ithin the Universal Grid Mechanics (UGM) framework, admissible states are finite, continuous, bounded under update, and memory-bearing. This paper constructs the conditional observation-sector closure by defining the admissibility-intersection operator that maps hidden admissible state structure into rank-three observable coordinates on certified resolved channel domains. We define the pointwise admissible fiber D0, the admissible state-structure domain DOmega, the finite reachable update tube RDelta (X), internally generated observation-channel constraints Cᵢ, the intersection core IC (X), the minimal-burden selector SelC, and the rank-three coordinate map Q^ (3) C. The resolved observation operator is: Pi^ (3) ₒbs (X; C) = Q^ (3) C (XC), where XC in SelC IC (X), with single-valuedness holding exactly when the admissible selector has a unique minimizer and rank DQ^ (3) C (X*C) = 3. The construction explicitly builds the channel admissibility topology tauC and marks selector existence as conditional on compact-regularity of the reachable tube. It classifies three regimes: inadmissible joint channel, resolved rank-three observation, and admissible but unresolved observation. The non-generation property holds by construction because selection occurs only inside the finite reachable admissible tube. Version 1. 04d restores the corpus-continuity title while preserving the hardened conditional scope. It hardens the paper as the corpus observation-interface reference. The admissible selector class Qₐdm remains owned by this paper and every admissible selector is scoped as qᵢ = qᵢS, M, PiM, L6, RDelta. The required selector-admissibility conditions are boundedness preservation, memory compatibility, non-generation, L6 support compatibility, projection continuity, and domain certification compatibility. The revision adds explicit export rules for channel-certificate targets Pi^ (L) ₒbs, Pi^ (M) ₒbs, and Pi^ (G) ₒbs. AIO exports the certification grammar only; it does not close any named channel certificate inside this paper, and no downstream channel becomes canonical unless its nonempty intersection, singleton selector, rank-three readout, and coordinate-status certificate are separately supplied. Version 1. 04d also formalizes relay certification and burden grammar for conditional observation-chain applications. Relay counts, burden decompositions, and the projection factor Lambda₃ ≈ 0. 97 remain application-layer objects. They are forbidden from entering the admissibility-intersection core, selector geometry, pseudometric, or rank-three readout. The bibliography and reference audit now use concept DOIs from the supplied corpus ledger whenever a Zenodo latest-version DOI differs from a displayed uploaded-record DOI by one in the final suffix.
J. G. Villarroel H. (Wed,) studied this question.