This paper presents a comprehensive, alternative non-linear geometric framework aimed at unifying classical general relativity with quantum mechanics under a cohesive paradigm termed Probabilistic Determinism. We propose that the smooth spacetime metric manifold constitutes the sole fundamental physical reality, and that subatomic fermions are localized, topologically stable metric solitons possessing spin-1/2 connection profile invariants. By introducing a novel covariant field relation—the Anbi Metric Deformation Equation—we demonstrate that localized energy-momentum density traces inherently compress the coordinate network itself at the sub-microscopic scale. This localized spatial contraction provides an asymptotic geometric buffer that regularizes field interactions, natively resolving the ultraviolet divergence catastrophes of quantum field theories without requiring arbitrary mathematical renormalization. Furthermore, utilizing a relativistic de Broglie-Bohm phase connection, we demonstrate how deterministic trajectories traversing this dynamically compressed, fluctuating background manifold scale up macroscopically to recreate observed quantum statistical probability distributions as a strict geometric continuity fluid law.
Saad Anbi (Wed,) studied this question.