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

This structure is not introduced here. It is already implicit in the Foundation Series and is isolated in the present paper. Papers D001 and D002 derived structural time and structural information as the backward and forward faces of LP admissibility restriction. This paper derives structural causality as the third necessary consequence: the ordered dependency structure generated when directed temporal ordering (D001) and restricted informational structure (D002) operate jointly on a persistent system. The central claim: causality is not primitive. It is the asymmetric dependency relation that LP admissibility necessarily generates between states connected by admissible transformations. Any LP-admissible system has structural causality — not as an additional assumption but as a direct consequence of what D001 and D002 already established. Three theorems are proven. Theorem D3.1 — Causal Dependency: admissible transformation generates an asymmetric dependency relation between predecessor and successor states. Theorem D3.2 — Causal Irreversibility: causal dependency is strictly irreversible in the Recovery Narrowing regime — causes cannot be undone. Theorem D3.3 — Causal Propagation: structural disturbance propagates causally through the admissibility class, bounded by integration capacity. Together these establish Corollary D3.4 (Class C): physical causation, biological signal transduction, organizational decision propagation, and psychological intention are domain instantiations of structural causality. Causality is not a metaphysical glue added to physics. It is the structural fact that admissible transformations generate asymmetric dependencies — and nothing more is needed.