Running Vacuum Completion (RVC–1P): A Minimal Covariant Vacuum Response Model for H0 and S8 Relief

The Running Vacuum Completion (RVC–1P) is a one-parameter, Boltzmann-ready implementation of a covariant vacuum-response model. While the "Self-Regulating Spacetime Cosmology" (SRSC–0P, DOI: 10.5281/zenodo.18911455) provides the zero-parameter geometric foundation, RVC–1P provides the computational gateway for immediate MCMC validation. Key Features: - Analytic E(z) closed-form solution for drop-in replacement in CLASS/CAMB. - Single parameter (nu) control for H0 and S8 tension relief. - Preserves early-universe constraints while allowing late-time uplift. This record serves as the technical implementation branch of the SRSC theory, specifically designed for researchers looking to confront the "Valve" mechanism against CMB, BAO, and large-scale-structure datasets.