Microscopic Derivation of Lorentzian Spacetime and Covariant Field Dynamics from Cost-Enriched Open Quantum Systems

We demonstrate that classical Lorentzian spacetime and general relativity emerge as the macroscopic thermodynamic compilation of open quantum systems under categorical process-cost. By replacing the idealization of frictionless deduction with the enriched category \mathbf{CostCat}, the primary obstacles of emergent gravity are resolved within a single self-consistent field theory.