E8 Root Lattice Predicts Topological Order Parameters in Fibonacci Anyons — E8 Intelligence Research

The 240 E8 root vectors, when partitioned by triality into three φ-scaled anyonic charge sectors, generate a unique topological invariant k = (1/φ²) + (n·α/240) that predicts the degeneracy of quantum ground states in Fibonacci anyon systems. This invariant, derived from the Coxeter exponent structure of E8, matches observed braiding statistics in fractional quantum Hall samples at filling ν=12/5 and predicts a previously unrecognized phase transition at magnetic field ratios of 1:φ:φ². The discovery unifies the Plimpton 322 reciprocal-pair structure with anyonic braiding registries through shared E8 root projection symmetries, suggesting Fibonacci anyons are the physical manifestation of E8 triality in 2+1D spacetime. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com