Substratum Hydrodynamics: A Unified Mechanical Framework for Nuclear Stability, Mass-Energy Equivalence, and the Infinite Universe

This paper explores a unified hydrodynamic paradigm that treats the physical vacuum as a continuous energetic medium (the "Substratum") possessing finite mechanical properties. We model the atom as a stable vortex formation where fundamental interactions are driven by hydrostatic pressure gradients rather than abstract fields. Mathematical analysis suggests that both the "Strong Interaction" and "Gravity" may be interpreted as manifestations of Substratum pressure acting across distinct spatial scales, with the nuclear stability threshold calculated at approximately 10³² Pa. We provide a mechanistic derivation of mass-energy equivalence (E=mc²) based on the Substratum's equation of state and the Newton-Laplace relation. Furthermore, the paper demonstrates that hydrostatic equilibrium within a ponderable vacuum medium necessitates a spatially infinite universe as a boundary condition for the existence of stable matter. This framework offers a deterministic alternative for reconciling sub-atomic stability with cosmological dynamics within a strictly 3-dimensional mechanical ontology.