ora-0093
6.6 Executions realize ORACLE sections
Every well-typed execution of a UOCL algorithm determines a section of the hypothesis fibration along its realized presentation path, together with comparison maps satisfying the algorithm’s declared coherence laws. Conversely, an abstract ORACLE section is realized by a UOCL algorithm only after effective or explicitly specified selection, probing, and repair data have been supplied.
At time \(t\), the execution supplies an object \(M_t\in H_d(T_t)\). Each successful assimilation supplies a comparison \(u_t^*M_{t+1}\to M_t\); a repair step supplies the corresponding comparison after change of base. The typing and coherence conditions therefore give a section along the path. The converse fails without additional data because existence of a lift does not provide a method for finding one, and existence of a separating probe or repair does not choose it uniformly.
This proposition locates a basic computability boundary. Universal properties can characterize a correct answer while equality, equivalence, extension, or selection in the relevant category remains undecidable. UOCL must therefore declare its representation of categories and its effective fragment; it cannot obtain an algorithm merely by appealing to Yoneda or Kan extension.