The Universal Quadratic Law for Fermionic Masses From Charged Fermions to Neutrinos: A Unified, Predictive Framework Across the Standard Model

We propose the Universal Quadratic Law for Fermionic Masses (UQLFM), a compact framework that reproduces the entire charged–fermion spectrum and yields falsifiable predictions across leptons, quarks, and neutrinos. In this model, the masses of each sector are organized by a parabola in a discrete family index, with the vertex position n ₀ (g) determined by intrinsic attributes: an electric–charge sector tag and a geometric mean mass scale. No free fit parameters are required once these sector invariants are specified. This elevates the UQLFM from a numerical pattern to a physically–anchored law. The framework accounts for charged fermion masses with sub–percent accuracy, predicts neutrino absolute masses in the tens–of–meV range consistent with oscillation and cosmological bounds, and implies strong constraints: exact matter–antimatter mass symmetry, exclusion of sequential fourth generations, and structural instability of heavy fermions as excitations above a sub–vacuum state. These features render the UQLFM highly testable against upcoming precision experiments in particle physics and cosmology.