Persistence, Entropy, and Geometry Gravity as an Admissibility Constraint on Quantum Identity

This manuscript applies a persistence-based admissibility framework for open quantum systems to causal regions in semiclassical gravity. Building on the companion preprint "Admissible Quantum Histories Under Irreversibility", the work interprets spacetime geometry as an entropy-accounting mechanism required for quantum systems to remain meaningfully identifiable under irreversible information loss. The analysis introduces no new dynamics, forces, or modifications of quantum theory or general relativity. Instead, it imposes a structural admissibility condition on physically interpretable histories: cumulative irreversible entropy production must remain bounded for system identity to remain well-defined. When applied locally at causal horizons, this requirement yields an Einstein-type field equation as a consistency condition rather than as a fundamental interaction. The contribution is interpretive and structural. Gravity is reinterpreted as the geometric response that preserves identity consistency of quantum subsystems in an irreversible universe. The results are fully compatible with standard quantum mechanics, horizon thermodynamics, and semiclassical gravity.