Temporal Algebra: Time Begins at $\delta(\psi) \neq 0$

Temporal Geometry redefines time as a structural phenomenon arising from perturbation-driven leaps within directed acyclic graph (DAG) systems, rather than as a continuous external parameter. Time emerges from non-zero structural pertur- bations δ(ψ), adhering to directional coherence and noncommutative composition. This framework introduces five axioms and two theorems that form a minimal generative system for time, supported by an algebraic structure and a categorical framework. Unlike classical models that treat time as absolute, metric-curved, or passive, Temporal Geometry captures time as a discrete, structural process trig- gered by misalignment. This paper outlines the axioms, theorems, algebraic rules, categorical formulation, symbol glossary, definition of path equivalence, and struc- tural testing using open-access gravitational wave data [1], emphasizing temporality as an emergent structural property.