 distinguishable states per coherence revival cycle before decoherence crosstalk exceeds the φ² resonance window. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com