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. The resulting separation gives a computability-theoretic limit on a broad class of recursive-improvement narratives in which repeated internal updating is treated as sufficient for qualitative capability ascent.

翻译：关于人工智能中递归自我改进的论断，往往从重复的内部修订滑向定性能力提升的可能性，却未清晰区分其底层的计算机制。本文在经典可计算性理论中给出一个形式化分离结果，在精确建模假设下阻断了这一滑移。对于预言机$A$，令$\mathcal{C}(A)=\{B : B \leq_T A\}$为对应的计算层。我们证明：有限内部自我修改仍停留在$\mathcal{C}(A)$内部，而稳定化修订则通过相对化极限引理由跃迁$A'$支配。结合局部封闭性与逃逸定理，这给出了层内迭代与跃升至更强相对层级之间的清晰形式化分离。关键并非在于更强层级永不出现，而在于它们无法被已在某一确立层内的有限重复所解释。由此得到的分离，为一大类将重复内部更新视为定性能力跃升充分条件的递归改进叙事，提供了可计算性理论层面的限制。