Silva-Tech Framework v16.3.1: Technical Addendum and Final Closure of the Dynamic Vacuum Model, Scalar-Tensor Shielding, and Numerical Stability Protocols

This Technical Addendum provides the definitive theoretical closure and computational validation for the Silva-Tech Cosmological Framework (v16.3.1). Designed to address the persistent S_8 tension and non-linear anomalies inherent to the standard \Lambda\text{CDM} paradigm, this work formalizes a Running Vacuum Model (RVM) dynamically coupled to Cold Dark Matter (CDM) via a late-time interaction channel (Q = \Gamma_{\text{int}} \rho_\Lambda for z < 1), while enforcing strict baryon conservation. To overcome numerical stiffness and gauge instabilities during background evolution, the computational backend integrates a modular system of ordinary differential equations (ODEs) solved via an implicit Radau algorithm within scipy.integrate.solve_ivp. Furthermore, spatial equivalence with Solar System gravity tests and Cosmic Microwave Background (CMB) anisotropy spectrum constraints is guaranteed through a scalar-tensor screening mechanism (Symmetron/Chameleon blindage). The resulting framework achieves complete mathematical stability, providing a robust baseline for upcoming cosmological validation pipelines, including hi_class/CLASS implementations and Bayesian Markov Chain Monte Carlo (MCMC) parameter estimation.