Topological Generation of the Fermion Mass Spectrum: From Worldline Knots to Fundamental Particle Inertia

This paper is further expanded based on "The Law of Absolute Kinematics" (doi.org/10.5281/zenodo.18358444). It introduces that fermion masses originate from the topological inertia of worldline knots, expressed as m_f = J(K_f) · M_topo · F_scale, where M_topo ≈ 4.137 MeV/c² is analytically locked from G, ℏ, α_0, and electromagnetic corrections, and F_scale accounts for generational phase transitions at the weak scale M_W. This zero-parameter mechanism reproduces the full fermion mass spectrum, including charged leptons, quarks, and neutrinos, with high consistency to experimental values. Gauge parameters, such as weak boson masses M_W and M_Z, weak coupling g, and strong string tension σ, are proven to be geometric projections of α_0, interpreting chirality, confinement, and asymptotic freedom as topological necessities. The supplementary appendix elaborates on the topological-geometric origins of fermion intrinsic quantum numbers (chirality, electric charge, color charge, magnetic moment, spin, lifetime, isospin), providing zero-parameter derivations, formulas, and quantitative results. It introduces composite knots and linking nuclei for molecular-scale interactions, unifying chemical bonds (covalent, ionic, metallic) as topological bindings with charge and density corrections. Furthermore, it derives zero-parameter spectra for hadrons (mesons, baryons), lepton anomalous magnetic moments (g-2), and QCD string theory, with predictions deviating from experiments by <3.5%, and verifies Regge trajectories.