On the Hydrostatic Boundary Conditions of Scalar Fields: A Geometric Complement to Relativistic and Quantum Mechanics

Modern theoretical physics has achieved unprecedented predictive accuracy through the mathematical frameworks of General Relativity and Quantum Electrodynamics. However, the persistent structural divergence between macroscopic metric space and subatomic probability fields suggests an incomplete description of the underlying medium. This paper introduces a scale-invariant hydrostatic framework operating via an inversion protocol, wherein the properties of a pressurized, supercritical fluid lattice are constrained by a fundamental fluidic boundary metric—the fine-structure constant (), derived here as a vortical slip coefficient relative to the integer resonance boundary of 137.0. Rather than seeking to displace established mathematical formalisms, this approach demonstrates that both the macroscopic cross-shear attenuation quantified by the Hubble Constant and the hydrodynamic standing-wave resonance profiles of atomic sub-structures can be natively derived as the mandatory boundary conditions of a single continuous substrate. Under this continuous variable paradigm, QCD and QED are shown to emerge directly from localized energy-density gradients () and infinite-axis fluid vorticity (), rendering rigid polyhedral scaffolds entirely superfluous. Empirical validation of this scale-invariant hydrostatic architecture is explored through the macroscopic topological yield limits and structural cavitation profiles of Fast Radio Bursts (FRBs).