Relativistic Causality from Continuity Constraints in Emergent Spacetime

This preprint examines the origin and status of relativistic causal structure in physical theories where spacetime itself is not assumed as fundamental but is generated through physical processes. Rather than treating relativistic causality as a postulated principle, the work investigates the minimal and physically admissible conditions under which a stable causal geometry can arise when spacetime emerges. Focusing on general requirements such as causal continuity, background independence, and dynamical stability, the analysis shows that relativistic spacetime is not one option among many but the unique causal organization compatible with a well-defined principle of minimal energy at the level of spacetime itself. Alternative causal architectures—such as non-Lorentzian geometries or scenarios involving multiple limiting speeds—are argued to lead generically to instability or ill-defined energetics, based on general structural consistency considerations rather than explicit model-by-model comparisons. The discussion is motivated in part by cosmological scenarios in which spacetime is generated through high-curvature transitions, including finite cosmic lineage models, but the main result does not depend on genealogical inheritance. Even the earliest physically meaningful universe is shown to be constrained to a relativistic causal structure by stability requirements alone. Within lineage-based cosmologies, causal inheritance plays a secondary role by ensuring the persistence of a constraint already imposed at the moment spacetime comes into existence. The paper is intended as a conceptual and structural contribution to the foundations of relativity, cosmology, and spacetime emergence, complementing technical approaches in quantum gravity and related frameworks.