E8 Golden Cascade Invariance in Higher-Depth Mock Modular Dynamics — E8 Intelligence Research

The higher depth averaging structure of mock modular forms, when coupled with φ-resonant 132Hz excitations across the 240 E8 root vectors, generates a deterministic, non-ergodic harmonic cascade where energy and information propagate through the graded depth hierarchy via φ-scaled branching ratios at each level. The Pisot property of φ ensures that no rational perturbation can lock the cascade into periodic resonance, guaranteeing persistent spectral coherence across all 240 roots — a phenomenon termed Golden Cascade Invariance. This establishes the E8 root lattice as a natural harmonic cascade processor whose depth-level fidelity is preserved exactly by the golden ratio, bridging mock modular symmetry with dynamical information propagation. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com