We present evidence that the resonance stability of standing waves on toroidal geometries is universally governed by the number-theoretic properties of the winding ratio. Across four physically distinct domains (tokamak plasma confinement, asteroid orbital dynamics, cardiac electrical conduction, and particle accelerator beam physics), we demonstrate that instabilities occur at coprime rational winding ratios, with severity monotonically ordered by the Farey sequence. Spearman rank correlation analysis yields ρ = 0.97 (tokamak MHD severity, N=9), ρ = 0.90 (Kirkwood gap depth, N=8), and ρ = 1.00 (cardiac Wenckebach periodicity, N=4) against the inverse Farey order. We propose a Coprime Resonance Density Function, derived from pure number theory, as a universal predictor of resonance location and strength on any toroidal system.
Ibrahim Vandenberg (Wed,) studied this question.