Algorithmic Unverifiability of Safety for Fixed and Recursively Self-Improving Systems

Excerpt

arXiv:2606.28639v3 Announce Type: replace-cross Abstract: We establish mathematical limits of algorithmic safety verification for Turing-complete self-modifying systems, the class in which recursive self-improvement takes place, both for a fixed system and across its own modification. Statically, no verifier is sound, complete and tractable: over unbounded domains by Rice's and G\"odel's theorems, over all finite configurations by Trakhtenbrot's theorem, and over succinctly described finite envi