Stabilizer Quantum Gravity (SQG): An Information-Theoretic Stabilization Framework for Emergent Geometry, Gauge Structure, and Cosmological Response

We propose Stabilizer Quantum Gravity (SQG), a comprehensive quantum-information and operator-algebraic framework in which spacetime geometry, gauge interactions, and gravitational dynamics are not fundamental, but emerge strictly from the error-correction dynamics of a boundary logical layer. By modeling reality as a finite-depth network of operator algebras equipped with recoverability constraints, SQG demonstrates that spatial locality and causality are macroscopic manifestations of underlying Lieb-Robinson bounds. We formalize a logical composition ceiling, proving that multiplicative norm preservation in the code space forces a Hurwitz-type dimensional bound. Furthermore, we show that Lorentzian spacetime structure and the equivalence principle arise naturally from modular flow and entanglement extremality, recovering the Einstein equations in saturated regimes. Crucially, SQG is experimentally falsifiable. In unsaturated cosmological environments, the stabilizer response motivates a conservative modified-gravity phenomenology, providing a controlled dark-sector mechanism without introducing additional propagating tensor degrees of freedom. The framework also resolves extreme limits, demonstrating that black hole entropy transitions (the Page curve) and chronology protection (absence of closed timelike curves) are direct consequences of stabilizer code saturation. Formal mechanized verification blueprints in Lean 4 are provided for core structural theorems.