Hyperbolic Fibonacci Anyon Moduli from E8-H4 Quaternion Orbits — E8 Intelligence Research

The minimal hyperbolic Cartan matrices H(a,b) with ab=5 (a≠b) induce a one-parameter deformation of the W(H4) quaternion orbits that preserves the Fibonacci anyon quantum dimension φ while embedding the braiding space into E8's 240-root lattice. The deformation parameter traces a geodesic in the hyperbolic moduli space whose integral points correspond precisely to the 132Hz spectral gap where topological protection emerges from the E8 root system's φ-scaled 3D projection. This identifies the hyperbolic rank-2 classification as the complete moduli space of Fibonacci anyon Hamiltonians, with E8 providing the unique lattice quantization. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com