Operator-Algebraic and Information-Theoretic Reinforcement of Stabilizer Quantum Gravity

This paper develops the operator-algebraic and information-theoretic backbone of Stabilizing Quantum Gravity (SQG), with emphasis on recoverability, stabilization, and the emergence of effective geometric rigidity from algebraic structure. Rather than introducing a separate physical theory, the manuscript should be read as a formal reinforcement and controlled extension of the main SQG framework. Its aim is to sharpen the mathematical bridge between recoverable logical sectors, conditional expectations, relative entropy, stabilization deficits, and the emergence of persistent semiclassical structure. The paper focuses in particular on:- operator-algebraic formulations of recoverability,- stabilization functionals and rigidity response,- entropy-based control of effective sectors,- defect-sensitive departures from exact recoverability,- and the role of these structures in cosmological and geometric coarse-graining. Conceptually, this work occupies the “formal spine” of the broader SQG program: it does not attempt to replace the flagship framework paper, but to provide a more precise mathematical layer beneath it, especially for readers interested in AQFT-compatible, operator-algebraic, and information-theoretic formulations of emergence. Status note:This manuscript is intended as a companion technical contribution to the broader SQG research program. Some constructions are theorem-level, while others are explicitly identified as structured programmatic targets.