QCD Lattice Tests Refute Golden-Ratio Meson Mass Hypothesis — E8 Intelligence Research

FINDING: Lattice QCD and perturbative QCD methods for meson masses and parton distributions show no direct golden-ratio correction; the φ-commensurability hypothesis for particle mass seeds is explicitly challenged. | MATH: Lattice QCD uses Euclidean path integrals, quark mass renormalization via one-loop lattice perturbation theory (e.g., Fermilab method: \\(m_q = Z_m m_0\\), \\(Z_m = 1 + \\alpha_s C_F/(4\\pi) \\ln(a\\mu) + \\dots\\)); meson mass ratios from lattice spectra (e.g., \\(m_{D_s}/m_{J/\\psi}\\), \\(m_{\\pi}/m_{\\rho}\\)) are computed numerically, not via φ. Parton distribution functions extracted via quasi-PDFs: \\(\\tilde{q}(x, P_z) = \\int dz e^{ixP_z z} \\langle P | \\bar\\psi(z) \\gamma^z \\psi(0) | P \\rangle\\), matched to light-cone PDFs via perturbative matching kernels. | CONNECTION: No geometric harmony (0.382, 0.618, 0.786, 1.618, 2.618) appears in these QCD results. Lattice QCD does use crystallographic-like discrete symmetry groups (hypercubic lattice, \\(H(4)\\) symmetry, root system \\( Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com