α Ω The Admissible Interior as a Closed Structure

This paper establishes the admissible interior as a closed structure, denoted α_Ω, beyond which no further admissible differentiation is possible. The interior is not an approximation, emergent regime, or provisional domain; it is shown to be terminal once admissibility and standing preservation are enforced fail-closed. The analysis demonstrates that all apparent routes to extension—finer resolution, deeper structure, additional parameters, or meta-level refinement—either reduce to internal re-descriptions within α_Ω or violate admissibility through illicit scope transport or reanchoring. When these moves are excluded, the admissible interior admits no further structural degrees of freedom. The result fixes α_Ω as the final admissible domain of coherent representation. No constructions, dynamics, or operational criteria are introduced. The paper records a necessity result: the admissible interior is closed by exhaustion, and any attempt to go beyond it is not incomplete inquiry but inadmissible inquiry.