Dynamic Substrate Theory (DST) — Analytical Formalism and Lagrangian Derivation of the Viscoelastic Vacuum

This paper advances the mathematical foundations of the Dynamic Substrate Theory (DST) by formulating a rigorous Lagrangian framework for the Maxwell-Oldroyd-B viscoelastic vacuum. Moving beyond heuristic models, we construct the action functional governing the substrate’s microscopic displacement field and its macroscopic stress tensor evolution. By introducing an internal strain-memory tensor coupled to background metrics, we derive the exact equations of motion, demonstrating how inertial mass emerges dynamically from local momentum coupling with the substrate. Furthermore, we analyze the energy-momentum tensor of the visco-elastic continuum, establishing a rigorous bridge between vacuum micro-rheology and effective gravitational fields.