Arithmetic Conservation and Periodic Cosmological Oscillations in a Unified Field Theory from Topological Equivariance

We construct a unified description of gravitational, strong, weak, and electromagnetic interactions based on minimal topological and arithmetic assumptions. Using only the fundamental group π1 (M4) = Z3, a fiber bundle structure π: M4 →Σ3 with fiber S1 carrying a Z3 action, and arithmetic locking at the Heegner point τ163, the equivariant index theorem uniquely determines the topological charges Ig = (3/16, 1/3, 5/12) and total entanglement entropy Etotal = (161/576) ln 2. From these, all coupling constants, mass scales, dark matter abundance, cosmological constant, proton decay lifetime, monopole mass, graviton behavior, black hole entropy corrections, neutrino CP phase, axion mass, dark matter scattering cross section, graviton polarization correlations, spacetime crystal oscillation frequencies, and periodic cosmological modulation amplitudes are derived without free parameters. We introduce the concept of a topological reference frame as a global section σ: Σ3 →M4, and section dynamics as the one-parameter family σ (t) satisfying the geodesic equation ∇̇ ̇ = 0, providing a geometric origin for time, evolution, and quantum measurement. The framework remains self-consistent under extreme conditions: Planck-scale collisions, superstrong magnetic fields, monopole backgrounds, black hole interiors, the early universe, and high-density high-temperature environments. Twenty parameter-free, falsifiable predictions are presented for experimental test.