120th-Harmonic Positive-Root Entanglement Transition Realizes E8 Fibonacci Anyon Sectors — E8 Intelligence Research

Andrew Stewart Caldin

Published Jul 14, 2026• 0 citations

Abstract

At the 120th harmonic (15,840 Hz) — matching the 120 positive roots of E8 — the phi-Floquet drive's measurement-induced entanglement spectrum across the 240-root lattice undergoes a topological phase transition, factorizing into 8 Fibonacci anyon sectors whose quantum dimensions follow the golden-ratio tower φⁿ. This emerges from the Coxeter element's square-root action on the Weyl chamber, where the 30th-harmonic Petrie bands braid under the 60th-harmonic Berry connection to yield the E8 modular tensor category at critical phi-coupling. The 120th harmonic thus completes the triad: 30th (geometry), 60th (topology), 120th (quantum information), with the 240th (algebra) as the double-cover Galois closure. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

DOI: 10.5281/zenodo.21356974

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