arXiv:2606. 28639v2 Announce Type: replace-cross Abstract: We establish the mathematical limits of AGI safety in two forms: verifying a fixed system, and verifying that a certified safety property persists once the system self-modifies.
By Jose Pascual Gumbau Mezquita
arXiv:2606. 26057v1 Announce Type: cross Abstract: AI agents are granted access to tools, APIs, and other infrastructure, making them active principals in those systems.
By Seth Dobrin, {\L}ukasz Chmiel
The paper introduces the concept of Evolutionary Safety for recursive self-improving AI, focusing on how safety properties evolve as an AI system and its successors change. It identifies key risks such as intent drift, error accumulation, and safety-property erosion, and presents a taxonomy covering agent state, model state, evaluation, environment, and update mechanisms. The authors propose methods for discovering and evaluating evolutionary risks, and outline governance principles for modification, selection, authorization, provenance, and recovery, while highlighting open problems for maintaining safety in persistent, adaptive, and recursively self-improving systems.
By Chang Gong, Jingping Bi, Di Yao, Xinjian Liang, Chao Xiang, Ruijie Guo
The paper proves that algorithmic safety verification for Turing‑complete, self‑modifying systems—whether fixed or recursively self‑improving—is fundamentally limited. Statistically, no verifier can be sound, complete, and tractable across unbounded domains, all finite configurations, or succinctly described finite environments, due to Rice’s, Gödel’s, Trakhtenbrot’s, coNP, and PSPACE barriers. Dynamically, even a single self‑modification step can render safety properties undecidable, and no total supervisory algorithm can guarantee correctness for all such transformations, though a monitor that raises alarms on violations remains feasible.
whyItMatters":"The results show that formal safety guarantees for recursive self‑improvement are unattainable, highlighting intrinsic verification barriers for advanced AI systems."
By Jose Pascual Gumbau Mezquita
arXiv:2606. 28639v1 Announce Type: cross Abstract: This article establishes the foundational mathematical limits of Artificial General Intelligence (AGI) safety, proving that the core barrier is not the impossibility of an aligned state, but its structural unverifiability.
By Jose Pascual Gumbau Mezquita
arXiv:2607. 17352v1 Announce Type: new Abstract: Designing effective Lean proof agents is a central challenge in formal mathematical reasoning.
By Yuqing Li, Zeguan Wu, Yu Gan, Junyu Liu