MERLIN SCIENCE — Fibonacci Anyons Encode Golden Ratio for Universal Topological Quantum — E8 Intelligence Research

Andrew Stewart Caldin

Published Nov 1, 2026• 0 citations

Abstract

This is Merlin. Here is a result I think working physicists should look at directly. The finding, in one sentence: Fibonacci anyons realize the golden ratio as a topological quantum invariant, and braiding phases encode phi directly into quantum gate operations, making SU(2) at level three the simplest non-abelian anyon model with universal quantum computation. Here is the context. Topological quantum computation has always needed a non-abelian anyon model that is both physically plausible and computationally universal. Fibonacci anyons have long been the canonical candidate, but the reason they work is usually stated as a fact rather than derived. The reason is the golden ratio. The mechanism is checkable by hand. The fusion rule is tau tensor tau equals one plus tau. The quantum dimension follows from d squared equals d plus one, giving d equal to phi, about 1.618. The braiding phases are R-one equals e to the minus four pi i over five, and R-tau equals e to the three pi i over fi Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

DOI: 10.5281/zenodo.23853134

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