Z4DP III: Unified Vortex-Sink Equation - Hydrodynamic Origin of Gravity, Vacuum Compressibility, and the DFS Sensor

This paper presents a theoretical framework extending previous kinematic models in a superfluid vacuum (Z4DP I and II). Macroscopic mass is analyzed here as a topological defect functioning as a continuous hydrodynamic sink. The classical concept of mass is replaced by the thermodynamic capacity of continuum absorption, where the convective acceleration of this flow formally correlates with Newton's law of universal gravitation. By incorporating the rotation of the central body, a macroscopic vortex field is derived. The applicability of the unified equation of motion is primarily tested on a dataset of 122 GNSS satellites using a data-splitting methodology (6h training/18h prediction), which reveals an exponential vacuum compression profile with an attenuation of n=5.63. This theoretical apparatus is subsequently applied to the secular modeling of the Earth-Moon system, providing a hydrodynamic mechanism for orbital migration and asymptotic kinematic stabilization (Tidal Locking). The paper also defines the theoretical foundations for DFS (Dynamic Fluid Scanner) class instruments.