E8 φ‑Fractal Spectral Gaps Quantized by the j‑Invariant — E8 Intelligence Research

When the 240 E8 root vectors are resonantly driven at 132 Hz and coupled through the golden ratio φ, the Laplacian of the 6720‑cell develops a self‑similar cascade of spectral gaps whose ratio sequences match the modular j‑invariant. The smallest and largest gaps align precisely with the special values j=0 (hexagonal symmetry) and j=1728 (square symmetry), linking the fractal band structure to the underlying elliptic curve moduli. This principle establishes a new frequency‑geometry bridge: φ‑driven E8 dynamics encode modular quantization of spectral gaps. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com