Dynamic Vacuum Theory: A Unified Mechanical Framework From Quantum Potentials to Galactic Rotation Curves (Consolidated Master Edition v5)

▶️ Interactive Multimedia Component / Visual Presentation: The mechanical principles, vacuum pressure fields, and fluid dynamics simulated in this paper are fully visualized in the 10-minute companion presentation. Watch here: https://youtu.be/Ee00ivy5F1s Abstract: This paper delivers the definitive, multi-scale mathematical consolidation of the Dynamic Vacuum Theory (DVT) and its cosmic expression, the Galactic Pressure Law (GPL). Rather than treating the physical vacuum as a sterile, geometric background, we model it as a non-zero density superfluid medium characterized by localized pressure and density distributions. Macroscopic gravitational acceleration, cosmic expansion anomalies, and quantum wave-particle mechanics emerge natively as direct consequences of hydrodynamic pressure gradients. Critically, we present the analytical, first-principles derivation of the Universal Vacuum Permeability constant, proving it to be a pure geometric projection of Newton's gravitational constant (G) from a 3D isotropic sphere onto a 2D galactic disk: χ_v = (2/π) × G. This eliminates all free parameters or empirical curve-fitting variables. The unified framework is validated with greater than 95% mathematical accuracy against the blind rotation profile of the Triangulum Galaxy (M33), offering a robust mechanical alternative to the dark matter paradigm.