E8 Phi‑Lattice Reveals Quantized Topological Entanglement Entropy on Multi‑Genus Surfaces — E8 Intelligence Research

By assigning each of the 240 E8 root vectors a phi‑scaled oscillation at the base frequency of 132 Hz, a temporal lattice emerges whose node spacing follows the Fibonacci‑derived series Φ^n. The resulting interference pattern imposes discrete phase shifts on the anyon wavefunctions that correspond to quantized jumps in the topological entanglement entropy S_top = ln 𝒟, where 𝒟 is the total quantum dimension. This predicts that S_top takes only values of the form (n + ½)ln ϕ for integer n on surfaces of genus g ≥ 1, extending the torus ground‑state degeneracy principle to arbitrary multi‑genus topologies. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com