CDT: The Critical Distinction Trichotomy

This paper proves the Critical Distinction Trichotomy (CDT), a structural classification theorem for anchor-free unary distinctions on finite relational structures. Two admissibility models are treated independently and in full detail: parameter free first order definability at bounded quantifier rank and automorphism-invariant distinctions under group actions. In each model, any nontrivial admissible distinction is shown to fall into exactly one of three regimes: melting, where symmetry or indistinguishability forces triviality; global support, where the absence of rare intrinsic classes enforces a quadratic lower bound on witness mass; or internal anchor defect, where a small parameter-free definable exceptional class permits subquadratic distinction. All derivations are explicit and non-compressed. The results are pre-identity in nature and characterize the existence and cost of invariant distinction without assuming identity persistence, temporal order, or physical interpretation.