Neutrino Masses and the Fermion Mass Spectrum — A Unified Explanation via Three Critical Crossings

The Standard Model of particle physics cannot explain why there are exactly three generations of fermions, nor why the mass spectrum of the three generations spans over a dozen orders of magnitude, nor why neutrino masses are so tiny. This paper demonstrates that the Order Parameter Spacetime Theory provides a unified geometric picture—the order-parameter field crosses Type-B traversable singularities sequentially along three independent directions of the internal space during the electroweak phase transition—that simultaneously explains all three problems. The three crossings produce three generations of fermions: the metric gradient at each crossing determines the mass of that generation, with larger gradients yielding larger masses. The three neutrinos correspond to the three crossings, with ν_e corresponding to the third crossing (smallest metric gradient, smallest baseline mass), and the mixing terms of all neutrinos are further suppressed by the geometric decoupling at the Type-B singularity. This unified picture introduces no additional free parameters—the existence of three generations, the mass hierarchy, and the tininess of neutrino masses are all geometric imprints of the order-parameter field crossing the Type-B singularity. If a fourth generation of fermions is discovered, or if the neutrino masses fall outside the range predicted by the geometric seesaw, this theory is falsified.