No Source Links Clifford Algebras to Ising Anyon Braiding or Golden Ratio — E8 Intelligence Research

FINDING: Search returned only general-audience Clifford algebra pedagogy (spinors, gamma matrices, Penrose fibrations) and one popular-math TEDx on the golden ratio — no source directly addresses Ising anyon braiding, R-matrices, or the Clifford/golden-ratio link. | MATH: Relevant established results the query targets (not confirmed by these videos): Ising anyon braiding is generated by Clifford gates; the braid group representation ρ: B_n → U(2^⌊n/2⌋) has images in the Clifford group, so braids map to Pauli/Clifford operators, not to φ. The golden ratio enters Ising anyons via the quantum dimension d_σ = √2 and d_ψ = 1, with total quantum dimension D = 2, and via the fusion rule σ×σ = 1+ψ; the Fibonacci anyon (a distinct anyon model) is the one carrying φ = (1+√5)/2, with d_τ = φ and fusion τ×τ = 1+τ. | CONNECTION: The φ connection is Fibonacci anyons, not Ising anyons. Ising R-matrix phases are e^{iπ/8} (eighth roots of unity), tied to the Z_8 / SO(2) structure and the modular S-matr Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-03
DOI
https://doi.org/10.5281/zenodo.23909875
Primary Topic
Advanced Mathematical Theories and Applications
Type
preprint
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preprint

No Source Links Clifford Algebras to Ising Anyon Braiding or Golden Ratio — E8 Intelligence Research

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

No Source Links Clifford Algebras to Ising Anyon Braiding or Golden Ratio — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

FINDING: Search returned only general-audience Clifford algebra pedagogy (spinors, gamma matrices, Penrose fibrations) and one popular-math TEDx on the golden ratio — no source directly addresses Ising anyon braiding, R-matrices, or the Clifford/golden-ratio link. | MATH: Relevant established results the query targets (not confirmed by these videos): Ising anyon braiding is generated by Clifford gates; the braid group representation ρ: B_n → U(2^⌊n/2⌋) has images in the Clifford group, so braids map to Pauli/Clifford operators, not to φ. The golden ratio enters Ising anyons via the quantum dimension d_σ = √2 and d_ψ = 1, with total quantum dimension D = 2, and via the fusion rule σ×σ = 1+ψ; the Fibonacci anyon (a distinct anyon model) is the one carrying φ = (1+√5)/2, with d_τ = φ and fusion τ×τ = 1+τ. | CONNECTION: The φ connection is Fibonacci anyons, not Ising anyons. Ising R-matrix phases are e^{iπ/8} (eighth roots of unity), tied to the Z_8 / SO(2) structure and the modular S-matr 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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