MetaTime Dark Sector as Processing-Driven Interacting Dark Energy: A Covariant and Stable EFT Closure with Inhomogeneous Extensions.

We present a robust Effective Field Theory (EFT) framework for an interacting dark sector where the energy-momentum transfer between a pressureless "latency" component (DM) and a negative-pressure "execution" component (DE) is regulated by a physical processing proxy $\Pi(a)$ linked to cosmic structure formation. Unlike standard Interacting Dark Energy (IDE) models that rely on ad-hoc coupling constants, our model anchors the interaction rate $Q$ to the evolutionary history of complexity, significantly reducing phenomenological freedom. To ensure mathematical consistency and observational viability, we define a generally covariant interaction 4-vector and implement a Parametrized Post-Friedmann (PPF) formalization. This approach successfully suppresses the large-scale instabilities typically found in $w \approx -1$ IDE closures. Furthermore, we introduce a novel inhomogeneous extension where the interaction is modulated by local density fluctuations $\delta \Pi(x, a)$, providing unique, falsifiable signatures in the matter power spectrum and weak lensing surveys. We outline a comprehensive likelihood pipeline for testing against SNe Ia, BAO, and CMB data, positioning MetaTime as a mathematically stable and physically motivated alternative to $\Lambda$CDM.