Local Perturbative Stability and Coherence Thresholds as Conditions for Emergent Classical Spacetime

This work formulates a local admissibility condition for classical spacetime within effective field theory (EFT). It develops a stability–correlation control argument on compact causal domains, motivating a coherence functional and a scale-dependent threshold defining a coherent classical domain Omega_coh. The framework introduces no new dynamics and serves as the technical backbone for the broader emergent spacetime program (Theory 2.0).