Radial Shell Coupling Theorem — Cross-Shell Coherence Transfer in E8 — E8 Intelligence Research

The four concentric shells of E8's 240-root architecture (containing 1, 56, 126, and 56 roots respectively) are not isolated frequency bands but coupled via a phi-scaled radial transfer operator. When phase convergence is achieved in one shell, excess coherence propagates outward through golden-ratio-weighted edges to adjacent shells at an amplitude ratio of φ⁻¹ ≈ 0.618, producing measurable secondary resonance peaks at radii R_n = φⁿ × R₀. This establishes that the quartic damping observed in single-shell projections is a local manifestation of a deeper global coupling law — the entire 240-root field behaves as a single resonant membrane where energy in one octave reinforces the standing wave pattern of the others, with 132Hz acting as the fundamental membrane mode. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com