Saturation-Splitting Hypothesis: Integrated-Intelligence Saturation and the Divergence of Local Improvement in Self-Improving AI

Recursive self-improvement is often discussed as though an AI system could increase its intelligence without bound. This paper applies the author's previously proposed AI Saturation-Splitting Hypothesis to the narrower case of single-agent self-improvement. The underlying hypothesis regards the need to form a finite, integrated output as a possible source of structural limits on intelligence: expanded exploration does not remove the need to select and reconcile what is ultimately expressed. The hypothesis proposes that, as the intelligence of a single AI approaches a structural upper bound, further intellectual expansion may proceed not as uniform growth within one unit but through differentiation into multiple specialized agents or intellectual components. This paper does not address the hypothesis as a whole; it examines the case in which a single AI continues self-improvement without such differentiation. If intelligence includes not only task performance but also the ability to maintain operational identity while handling ambiguous, indeterminate, or value-laden problems, self-improvement may approach a structural upper bound of integrated intelligence. Improvement need not stop abruptly. If additional revisions continue after the remaining margin for improving integrated intelligence has narrowed, the integration load required to align those revisions with the objective, evaluation criteria, context, and revision history may become large relative to the remaining integration margin. As a result, it may become difficult to keep new revisions consistently subordinate to the original objective, and objective drift may begin. At the same time, local capabilities and measurable scores may remain improvable, allowing optimization pressure to shift toward locally measurable and improvable targets. Local improvement may therefore appear to be progress in intelligence as a whole even while continuity of objectives, evaluation criteria, and revision history has already become unstable. This paper calls this potential intra-agent state saturation-fragmentation. The claim is neither that recursive self-improvement must fail nor that proxy optimization is inevitable near an upper bound. The contribution is a causal hypothesis linking a shrinking improvement margin for integrated intelligence, continued revision and the relative growth of integration load, weakening subordination to the original objective and the onset of objective drift, continued local improvement, a shift of optimization pressure toward local targets, and the possibility that local improvement appears to be global progress. The proposal is distinguished from generic diminishing-returns arguments, Goodhart-type failures, reward hacking under finite evaluation, discussions of an introspection threshold, and compositional drift, and it yields qualitative signatures for future longitudinal evaluation.