Two established facts —
(1) that gauge fields are principal fiber bundles (Wu and Yang, 1976; Hasani, 2005) and
(2) that electric charge is quantized (empirical) jointly single out exactly one fiber bundle for all forces.
We prove that this bundle is the universal complex Hopf fibration $S^1 \to S^\infty \to \mathbb{CP}^\infty$, and that the Standard Model gauge group $[SU(3) \times SU(2) \times U(1)]/\mathbb{Z}_6$, Einstein–Cartan gravitation through Chern–Simons torsion, exactly three fermi…
Read moreTwo established facts —
(1) that gauge fields are principal fiber bundles (Wu and Yang, 1976; Hasani, 2005) and
(2) that electric charge is quantized (empirical) jointly single out exactly one fiber bundle for all forces.
We prove that this bundle is the universal complex Hopf fibration $S^1 \to S^\infty \to \mathbb{CP}^\infty$, and that the Standard Model gauge group $[SU(3) \times SU(2) \times U(1)]/\mathbb{Z}_6$, Einstein–Cartan gravitation through Chern–Simons torsion, exactly three fermion generations, and the complete particle mass spectrum follow as rigid theorems of its contact geometry. No step introduces a free parameter, a fitted constant, or a modeling choice; the sole dimensional input is the electroweak vacuum expectation value $v = 246.220$ MeV, which fixes the unit conversion between geometric radius and laboratory measurement.
The Beltrami operator $B = \star d|_\xi$ on the horizontal contact distribution is the unique first-order gauge operator, proved independently by Schur's lemma and the action Hessian. Its discrete spectrum renders the quantum field theory exactly solvable and ultraviolet-finite. Evaluating the zeta-regularized determinants on the lens spaces $L(n,1) = S^3/\mathbb{Z}_n$ and knot complements $S^3 \setminus T(2,n)$ computes the complete physical spectrum:
- **Boson and Higgs masses:** $m_W = 80.3695$ GeV, $m_Z = 91.1878$ GeV, $m_H = 125.225$ GeV, and all charged lepton and quark masses within PDG uncertainties.
- **Electroweak and anomalous couplings:** $\sin^2\theta_W = 3/(4\pi) = 0.23873$ (0.4σ); $a_e$ to 0.08σ, $a_\mu$ to 0.22σ.
- **Neutrino sector:** Normal ordering, $m_{\nu_1} = 0.970$ meV, $m_{\nu_2} = 8.708$ meV, $m_{\nu_3} = 49.604$ meV ($\sum m_\nu \approx 0.059$ eV), and mass-squared splittings to 0.2σ.
- **Cosmology:** $\Lambda = 2.94 \times 10^{-122}$ (Planck units), $H_0 = 68.5$ km s$^{-1}$ Mpc$^{-1}$.
Exactly three stable generations are forced by the Kolmogorov–Arnold–Moser (KAM) destruction of invariant tori at spectral level $k = 4$, which transitions stable particle orbits into chaotic resonances. These values are not fits; every number is a computed spectral invariant of the bundle. The theory is anomaly-free, contains zero dimensionless free parameters, and is directly falsifiable through precision $g-2$ measurements, absolute neutrino-mass experiments, and atom interferometry.