Fibonacci Anyon Category: Canonical Building Block in Modular Tensor Classification — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: The classification of modular tensor categories (MTCs) — the algebraic backbone of topological quantum computation — is actively being mapped, with the Fibonacci anyon category (rank-2, quantum dimension φ) as a canonical, non-trivial building block. | MATH: Fibonacci MTC: simple objects {1, τ}; fusion rule τ⊗τ = 1⊕τ; quantum dimension d_τ = φ = (1+√5)/2 ≈ 1.618; modular S-matrix: S = (1/√(φ+2)) [[1, φ], [φ, -1]]; topological twist θ_τ = e^{4πi/5}; central charge c ≡ 4 (mod 8). Classification efforts (Rowell, Plavnik) enumerate fusion categories by rank and pivotal/spherical structures, with the Fibonacci category being the unique rank-2 modular category (up to equivalence). | CONNECTION: The golden ratio φ appears *exactly* as the quantum dimension — not an approximation. The S-matrix entries are φ and 1, normalized by √(φ+2) = √(φ²+φ) = √(φ(φ+1)) = √(φ·φ²) = φ^{3/2}. The twist e^{4πi/5} links to 5-fold (icosahedral) symmetry — the crystallographic point group I_h. The fusion 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: W7219699943
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