Geometric Unification of Spacetime and Particles (I): First-Principles Derivation of Standard Model Parameters based on Phase Interference and Topology

Although the Standard Model in modern particle physics agrees with experiments to an extremely high precision, the origins of ”local gauge invariance,” ”parity violation,” ”neutrino masslessness,” and dozens of free parameters (mass ratios, coupling constants, and mixing angles) are treated as phenomenological assumptions rather than theoretical inevitabilities. In this paper, starting from the first principle that the universe is a ”minimal entity of existence rather than nothingness,” we present a geometric framework based on spatial directionality and wave phase interference. In this theory, gauge interactions and the Higgs mechanism are reconstructed as geometric compensation mechanisms for phase shifts accompanying particle propagation, and the left-handed selectivity of the weak interaction (parity violation) is mathematically proven as a theorem regarding the radiation causality of space. Furthermore, by formulating spacetime as a 4-dimensional tensor product Hilbert space (degrees of freedom N = 81), and utilizing the trace of the projection tensor for the spatial metric and topological measure integrals in phase space, we derive the coupling constants, fermion masses, mixing matrices (CKM and PMNS), and the gravitational constant from first principles. Except for the calibration of the Higgs scale using the electron mass and the identification of the cosmological environmental variable (decay rate χ0), this model calculates all major parameters of the Standard Model within 1σ accuracy without employing any arbitrary parameter fitting. This study suggests that a superstring-like geometric approach functions extremely powerfully even as a low-energy effective theory, and that the Standard Model is a topological inevitability of space itself.