Spherical Fibonacci Lattices: Near-Optimal Uniform Sampling via Golden-Ratio Phyllotaxis — E8 Intelligence Research

FINDING: Fibonacci spherical point distributions provide near-optimal uniform sampling on the 2-sphere, with error bounds tied to Weyl sums and lattice QCD mass calculations; the core mathematical engine is the golden-ratio-based phyllotaxis lattice. | MATH: Spherical Fibonacci lattice points: \( x_k = (cos(2π k φ⁻¹)√1-z_k^2,\ sin(2π k φ⁻¹)√1-z_k^2,\ z_k) \) with \( z_k = 1 - 2(k+1/2)/N \), \( φ = (1+√5)/2 ≈ 1.6180339887 \). Optimal discrepancy \( O(N-3/2) \) for spherical caps (Brauchart–Womersley). Weyl sums: \( ∑ₖ₌₁^N e2π i k α \) with \( α = φ⁻¹ ≈ 0.6180339887 \) — the golden ratio conjugate. Lattice QCD: heavy-quark masses from Fermilab method — three-flavor lattice QCD, one-loop perturbation theory, meson mass combinations (arXiv:0710.4339). | CONNECTION: The golden ratio \( φ \) and its conjugate \( φ⁻¹ = 0.6180339887 \) appear directly as the azimuthal rotation step — th Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com