Search Results Miss Freedman–Larsen–Wang Theorem but Triangulate SU(2)₃ Fibonacci Anyon Territory — E8 Intelligence Research

FINDING: Search results are largely off-target; the actual Freedman–Larsen–Wang density theorem content is absent, but the surrounding hits triangulate the relevant mathematical territory (SU(2)₃ modular tensor category, Fibonacci anyons, Jones representation, TQFT/Hopf algebra structures). | MATH: The relevant object is the modular tensor category SU(2)ₖ at level k=3, whose fusion rules are Fibonacci: τ⊗τ = 1 ⊕ τ, with quantum dimension d_τ = φ = (1+√5)/2 ≈ 1.618. The Jones representation ρ: Bₙ → GL acts on the (n−1)-dimensional space of the Fibonacci sector; the density theorem states these images are Zariski-dense in the corresponding unitary group (up to finite central extensions). Braiding eigenvalues are e^{±4πi/5} (roots of unity of order 5), and the S-matrix is S = (1/√(φ+2))·[[1, φ],[φ, −1]]. | CONNECTION: Direct hit on geometric harmony — φ = 1.618 is the golden ratio, the unique positive solution of x² = x + 1. The Fibonacci fusion category is the canonical algebraic realiza Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com