Structural Time: Time as a Necessary Consequence of Admissible Persistence Architecture

The Foundation Series (Papers 000–005) derived the minimal structural admissibility architecture of determinate persistence: distinguishability, restricted admissibility, asymmetric transformation topology, finite integration capacity, and bounded identity continuity. This paper derives structural time as a necessary consequence of this architecture. The central claim: time is not primitive. It is the directed partial ordering generated by restricted admissibility and asymmetric transformation topology on a persistent system's state space. Any LP-admissible system generates structural time necessarily — not as an additional assumption but as a direct structural consequence of Papers 000–004. Three theorems are proven. Theorem D1.1 — Directed Ordering: LP admissibility generates a non-symmetric directed partial order on Q. Theorem D1.2 — Structural Irreversibility: the directed ordering is irreversible in the Recovery Narrowing regime. Theorem D1.3 — Path Dependence: structural time intervals are path-dependent under structural hysteresis. Together these establish Corollary D1.4 — the Structural Arrow of Time: every LP-admissible system generates an asymmetric temporal direction without assuming time primitively. Structural time is not physical time. It is the structural ordering that any physical, psychological, or institutional time must instantiate to function in a persistence-capable domain.