Dynamic Substrate Theory (DST): A Continuous Medium Framework for Field Unification⁠

Abstract The fundamental incompatibility between General Relativity (GR) and Quantum Mechanics (QM) stems largely from modeling space-time as an abstract geometric manifold and fundamental particles as zero-dimensional point-masses. This work presents the Dynamic Substrate Theory (DST), a classical continuous medium framework where physical reality emerges from a dense, compressible, viscoelastic substrate. All fundamental forces and matter states are represented through a unified Substrate Stress Tensor (\mathbf{T}_{ij}). Hydrostatic pressure gradients (\nabla P) give rise to gravitation without action-at-a-distance, while vorticity (\vec{\omega}) governs electromagnetic fields and particle spin. Topological solitons (vortex knots) model elementary particles with quantized circulation (\Gamma = n\kappa). Furthermore, applying the Madelung transformation to the substrate's fluid continuity equation yields the time-dependent Schrödinger equation, framing quantum mechanics as an emergent hydrodynamical wave behavior. Testable predictions include quantized galactic rotation plateaus (v_{\text{plateau}} = \sqrt{\frac{n \kappa c_s}{2\pi r}}) without invoking dark matter, as well as phase-refraction dispersion in high-energy gravitational lensing. Keywords: Field Unification, Fluid Dynamics, Quantum Hydrodynamics, Stress Tensor, Galactic Rotation, Viscoelastic Media.