Sharp Computability Bounds for Nonforking Sections

We study computability of sections of the restriction map S_1(N) to S_1(M) for countable stable models M elementary in N. Types are represented by characteristic functions on formulas with named parameters, and the two elementary diagrams are separately decidable. Classical stable definability gives a continuous section computable from the input type together with the fixed oracle 0'. This bound is sharp, already for the decidable, omega-stable, omega-categorical theory of infinitely many infinite equivalence classes. For a fixed decidable-range elementary inclusion in this theory, an oracle X computes a section exactly when it computes the set of classes of N that meet M. Explicit inclusions realize every computably enumerable degree as this least auxiliary degree. Thus a computable section need not exist, although every individual type in the example is computable. In contrast, a decidable full diagram of the predicate expansion (N,M) gives a computable section for every stable theory. The result addresses a Type-2 formulation of an AIM question whose printed statement leaves the effective presentation unspecified. Unrefereed preprint released for independent mathematical scrutiny. Publication on Zenodo does not constitute peer review. AI-assisted tools supported research, computation, proof development and manuscript preparation. The author remains responsible for all claims and the final text. The theorem is presentation-sensitive: the original AIM question does not state an effective coding convention, and the full predicate-pair input yields a positive answer. No absolute priority or independent-verification claim is made. Corpus identifier: AIM-LOGIC-0084.