Stabilizer Quantum Gravity VI: Black Holes, Generalized Entropy, and Saturation Transitions

This paper forms Part VI of the Stabilizer Quantum Gravity (SQG) research program, formulating the black-hole sector as a near-critical regime of recoverability and stabilization. In the SQG framework, black holes are not viewed merely as geometric solutions of a classical theory, but as critical sectors of the underlying recoverable operator-algebraic substrate in which logical compression, generalized entropy, and saturation structure become extreme. Within this perspective, horizons are interpreted as effective transition interfaces separating differently stabilized sectors, while black-hole entropy measures the logical compression cost of maintaining effective recoverability across that interface. The purpose of this paper is not to claim a complete microscopic resolution of the information paradox, but to formulate the minimal structural picture in which black-hole formation, evaporation, and instability can be understood as saturation transitions. We define critical recoverability, horizon sectors, and saturation transition laws, while explicitly identifying the failure modes of the framework. This establishes a constructive program for analyzing black hole thermodynamics through the lens of operator-algebraic stabilization.