This work develops a necessity based structural law governing physical and chemical evolution under coherence constraints. It derives a condition for admissible evolution requiring closure of the structure set under coherence preserving updates: if closure fails, additional structures must exist to restore admissibility. The framework introduces coherence as a primitive admissibility condition and formalizes evolution as an update process constrained by coherence preservation. Three equivalent formulations of coherence are presented predicate, scalar functional, and certificate (verifier) form and their equivalence is established within the formal system. The resulting law is domain independent and does not presuppose physical, chemical, logical, or computational primitives. It applies wherever structures evolve under admissibility constraints and yields a necessary completion principle: incomplete structure sets imply the existence of further admissible structures required for coherent evolution. This theory provides a structural foundation for physical and chemical ontology grounded in admissible evolution rather than empirical field assumptions, offering a minimal, necessity-based completion principle for coherent systems.
Kearon Allen (Mon,) studied this question.