Quantum Determinism: A Complete Field Theory from Topological Equivariance and j-Invariant Arithmetic

Abstract

The Standard Model of particle physics and the ΛCDM cosmological model leave four foundational questions unanswered: the origin of three fermion generations, the value of the cosmological constant, the nature of dark matter, and the holographic encoding of spacetime geometry. We demonstrate that these puzzles share a common resolution rooted in a topological–arithmetic structure. From equivariant index theory on K3 surfaces, the arithmetic geometry of the Heegner point τ_163, the Z2 outer automorphism of Z3, and the holographic principle, we derive a unique set of axioms: the spacetime manifold M₄ has fundamental group π₁(M₄) = Z3, its modular parameter is locked to τ_phys = τ₁₆₃, and a Z2 mirror sector accounts for dark matter. From these axioms alone, all physical parameters—including the three family mixing angles, the cosmological constant, the dark matter abundance, and quantum measurement probabilities—are uniquely determined without any free parameter. We derive the complete field equations, the universal path integral, and the exact universal wave function governing all matter and entanglement. The theory predicts testable correlations in neutrino oscillations, cosmic microwave background anisotropies, and dark matter direct detection rates. This work represents a mathematically rigorous unification of fundamental interactions based on geometry and number theory, with quantum determinism emerging from reverse dimensional reduction.