A Forcing Theorem for Admissibility Under Transformation: Coherent Admissibility, Representation Invariance, and the Structural Floor Beneath Persistence

Abstract This paper develops a forcing theorem for admissibility under transformation. Rather than asking whether a declared invariant basis uniquely determines an admissibility rule, it asks a weaker and more fundamental question: what structural roles must any coherent admissibility rule instantiate at all? Under assumptions of applicability, representation non-arbitrariness, non-degeneracy, compositional stability, and verdict legibility, the paper proves that coherent admissibility necessarily instantiates a structural floor comprising an admissibility-bearing transformation domain, an identity-bearing target, quotient-relative evaluation (possibly trivial), a drift or corridor boundary, an exact preservation floor, composition or explicit regime exit, and a verdict space. Genuine conflict further forces either a declared resolver or partiality, with asymmetric hidden resolvers excluded by representation invariance and symmetric hidden resolvers requiring an explicit regime-specification discipline. For finite conflict structures, lawful determinate refinements form the resolution-space lattice. The theorem is intentionally non-unique. It does not identify a canonical admissibility rule, derive governance from the invariant basis, or determine tolerance, aggregation, or conflict structure. Those remain explicitly open. Instead, the contribution is structural: any coherent admissibility rule satisfying the stated problem conditions must instantiate the forced roles established here. The paper is positioned as a theorem-layer companion to the Identity–Persistence Program. It supplies the admissibility structure required for identity-preserving transformation and inherits previously established capacity results by composition without reproving them. The most load-bearing shared frontier is the characterization of a sufficient regime specification capable of supporting coherent persistence and admissibility.