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 m_SG = 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 sin^2θ_W to 0.029%, the Z and W boson masses to 0.10% and 0.63%, the Fermi constant G_F to 5.8% (attributed to the ∆r radiative correction), the Higgs self-coupling λ_H = 1/6 cos^2θ_W (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: λ_H = 1/6 cos^2θ_W at the HL-LHC; ∆ρ = 0 exactly in precision electroweak data; and Majorana neutrinos confirmed by neutrinoless double beta decay.