This paper establishes a minimal, purely structural foundation for distinction inrelational systems. Starting from a nonempty underlying set equipped with a primitive identity relation satisfying reflexivity and relational congruence, we introduceincidence-based relational signatures and define structural distinction independentlyof any interpretation or semantics. We show that identity alone cannot generate distinction, and that distinction arises if and only if partial relational incidence exists.This condition is shown to be the unique structural boundary separating distinctionfrom indistinction. Relational refinement is identified as a necessary structural precondition for the possibility of partial incidence, while coarsening operations eliminatedistinction precisely by removing partial incidence. These results position partial incidence as the sole irreducible source of distinction and collapse as its exact structuraldual. All constructions are strictly formal and constitute a foundational component ofthe Anti-Ruin Program.
Swarup (Sat,) studied this question.