Emergent Lorentzian Causality from Temporal Propagation Dynamics: Operational Reconstruction of Effective Null Structure and the Causal Cone

Emergent Lorentzian Causality from Temporal Propagation Dynamics proposes a structural reconstruction of causal geometry starting from propagation dynamics rather than assuming spacetime geometry a priori.In standard relativistic physics, the causal structure of spacetime is introduced through a pre-given metric that determines the light cone and the propagation of signals. In contrast, this work develops a propagation-first framework in which the causal cone and the associated effective Lorentzian metric emerge directly from the principal symbol of a temporal propagation operator.The paper demonstrates that hyperbolic temporal dynamics naturally induce an effective metric structure whose null surfaces define the causal propagation cone. This construction provides an operational bridge between the mathematical theory of hyperbolic partial differential equations and the geometric notion of causality in relativistic physics.The framework suggests that causal geometry may be understood as an emergent structural property of propagation dynamics within a temporal medium. Rather than proposing a complete dynamical theory of spacetime, the work establishes a foundational step toward propagation-based formulations of spacetime geometry and causal structure.Key elements of the study include:reconstruction of the effective Lorentzian metric from the principal symbol of the propagation operator,emergence of the causal cone directly from temporal propagation dynamics,a theorem-level structural result connecting propagation operators to causal geometry,conceptual clarification of propagation-first approaches to spacetime structure.This work contributes to ongoing research on emergent spacetime, causal structure, and the mathematical foundations of relativistic field theories.