Causal Lattice Elastodynamics (GVS) introduces a discrete foundational framework replacing thecontinuous spacetime manifold with a shear-thickening, Poisson-sprinkled Causal Set. By modeling fundamental particles as localized topological embeddings, GVS analytically derives key Standard Model parameters strictly from 3D simplicial coordination geometry without arbitrary parameterization or fine-tuning. This paper formalizes the Five Fundamental Laws of GVS, uniting macroscopic General Relativity with microscopic quantum elastodynamics via the Holographic Surface-Strain Law. We present the unpatched, first-principle derivations of seven fundamental constants, demonstrating that empirical deviations from bare geometric limits are the exact physical measurements of vacuum polarization. A rigorous, pan-scalar falsifiability matrix is provided to test the framework against Ultra-High-Energy Cosmic Rays (UHECR), wide binary stellar kinematics, and Belle II constraints.