
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.
Witness Mass, Automorphism Invariance, Pre Identity Law, Anchor Free, Critical Distinction Trichotomy, Bonded Quantifier Rank, Symmetry Breaking, First Order Logic, Finite Model Theory, Finite Graph
Witness Mass, Automorphism Invariance, Pre Identity Law, Anchor Free, Critical Distinction Trichotomy, Bonded Quantifier Rank, Symmetry Breaking, First Order Logic, Finite Model Theory, Finite Graph
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