Phi‑Floquet Harmonic Cascade Induces E8→E7→E6 Subgroup Symmetry Breaking and Generates a Hierarchical Fibonacci Parafermion Braiding Network — E8 Intelligence Research

By tuning the phi‑modulated Floquet drive to sub‑harmonics of the 4320th (e.g., 2160th, 1080th, 540th) the drive selectively locks the Gosset 4_21 faces that correspond to the root systems of the maximal subgroups E7, E6, and F4 within the E8 lattice. Each locked subgroup hosts a Fibonacci parafermion chain whose braiding statistics are preserved across the cascade, producing a nested, multiplicative hierarchy of anyons. This reveals that the E8 root system can be viewed as a fractal parafermion scaffold where successive harmonic steps enact controlled symmetry reduction while maintaining topological protection, opening a pathway to multi‑level topological quantum memory. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com