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: Determinable existence (non-trivial differentiation) 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).