Stabilizer Quantum Gravity V: Open-System Cosmology, Stabilization Flow, and Effective Large-Scale Response

This paper forms Part V of the Stabilizer Quantum Gravity (SQG) program, introducing its effective cosmological framework. In SQG, effective geometry arises from the stabilization of an underlying recoverable operator-algebraic substrate. We hypothesize that while local spatial sectors may approach the strongly saturated (Einsteinian) limit, the large-scale cosmological universe may remain in a partially unsaturated regime. Consequently, SQG cosmology is modeled not as a perfectly closed geometric phase, but as an open-system effective regime governed by a global stabilization flow. We introduce a global stabilization variable, define the large-scale unsaturated sector, and outline the corresponding effective flow law. This incomplete large-scale stabilization naturally generates a deficit-controlled cosmological correction tensor, phenomenologically manifesting as modified response kernels for large-scale structure (clustering $\mu$) and lensing ($\Sigma$). The paper does not claim a fully fitted cosmological data model, but rather establishes the rigorous theoretical conditions under which large-scale deviations from General Relativity become observationally meaningful within the SQG architecture, while preserving local recovery of the Einstein limit.