RG Analysis Reproducibility Package for Nonlocal Field Theories with Causal Memory

We present a relational cosmological framework that reconstructs the vacuum as an active presence rather than an empty background. Central to this formulation is the Relative Zero operator, a covariant functional operator that measures dynamical imbalances with respect to a causal reference state. Within this framework, the Active Vacuum emerges as a regulatory field mediating between informational and gravitational scales, while the Circuital Universe is described as a multiscale network endowed with causal memory and average conservation. We formalize an effective Lagrangian incorporating a nonlocal coupling between the Active Vacuum field and the Relative Zero operator, and derive the corresponding equations of motion, conservation laws, and stability conditions. The theoretical structure includes a consistent treatment of renormalization with counterterms, a discrete-to-continuous statistical mapping linking microscopic contributions to macroscopic fields, and a perturbation solver incorporating a causal memory kernel. Technical analyses are provided to ensure internal consistency between the formalism, functional variations, and dynamical evolution. The framework is formulated to allow its implications to be expressed in terms of standard cosmological observables, such as the expansion history and structure growth, without performing direct observational inference at this stage. This work establishes the foundational architecture of the Circuital Universe paradigm and prepares the ground for subsequent mathematical, dynamical, and phenomenological developments.