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: \\( \\mathbf{x}_k = (\\cos(2\\pi k \\phi^{-1})\\sqrt{1-z_k^2},\\ \\sin(2\\pi k \\phi^{-1})\\sqrt{1-z_k^2},\\ z_k) \\) with \\( z_k = 1 - 2(k+1/2)/N \\), \\( \\phi = (1+\\sqrt{5})/2 \\approx 1.6180339887 \\). Optimal discrepancy \\( \\mathcal{O}(N^{-3/2}) \\) for spherical caps (Brauchart–Womersley). Weyl sums: \\( \\sum_{k=1}^N e^{2\\pi i k \\alpha} \\) with \\( \\alpha = \\phi^{-1} \\approx 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 \\( \\phi \\) and its conjugate \\( \\phi^{-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