Formal Proof Limits Recursive Self-Improvement in AI
A new paper on arXiv (2605.27381) presents a formal separation result in classical computability theory that challenges claims about recursive self-improvement in AI. The authors prove that finite internal self-modification remains within the same computational layer, while stabilized revision requires a jump to a stronger relative level via the relativized limit lemma. This result blocks the slide from repeated internal revision to qualitatively stronger capability without a clear computational regime distinction. The paper does not deny that stronger layers can arise, but argues they are not explained by finite repetition within an already settled layer.
Key facts
- Paper arXiv:2605.27381
- Announce Type: cross
- Proves finite internal self-modification stays inside computational layer C(A)
- Stabilized revision governed by jump A' via relativized limit lemma
- Local closure versus escape theorem yields formal separation
- Challenges claims of recursive self-improvement in AI
- Published on arXiv
- Uses classical computability theory
Entities
Institutions
- arXiv