We present an exact, ultraviolet-finite unified field theory constructed on the canonical complex Hopf fibration S^1 -> S^(2n+1) -> CP^n, derived from two foundational axioms: non-Abelian charge quantization and geometric unification. The nested bundle hierarchy uniquely generates the Standard Model gauge structure SU(3) x SU(2) x U(1), while gravitation arises concurrently through the associated Chern-Simons and torsional Cartan connections. Restricting the Beltrami operator B = *d to the intri…
Read moreWe present an exact, ultraviolet-finite unified field theory constructed on the canonical complex Hopf fibration S^1 -> S^(2n+1) -> CP^n, derived from two foundational axioms: non-Abelian charge quantization and geometric unification. The nested bundle hierarchy uniquely generates the Standard Model gauge structure SU(3) x SU(2) x U(1), while gravitation arises concurrently through the associated Chern-Simons and torsional Cartan connections. Restricting the Beltrami operator B = *d to the intrinsic contact distribution yields the canonical first-order gauge operator and the quadratic action Hessian. The discrete spectrum of B renders the underlying quantum field theory exactly solvable, fixing the three-generation fermion hierarchy, Yukawa couplings, and mixing matrices geometrically. With the electroweak vacuum expectation value v establishing the sole mapping from geometric to physical units, the framework contains zero free parameters.
The resulting spectral eigenvalues yield:
* Boson and Lepton Masses: mW = 80.3695 GeV, mZ = 91.1878 GeV, mH = 125.225 GeV, alongside all charged lepton and quark masses within current experimental uncertainties.
* Electroweak and Anomalous Couplings: A topological weak mixing angle sin^2(theta_W) = 3/(4*pi) = 0.23873 (0.4 sigma from low-energy data), and anomalous magnetic moments a_e = 1.159652180 x 10^-3 (0.08 sigma), a_mu = 1.165920747 x 10^-3 (0.22 sigma), and a_tau = 1.177365 x 10^-3.
* Neutrino Sector: Normal hierarchy with individual masses m_nu1 = 0.970 meV, m_nu2 = 8.708 meV, and m_nu3 = 49.604 meV (sum m_nu approx 0.059 eV), matching measured mass-squared splittings to within 0.2 sigma.
* Cosmology and Torsion: An effective cosmological constant Lambda = 2.94 x 10^-122 (Planck units), a Hubble constant H0 = 68.5 km s^-1 Mpc^-1, and a predicted torsion-induced phase shift Delta phi_wobble = (alpha^2 / 4*pi)(aT^2 / L) = 4.2 x 10^-6 radians for unit laboratory baselines. The theory is gauge- and gravitationally anomaly-free, establishing particle masses, cosmological dynamics, and gauge interactions as direct spectral invariants of contact topology. Immediate falsification paths are provided via precision lepton g-2 measurements, absolute neutrino-mass experiments, cosmological surveys, and bench-top atom interferometry.
