Numerical Implementation and Observational Constraints of the Minimal rCVGT Model

This work presents the first numerical implementation and observational analysis of a minimal specified realization of Relativistic Coherent Vacuum Gravity Theory (rCVGT). Building on the covariant theoretical framework developed in a companion paper, we construct a self-consistent numerical pipeline for computing cosmological observables, including the background expansion, effective gravitational coupling, gravitational slip, and the growth of structure. The implementation focuses on large-scale structure observables such as fσ₈(z) and the linear matter power spectrum. We show that the model admits viable parameter regimes with both enhanced and suppressed late-time structure growth relative to ΛCDM, while preserving a ΛCDM-like background expansion. In particular, mildly suppressed growth consistent with current large-scale structure observations can be obtained within controlled parameter ranges. The numerical framework is implemented as a lightweight pipeline designed for phenomenological analysis in the quasi-static regime. A summary of benchmark parameter choices and derived observables is provided alongside the public code release to ensure reproducibility. This work establishes a direct bridge between the covariant formulation of rCVGT and observational cosmology, providing a foundation for future extensions including full Boltzmann solver implementations and precision likelihood analyses.