CDT: The Critical Distinction Trichotomy

This paper proves the Critical Distinction Trichotomy (CDT), a structural law governing anchor-free internal distinctions in finite relational systems. For admissible distinctions invariant under internal symmetries such as automorphism invariant distinctions or parameter free bounded rank first-order (FO) distinctions the paper shows that any nontrivial distinction necessarily falls into exactly one of three regimes: melting (collapse to triviality under full symmetry), global support (a quadratic lower bound on witness mass), or internal anchor defect (subquadratic distinction enabled only by a rare intrinsic structural class). The results are established using standard tools from graph automorphisms, finite model theory, and combinatorial counting, and are formulated independently of identity persistence assumptions, yielding a pre identity law characterizing the necessity and cost of intrinsic distinction.