Structural Time as a Derived Multi-Component Field: A Formal Derivation of Temporal Structure from Persistence Conditions

This paper derives time as a structural consequence of restricted transformability under persistence conditions. It does not assume time as a primitive parameter. Instead, it shows that determinable existence under real transformation induces a reachability structure whose condensation yields a directed acyclic graph, establishing a partial order. From this partial order structure, three irreducible temporal components are derived and shown to be exhaustive within the persistence problem. (T1) Order time, arising from reachability depth in the condensation DAG. (T2) Load time, arising from proximity to the persistence boundary IR = 1. (T3) Integration time, arising from structural reconstruction dynamics along DAG paths. Tₛtruct (C) = (TO (C), TL (C), TI (C) ) = (DAG depth, 1/Dc (C), ∇O I (C) ) The exhaustivity of these three components is established by a functional analog of the Q1–Q3 exhaustion argument in Paper 103 (PAT Lemma 4): any temporal function on C must answer at least one of three questions about the system's position, stress, or trajectory, and these questions are pairwise non-merging and jointly exhaustive within the persistence problem. Scalar time emerges as a regime-dependent projection of this field. The result establishes time, directionality, and structural information as derived properties of the same underlying constraint: restricted transformability under persistence.