Unified Hydrodynamics of Spacetime (UHST): A Vacuum Rheology Framework for Galactic Rotation Curves

This paper introduces the Unified Hydrodynamics of Spacetime (UHST), a non-linear framework that replaces the Dark Matter paradigm with a vacuum rheology model. We propose that the vacuum is a physical, non-Newtonian superfluid condensate subject to a Density-Driven Phase Transition. By analyzing the full SPARC database (N=175), we demonstrate that a single set of three global parameters can explain galactic rotation velocities across five orders of magnitude in mass. The model achieves a global average chi^2 = 2.04 and a median chi^2 = 1.76, while naturally recovering the Baryonic Tully-Fisher Relation (BTFR) with an empirical slope of 4.01 +/- 0.03. Results suggest that galactic rotation anomalies are an emergent property of vacuum stiffness rather than the result of invisible particle halos.