Stabilizer Quantum Gravity VII: Information Release, Recoverability Transfer, and Page-Like Transition

This paper constitutes Part VII of the Stabilizer Quantum Gravity (SQG) research program, addressing the black-hole information paradox through the lens of operator-algebraic recoverability. Within the SQG framework, black-hole evaporation is not viewed as a purely geometric disappearance of hidden degrees of freedom, but as a dynamic transfer of recoverability. A black hole represents a critical recoverability object whose horizon sector stores information in a highly compressed form. We interpret the evaporation process as a redistribution mechanism, wherein recoverable structure is progressively transferred from the horizon-critical sector to exterior radiation-like sectors. Rather than claiming a full microscopic derivation of unitary evaporation, this paper isolates the minimal effective structure required for information release. We define radiation sectors, recoverability transfer, and release functionals, and formulate a Page-like transition principle that distinguishes an early compression-dominated regime from a late transfer-dominated regime. By identifying the explicit failure modes of the framework, this work establishes a rigorous, constructive program for understanding information release and Page-curve dynamics in emergent semiclassical gravity.