Transformation Under Constraint - A Structural Derivation of Transformation from the Persistence Condition

Transformation is not a primitive. The persistence condition determines what counts as transformation, whether a transformation is admissible, and whether transformation can be defined at all. A transformation is a state transition that imposes a non-zero integration requirement on the persistence relation — and this definition is not a choice. Any alternative definition cannot generate a persistence-relevant admissibility condition. Three results follow necessarily: (1) the Transformation Constraint Theorem — admissibility of transformation is equivalent to satisfaction of the persistence condition; (2) the Persistence Primacy Theorem — transformation is definable only for systems that admit a persistence relation; (3) the Monotonic Expansion Proposition — the admissible transformation set is ordered by integration capacity. Transformation is therefore derived, structured, and system-relative. It is not prior to the persistence condition. It is defined by it.