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

This paper develops a structural forcing theorem for admissibility under transformation. It asks not whether identity uniquely determines admissibility, but what any coherent admissibility rule must instantiate before questions of realization or governance arise. From representation non-arbitrariness, compositional stability, non-degeneracy, and verdict legibility, the paper derives a forced admissibility floor comprising quotient-relative evaluation, drift boundaries, exact preservation, composition or regime exit, verdict structure, and conflict partiality under appropriate conditions. The theorem deliberately does not establish a unique admissibility rule, canonical governance, or tolerance selection. These remain open realization questions. The result is presented as a theorem-layer companion to the Identity–Persistence Program, supplying the admissibility structure required for identity-preserving transformation and inheriting previously established capacity results by composition without reproving them. The paper concludes by identifying the characterization of a sufficient regime specification as the most load-bearing shared open problem underlying identity, admissibility, and verification.