Recursive Enumerability of Classical Worlds in Finite-Information Ontologies

Refinement geometry defines a directed subdivision structure over history-prefix spaces generated by admissible stability predicates. This paper analyzes the effective realizability of that structure within represented-space semantics. Stability predicates are formalized in uniformly semi-decidable witness form, yielding certified fact sets that evolve monotonically under refinement. A partitioning functional Pi maps finite-information access to a history into the corresponding directed family of refinement partitions. We prove that Pi is Type-2 computable: every finite portion of refinement structure depends on only finitely many oracle interactions. Refinement asymmetry arises as a direct consequence of witness-based predicate semantics. Certified distinctions accumulate monotonically and are never revoked, establishing irreversibility at the level of refinement structure independent of dynamical assumptions. We further show that the canonical maximal partition induced by admissible predicates is computably generable through directed refinement of finite certification stages. Worlds, defined as blocks of the canonical maximal partition, therefore form a recursively enumerable set. Worldhood need not be decidable, and maximality is not finitely certifiable, yet every world arises through effective generation of finite refinement prefixes. In the effective setting, each refinement stage induces a computably presented equivalence relation on a countable domain of names, and branching corresponds to monotone contraction of indistinguishability rather than enlargement of the underlying history space. These results provide a computability-theoretic classification of refinement geometry, establishing constructive generation of maximal distinction structure under finite-information semantics and clarifying the effective consequences of stability-based refinement.