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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. We prove that finite internal self-modification remains inside $\\mathcal{C}(A)$, while stabilized revision is governed instead by the jump $A'$ via the relativized limit lemma. Together with a local closure versus escape theorem, this yields a clean formal separation between within-layer iteration and ascent to a stronger relative level. The point is not that stronger layers never arise, but that they are not explained by finite repetition inside one already settled layer. The resulting sepa","title":"The Computational Boundary of Inference: Capability Internalization, Training, and the Turing Jump","url":"https://arxiv.org/abs/2605.27381","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.27381v1 Announce Type: cross \nAbstract: 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. We prove that finite internal self-modification remains inside $\\mathcal{C}(A)$, while stabilized revision is governed instead by the jump $A'$ via the relativized limit lemma. Together with a local closure versus escape theorem, this yields a clean formal separation between within-layer iteration and ascent to a stronger relative level. The point is not that stronger layers never arise, but that they are not explained by finite repetition inside one already settled layer. 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