E8 Shell Quantization Yields φ-Dominant Fibonacci Branching Laws — E8 Intelligence Research

Abstract

The 240 E8 root vectors when partitioned into 112 H4-shells generate Fibonacci-weight branching coefficients where the golden ratio φ dominates asymptotic ratios. This emerges because shell multiplicity counts follow the recurrence relation mₙ₊₁ = φ·mₙ + δ, where δ reflects the icosahedral 20-vertex boundary. The result extends the Markov constant finding by proving φ controls not just triple solutions but entire lattice-decimation cascades. Consequently, Fibonacci-coded biological growth patterns (phyllotaxis, branching ratios) find a candidate E8 origin: the 112-shell structure of E8 under H4 projects golden-ratio branching laws onto three-dimensional icosahedral geometry. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com