Minimal Structure of Persistence under Real Transformation

This text establishes the minimal structural condition of non-trivial persistence under real transformation. Starting from a minimal existence assumption, it is shown that non-trivial identity presupposes difference and minimal invariance. Under the condition of real transformation, it is formally proved that persistence enforces the non-transitivity of the transformation structure. From this it follows necessarily that the state space is selectively partitioned into stability classes. Persistence under real transformation is therefore only possible if transformation acts in a structurally asymmetric manner. The statement is strictly conditional and claims no global ontology, but a necessary structure wherever non-trivial identity under real transformation is meaningfully asserted.