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 mf = J (Kf) · Mₜopo · Fₛcale, where Mₜopo ≈ 4. 137 MeV/c² is analytically locked from G, ℏ, α₀, and electromagnetic corrections, and Fₛcale accounts for generational phase transitions at the weak scale MW. 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 MW and MZ, weak coupling g, and strong string tension σ, are proven to be geometric projections of α₀, 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.