This companion paper to Relational Dynamics Theory (RDT) develops the mathematical formalization required to move the framework from philosophical coherence toward empirical falsifiability. Three central contributions are presented. First, a rigorous phase-space formulation situates RDT within the language of differential geometry and dynamical systems. Second, a formal proof of structural isomorphism is offered between the five phases of the Stem Process for Change of State and the oscillatory cycle described by RDT's core equations, demonstrating that the operational process model and the physics are the same object viewed from different positions. Third, entanglement is reinterpreted as phase coincidence within the oscillatory field, yielding a specific, testable prediction: that decoherence rates should vary inversely with the characteristic frequency of the entangled system. Throughout, the paper shows how RDT's observer-dependent time formulation extends general relativity by replacing geometric curvature with phase topology as the primary description of temporal experience.