Empirical Geometric Correlations in Particle Masses (Geometry of Sound v18.6) This work presents an empirical study of geometric correlations between the masses of 12 fundamental particles (including the Z boson) and the nested Platonic solids. The mass formula is m=mP⋅αN⋅G⋅Rm=mP⋅αN⋅G⋅R, where NN is a hierarchy level, GG are geometric factors expressed through ππ, φφ, 22, 33, 55 and integer Platonic counts, and RR are empirical radiative corrections. The resulting masses agree with PDG 2024 within 1σ1σ (except the top quark at ∼1.9σ∼1.9σ). Cross‑validation of the corrections yields Rloo2=0.281Rloo2=0.281, indicating modest predictive power. Vesica intersection volumes of inscribed/circumscribed spheres between adjacent solids correlate strongly with the hierarchy levels NN (Pearson r=0.988r=0.988 based on four layer pairs). Cosmological parameters (Ωb,ΩDM,ΩΛ,ns,rΩb,ΩDM,ΩΛ,ns,r) are empirically matched by simple rational fractions involving Platonic integers and φφ. No dynamic Lagrangian or gauge structure is provided; the work is purely empirical and aims to stimulate further theoretical investigation.
Yuriy S. Vinogradov (Tue,) studied this question.