Dynamic Vacuum Theory (DVT) v19.1: First-Principles Derivation of the Cosmic Acceleration Threshold and Zero-Parameter Galactic Rotation Curves

This document presents the complete first-principles derivation of the Dynamic Vacuum Theory (DVT) v19 acceleration law. We demonstrate that the cosmic acceleration threshold a_0, the tanh(sqrt(x)) transition function, and all geometric projection factors arise from fundamental physical considerations—eliminating all empirical fitting parameters. The theory successfully predicts galactic rotation curves across 135 SPARC galaxies using cosmological constants alone, establishing a zero-parameter framework for galactic dynamics and vacuum hydrodynamics.