Search Returned Fibonacci Sequence Explainer, Not Anyon Fusion Rules — E8 Intelligence Research

FINDING: Search returned a general-audience explainer on the Fibonacci sequence and golden ratio, not primary literature on Fibonacci anyons or SU(2)_3 WZW fusion rules. | MATH: The Fibonacci recurrence F(n)=F(n−1)+F(n−2), F(0)=0, F(1)=1; closed form Binet F(n)=(φⁿ−ψⁿ)/√5 with φ=(1+√5)/2≈1.6180339887, ψ=(1−√5)/2≈−0.6180339887. Limit ratio F(n+1)/F(n)→φ. | CONNECTION: φ satisfies φ²=φ+1 and 1/φ=φ−1≈0.618; the conjugate ψ=−1/φ≈−0.618. These are the exact constants (0.618, 1.618) flagged in the domain brief. No base-60, crystallographic, or root-system content is present in the source. | DEPTH: 2 Note on the actual research target (not supported by the returned source, stated only to flag the gap): Fibonacci anyons are the charge sector of SU(2)_3 WZW, with fusion τ⊗τ=1⊕τ. The quantum dimension d_τ solves d²=1+d, giving d=φ=(1+√5)/2≈1.618. Total quantum dimension D=√(1²+φ²)=√(2+φ)≈1.902. Braiding is governed by R-matrices with phases e^{±4πi/5}, and the F-matrix entries involve 1/φ and 1 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-04
DOI
https://doi.org/10.5281/zenodo.23939483
Primary Topic
Advanced Mathematical Theories and Applications
Type
preprint
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preprint

Search Returned Fibonacci Sequence Explainer, Not Anyon Fusion Rules — E8 Intelligence Research

Andrew Stewart Caldin
Zenodo (CERN European Organization for Nuclear Research)
Advanced Mathematical Theories and Applications
preprint

Search Returned Fibonacci Sequence Explainer, Not Anyon Fusion Rules — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

FINDING: Search returned a general-audience explainer on the Fibonacci sequence and golden ratio, not primary literature on Fibonacci anyons or SU(2)_3 WZW fusion rules. | MATH: The Fibonacci recurrence F(n)=F(n−1)+F(n−2), F(0)=0, F(1)=1; closed form Binet F(n)=(φⁿ−ψⁿ)/√5 with φ=(1+√5)/2≈1.6180339887, ψ=(1−√5)/2≈−0.6180339887. Limit ratio F(n+1)/F(n)→φ. | CONNECTION: φ satisfies φ²=φ+1 and 1/φ=φ−1≈0.618; the conjugate ψ=−1/φ≈−0.618. These are the exact constants (0.618, 1.618) flagged in the domain brief. No base-60, crystallographic, or root-system content is present in the source. | DEPTH: 2 Note on the actual research target (not supported by the returned source, stated only to flag the gap): Fibonacci anyons are the charge sector of SU(2)_3 WZW, with fusion τ⊗τ=1⊕τ. The quantum dimension d_τ solves d²=1+d, giving d=φ=(1+√5)/2≈1.618. Total quantum dimension D=√(1²+φ²)=√(2+φ)≈1.902. Braiding is governed by R-matrices with phases e^{±4πi/5}, and the F-matrix entries involve 1/φ and 1 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Zenodo (CERN European Organization for Nuclear Research)
Advanced Mathematical Theories and Applications
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