Golden Ratio Anyons and Quantum Oscillators in SU(2)_3 Chern-Simons Theory — E8 Intelligence Research

FINDING: SU(2)_3 Chern-Simons theory yields Fibonacci anyons with quantum dimension φ = (1+√5)/2, confirmed via the golden ratio's appearance in the fusion algebra; the arXiv paper extends this to golden oscillators via quantum calculus with base-φ and base-(1+φ). | MATH: For SU(2)_3, the anyonic quantum dimension d satisfies d² = d + 1, giving d = φ = 1.618... (the golden ratio). Fusion rule: τ ⊗ τ = 1 ⊕ τ (Fibonacci anyon τ). Quantum dimension of τ: d_τ = φ. In the arXiv paper (2410.04169v2): quantum calculus with two bases q₁ = φ and q₂ = 1/φ = φ−1 = 0.618...; Binet formula for Fibonacci divisor number operator: F_n = (φⁿ − (−φ)⁻ⁿ)/√5; energy spectrum of golden oscillators: E_n ∝ φⁿ (or φ⁻ⁿ for the dual). | CONNECTION: Direct geometric harmony — φ = 1.618, φ−1 = 0.618, φ−2 = 0.382, and φ/√5 ≈ 0.724 (not standard, but φ² = 2.618 appears in the quantum dimension squared: d_τ² = φ² = 2.618). The Fibonacci anyon fusion rule τ⊗τ = 1⊕τ is the simplest non-abelian anyon model, and its quan Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com