A Harmonic Origin for the Standard Model Mass Spectrum

The Standard Model of particle physics relies on over nineteen experimentally-fitted parameters. This work proposes a mechanical principle from which the particle mass spectrum can be derived. We model particles as stable, resonant modes of a universal, non-linear oscillator governed by a single differential equation. By calibrating the oscillator's non-linearity constant with the known electron-muon mass ratio, the model becomes fully predictive. It subsequently yields, without further input, the masses of the tau lepton and the Higgs boson to within experimental uncertainty. The model also predicts the absence of a stable fourth-generation lepton and derives the energy scale of the Higgs Vacuum Expectation Value (VEV) as a field saturation limit. These results suggest the Standard Model's mass hierarchy may be a manifestation of a deeper, deterministic harmonic structure.