Distinguishability Structures and the Exclusion of Collapse

We introduce a minimal formal framework for encoding distinction without presupposing time, dynamics, refinement, interpretation, or representation. The framework consists of a carrier equipped with a primitive relation,interpreted minimally as distinguishability. Collapse is defined as the absenceof all distinction. We isolate non-collapse as a boundary condition and showthat, by itself, it entails almost no structure. We then introduce a singleadditional notion—admissible weakening—and prove that non-collapse ispreserved under admissible weakening if and only if at least one distinctionis irreducible. This establishes the minimal structural content forced byexclusion of collapse, without introducing dynamics, laws, or domain-specificassumptions.