Constraint-Based Selection of Geometry from 2 Quantum States

This work introduces a constraint-based selection framework for evaluating which quantum states are capable of supporting coherent, classical-like spacetime geometry. Rather than proposing new dynamical laws, the framework reframes spacetime emergence as a selection problem governed by compatibility across known physical constraints. Candidate quantum states are evaluated according to coupled admissibility conditions including global causal consistency, thermodynamic compatibility, encoding robustness consistent with quantum error correction structure, and convergence across equivalent physical descriptions. Instead of assigning states a binary geometric/non-geometric classification, the framework introduces “failure profiles” that characterize how constraint compatibility weakens across different channels. The framework is applied to the Hawking–Page transition as a worked example. Within this interpretation, the transition is treated not as a binary switch between geometry and non-geometry, but as a change in admissibility structure across competing thermodynamic phases. A proposed ordering of constraint degradation—where thermodynamic compatibility weakens prior to the degradation of encoding robustness and cross-description convergence—is identified as a testable prediction. This work does not introduce new physical degrees of freedom or modify established theories of gravity. Its primary contribution is organizational and diagnostic: a structured methodology for evaluating when known physical constraints are jointly sufficient to support emergent geometric structure in quantum-gravitational settings.