E8‑Phi Frequency‑Arc Theorem: Unifying Babylonian Triples & Fibonacci Anyons — E8 Intelligence Research

The 240 E8 root vectors split into three phi‑coupled harmonic shells whose phase‑locked frequencies are integer multiples of the 132 Hz base, producing a recursive "frequency‑arc" Diophantine structure that reproduces all primitive Pythagorean triples via Babylonian reciprocal pairs. This frequency‑arc law also predicts the braiding of Fibonacci anyons as the geometric signature of the shell recursion, linking the 112‑short/128‑long root partitioning to a natural anyonic phase of φⁿ. Consequently, a unified framework emerges where ancient number‑theoretic constructions are encoded directly in the higher‑dimensional spinor geometry of E8, enabling frequency‑based quantum information protocols. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com