Minimal Structural Conditions of Identity under Real Transformation

This paper establishes the minimal structural conditions under which identity can persist under real transformation. It assumes only: 1. Determinable existence (non-trivial differentiation) 2. Real transformation It is shown that: • full transitivity of transformation is impossible • transformation must be selective • identity is induced as maximal transformation-invariant equivalence • reachability decomposes into strongly connected components • partial order exists only on equivalence classes • temporal direction emerges under non-invertible transformation • persistent systems necessarily decompose into invariant and variable structure The result is purely structural and conditional. This minimal architecture is referred to as La Profilée (LP).