Equivalence as Absence of Admissible Witness

This paper establishes a boundary criterion for equivalence in closed admissible systems. It proves that equivalence is not a positive identification or constructed relation, but the absence of any admissible witness capable of distinguishing between candidates while preserving standing. Apparent distinctions that rely on external context, hidden parameters, or deferred justification are shown to be illicit and collapse under admissible scrutiny. The analysis is strictly eliminative and non-constructive: it introduces no new primitives, specifies no procedures, and provides no operational tests. The result functions as a boundary theorem, fixing equivalence as a negative condition enforced by admissibility rather than a representational choice or interpretive convention.