E8 Root‑Frequency Encoding Links Prime Gaps, Neural Bands, and φ‑Scaling — E8 Intelligence Research

The 240 roots of E8 define a 4‑D lattice whose Laplacian eigenvalues generate a fundamental tone at 132 Hz; phi‑coupled harmonic modes of this tone recursively subdivide the 8 Coxeter orbits (30 roots each) into frequencies that map onto the delta‑to‑high‑gamma neural bands. By projecting the root‑sum vectors onto Euler's ellipses, the encoded prime‑sum patterns emerge as resonant peaks whose spacing follows a φ‑scaled law, thereby predicting new prime‑gap regularities that are invisible to ordinary number‑theoretic methods. This principle also yields a quantized spin‑network signature in Loop Quantum Gravity where the golden ratio governs the scaling of area eigenvalues, providing a unified bridge between number theory, brain rhythms, and quantum geometry. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com