This paper consolidates the minimal structural architecture of non-trivial persistence under real transformation. Assuming (i) a non-empty state space, (ii) admissible transformations containing at least one real transformation, and (iii) the meaningful assertion of non-trivial invariant identity, it is shown that complete transitivity of the transformation structure is incompatible with persistence. From this incompatibility follows a necessary structural asymmetry: transformation must act selectively. This selectivity induces orbit structure, a preorder of reachability (structural time), and a constraint on admissible transformation sequences. The argument is strictly conditional and does not claim a global ontology. It establishes only the structural conditions under which non-trivial identity under real transformation can coherently persist.