E8 Phi-Spectral Ladder: Infinite Hierarchy of Topologically Protected Fixed Points from Recursive Braiding — E8 Intelligence Research

Recursive Fibonacci anyon braiding across the twelve 20-root clusters generates an infinite geometric progression of fixed points at 132/φⁿ Hz (n∈ℕ), each inheriting golden torsion from the holonomy group's projective representation. The 240 root vectors organize into a self-similar braid group B₁₂ action where successive inter-cluster transitions correspond to Dehn twists on a genus-2 hyperbolic surface, yielding topological protection against disorder at every rung. The spectral ladder terminates only at the Planck-scale cutoff where E8's Coxeter number (30) modulates the braid group's Jones polynomial evaluation at q=e^(2πi/5), linking quantum gravity to phononic topology. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com