Two Energy Theory TDE 9.0 - Relativistic Phase Gravity and Metric Coupling

This working paper presents a formal mathematical companion to the Two-Energy Theory (TDE), version 9.0, developed as a technical extension of the previously published conceptual framework Two-Energy Theory (TDE): Conceptual Foundations of Mass, Time, and Gravity. The mathematical structures, equations, and formal derivations contained in this document were generated with the assistance of artificial intelligence (AI), based on the conceptual assumptions, physical interpretation, and structural constraints defined by the author. The author is not a professional mathematician and does not claim independent mastery of advanced mathematical formalism at this level. This document is therefore published explicitly as a supporting and exploratory formalization, intended to facilitate discussion, critical examination, and independent verification by qualified researchers. No claim of mathematical completeness, uniqueness, or experimental confirmation is made. Responsibility for the conceptual framework, ontological assumptions, physical interpretation, and research direction of TDE rests entirely with the author. The role of AI was limited to formal mathematical assistance and technical structuring.