The Persistence Condition Across Theories - What every established theory of transformation presupposes - and what changes when the presupposition is made explicit

Every theory of transformation, adaptation, development, or change operates under a necessary structural condition that is not made explicit: that the systems it describes persist as identifiable units through the processes it analyzes. None of these theories derive the condition under which this structural condition is satisfied. The persistence condition IR = R / (F·M·K) ≤ 1 is the formally derived necessary and sufficient condition for what they all assume. This paper establishes a Universality Theorem — Theories of transformation describe how systems change. This description is only possible if the changing states are attributable to a single system. This is not an assumption. It is a condition of coherence. If no persistence relation holds, there is no transformation — only a sequence of unrelated states. A theory that describes transformation therefore does not merely assume persistence. It can only be formulated if persistence is structurally satisfied. Theorem (Universality of the Persistence Condition). A coherent theory of transformation can only be formulated for systems that satisfy a persistence relation. A description that does not satisfy this condition is not a theory of transformation, but a description of unrelated state sequences. The persistence condition is the unique formally derived specification of this necessary structural condition — as formally proved in Paper 103 (DOI: 10.5281/zenodo.19597721). Across established theories in all major domains of science and philosophy, this paper identifies: (1) what each theory can do without the persistence condition; (2) what the persistence condition adds structurally; and (3) what becomes determinate once the condition is made explicit.