The Standard Model Mass Spectrum and Electroweak Sector from Metric Phase Transition Theory

We extend Metric Phase Transition Theory (MPT) to derive the complete Standard Model mass spectrum and electroweak sector from a single physical input: the sine-Gordon field mass mSG = 134. 59 MeV. From this one parameter, together with the fine structure constant α = 1/137. 037 derived in Rogers Rogers, 2026 and mathematical constants π and φ = (1+√5) /2, we obtain: all six quark masses (errors below 1. 1%), all three charged lepton masses (errors below 0. 25%), the electroweak mixing angle sin²θW to 0. 029%, the Z and W boson masses to 0. 10% and 0. 63%, the Fermi constant GF to 5. 8% (attributed to the ∆r radiative correction), the Higgs self-coupling λH = 1/6 cos²θW (0. 75% error), the Higgs vacuum expectation value v to 0. 32%, and the Higgs boson mass to 0. 69%. The ρ parameter satisfies ρ = 1 exactly from the sl (2, R) custodial symmetry. The field space of the complexified sine-Gordon equation has dipole topology — two circles connected by a helical kink — which classifies all Standard Model particles by two quantum numbers (B_ψ, Q_χ) and identifies the neutrino as a Majorana sinh-Gordon soliton. In total 17 physical quantities are derived with zero free parameters. The probability that this agreement is numerical coincidence is below 10^−34. Three falsifiable predictions are stated: λH = 1/6 cos²θW at the HL-LHC; ∆ρ = 0 exactly in precision electroweak data; and Majorana neutrinos confirmed by neutrinoless double beta decay.