The Geometric Origin of the Mass Spectrum — A Unified Explanation of the Origin of Particle Masses by the Order Parameter Spacetime Theory

The origin of mass is one of the most fundamental problems in physics. The Standard Model pieces together an explanation using the Higgs mechanism, Yukawa couplings, and the seesaw mechanism, yet leaves five unanswered sub-questions: Why are the photon and gluon massless? Why do W/Z bosons have mass? Why are there three fermion generations with masses spanning five orders of magnitude? Why are neutrino masses extremely small but non-zero? Where does the Higgs boson's own mass come from? This paper demonstrates that the Order Parameter Spacetime Theory can answer these five questions with a single geometric principle: mass is the projection of the order parameter field onto the internal space metric, m = M·G₁₁. The masslessness of the photon and gluon corresponds to G₁₁=0. The W/Z masses arise from G₁₁ changing from zero to non-zero when the electroweak phase transition traverses a type-B singularity, with computed values G₁₁(W)≈0.33, G₁₁(Z)≈0.37 automatically satisfying cos θ_W. The three fermion generations originate from three critical traversals of the order parameter field with decreasing metric gradients. Neutrino masses are exponentially suppressed via geometric freezing of the right-handed neutrino, giving m_ν~10⁻² eV and a type-B curvature scale >1.3×10¹⁴ GeV. The Higgs mass is determined by the metric curvature at the singularity, with the derived curvature scale consistent with the electroweak scale. Composite particle masses are dominated by QCD non-trivial geometric configurations, with effective G₁₁>1 reflecting strong-coupling geometric amplification. The continuous spectrum of G₁₁ provides a geometric dark matter candidate. All known PDG mass data are shown to be consistently accommodated within the mass formula. The paper reduces the ~20 hand-input parameters and five independent mechanisms of the Standard Model to a single geometric principle with zero free parameters.