The Computational Boundary of Inference: Capability Internalization, Training, and the Turing Jump

ArXi:2605.27381v1 Announce Type: cross Claims about recursive self-improvement in AI often slide from repeated internal revision to the possibility of qualitatively stronger capability without clearly distinguishing the underlying computational regimes. This paper gives a formal separation result in classical computability theory that blocks that move under a precise modeling assumption. For an oracle $A$, let $\mathcal{C}(A)=\{B: B \leq_T A\}$ be the corresponding computational layer.