Admissibility and Stability Constraints on Emergent Lorentzian Spacetime

This paper develops a structural admissibility framework for emergent spacetime models, identifying minimal pre-geometric conditions required for physically meaningful description. It shows that stability and coarse-grainability constrain admissible continuum phases to hyperbolic operator classes admitting a single distinguished direction, thereby structurally selecting Lorentzian signature within the specified framework. This work complements: Dynamical Emergence of Lorentzian Spacetime from a Non-Spatiotemporal Substrate (Zenodo DOI: 10.5281/zenodo.18131656.) Exclusion of Multi-Time Signatures and the Uniqueness of Lorentzian Continuum Phases (Zenodo DOI: 10.5281/zenodo.18839675) Together, these works form a programmatic investigation of emergent Lorentzian structure derived from minimal structural principles.