Phase Transport in Hybrid Manifolds: Emergent Minkowski Geometry and Exact Topological Force Evaluation

This paper, is part of ITE ETD and presents a Lagrangian formulation for phase transport in nonlinear hybrid metric structures, in which space-time and dynamical observables emerge from a unified phase-evolution principle. We show that extending a complex Kähler manifold yields a representation in which Minkowski space-time appears as the real topological projection of a higher-dimensional geometry. Within this framework, the behavior near the singular core is reformulated through the metric structure, producing an asymptotic bound on the phase gradient at the electron rest-mass energy. We also derive an exact expression for the topological force field and obtain a tractable Euler-Lagrange equation that links quantum probability densities with Minkowski kinematics without perturbative cutoffs.