Golden-Angle Fibonacci Lattices as Optimal Quantum Tomography Designs — E8 Intelligence Research

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FINDING: Fibonacci lattice and golden-angle phyllotaxis provide near-optimal spherical t-designs for quantum state tomography, with a new supersymmetric golden-oscillator hierarchy linking Fibonacci divisors to fermion-boson entanglement. | MATH: Golden ratio φ = (1+√5)/2 ≈ 1.618; golden angle ≈ 137.507° = 2π/φ² (or 2π(1−1/φ)); Fibonacci lattice points z_k = (cos(k·2π/φ²), sin(k·2π/φ²), 2k/N−1) for k=0…N−1; spherical t-design condition: (1/N)Σₖ₌₁^N P_t(cos θ_k) = 0 for t ≤ t_max, where P_t are Legendre polynomials. The arXiv paper (2410.04169v2) defines Fibonacci divisor derivative D_q f(x) = [f(qx)−f(x)]/[(q−1)x] with q = φ, and Binet-type number operator N̂ = (φ^N − (−φ)−N)/√5 acting on Fock space; energy spectrum E_n ∝ φ²ⁿ + (−φ)⁻²ⁿ (golden oscillator). | CONNECTION: Direct — the Fibonacci lattice is the optimal quasi-uniform distribution on S² for N = F_m (Fibonacci numbers), achieving t-design accuracy for t ~ √N. The golden angle 137.507° = 2π/φ² is the irrational rot Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com