TITLE:
Phase Transport in Hybrid Manifolds: Emergent Minkowski Geometry and Exact Topological Force Evaluation
AUTHORS:
Gruia Constantinescu
KEYWORDS:
Phase Dynamics, K?hler Manifolds, Nonlinear Minkowski Projection, Cauchy Contour Integral, Exact Analytical Evaluation, Topological Force, Hybrid Metric Coefficients, Generalized Euler-Lagrange Equation
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.14 No.7,
July
31,
2026
ABSTRACT: Background: Standard quantum and classical electrodynamics often rely on artificial cut-offs or ad-hoc regularization to avoid divergences near singular particle cores. This paper addresses that limitation with a background-independent framework in which spacetime geometry and dynamical observables emerge from a unified phase-evolution principle. Methods: Building on the ITE Extended Theory Dissertations (ITE ETD, DOI: 10.5281/zenodo.18206804), we extend a complex Kähler manifold into a non-homogeneous hybrid metric structure. Replacing the abstract phase potential with physical presence density makes the hybrid metric determinant a natural scaling operator. We evaluate the analytical extensions in a universal open domain using generalized Bürmann power series and a Borel-type contour integral. Results: We show that Minkowski spacetime emerges exactly as the real topological projection of a higher-dimensional Kähler geometry. Near the core, growing presence density counterbalances the geometric field gradient, bounding the phase gradient at the electron rest-mass energy limit without ad-hoc parameters. The squared phase wave vector also reproduces the vacuum dielectric permittivity constant. A closed singularity contour yields an exact exponential topological force field and a tractable Euler-Lagrange equation of motion. The model is numerically validated against the Hydrogen Lamb-shift spectral anomaly for the state, achieving exact experimental alignment from intrinsic geometric phase-curvature equations alone. Conclusions: This formulation provides a rigorous, gauge-invariant link between quantum probability densities and Minkowski kinematics without perturbative cutoffs. It supports the view that geometry, electric charge, and energy are unified expressions of a single-phase evolution.