Unified Dirac Formulation from the Physical Time (ρₜ–k) Field

This paper derives the Dirac equation as the relativistic spinor limit of the Physical Time (rho_t–k) field. Starting from the covariant continuity law governing the Time-density medium, we obtain the Klein–Gordon operator and factorize it into the first-order Dirac form. The resulting equation represents structured multi-component flow states of the Physical Time continuum, in which mass, spin, and particle–antiparticle symmetry arise from harmonic modes of rho_t. This work completes the unified Physical Time trilogy: the Einstein energy-flow formulation, the Schrödinger quantum limit, and the Dirac relativistic spinor dynamics. The model establishes a continuous physical origin for relativistic quantum behavior without introducing external mass parameters.