Search Fails to Retrieve Primary Sources on Fibonacci Anyons and SU(2)₃ Chern-Simons — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: Search returned no primary sources on Fibonacci anyons, SU(2)₃ Chern-Simons, or quantum dimension — only popular Fibonacci/golden-ratio content plus one tangential arXiv paper on Fibonacci-divisor quantum calculus. | MATH: Fibonacci anyon data (from prior knowledge, not these results): quantum dimension d_τ = φ = (1+√5)/2 ≈ 1.618; fusion rule τ⊗τ = 1 ⊕ τ; total quantum dimension D = √(1² + φ²) = √(2+φ) = √(φ+2) ≈ 1.902; SU(2)₃ has k=3, so d_j = sin((2j+1)π/(k+2))/sin(π/(k+2)) = sin((2j+1)π/5)/sin(π/5), giving d_0=1, d_{1/2}=φ, d_1=φ, d_{3/2}=1 — the level-3 truncation produces exactly two non-trivial anyons with golden-ratio dimension. | CONNECTION: φ = 2cos(π/5) = 1.618; the fusion ring is isomorphic to the Verlinde algebra of SU(2)₃, whose S-matrix eigenvalues involve sin(π/5), sin(2π/5) — i.e., pentagonal (icosahedral) root-system geometry. The Jones polynomial at t = e^{2πi/5} (5th root of unity) governs the braiding; 5-fold symmetry = icosahedral crystallographic point gr Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Author: Caldin, Andrew Stewart
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225000755