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:2609.06036v1 Announce Type: new
Abstract: Proposal-based controllers---learned policies, language-model planners, and other black-box \emph{generators}---are increasingly deployed behind runtim...
By Guangxi Wan, Yongbo Xie, Yuqi Liu, Qingwei Dong, Qingxin Li, Hongfei Bai, Peng Zeng
arXiv:2609. 11326v2 Announce Type: replace-cross Abstract: We ask whether it can be certified algorithmically that a self-modifying computational system preserves a safety property at its next step (preservation) and along its whole evolution (persistence).
By Jose Pascual Gumbau Mezquita
arXiv:2607. 11951v1 Announce Type: new Abstract: Large language models can write SQL, but enterprise deployment demands more than plausible text: outputs must be syntactically valid, must respect per-role and per-schema policy, must carry provable (not best-effort) guarantees, must not slow down as generations grow, and must leave a compliance-grade record of every decision.
By Mohsen Arjmandi
The paper presents a production streaming guardrail system that ensures exact release‑boundary equivalence for language‑model outputs. It compiles regular‑language predicates into persistent NFAs, distinguishes stable from provisional states, and applies document‑order priority to decide before each chunk release. Evaluations on over 200,000 partitioned cases show zero mismatches and demonstrate that incremental matching can outperform native regex at larger chunk sizes while remaining competitive at smaller ones.
By Christopher M. Frost
arXiv:2607. 22868v1 Announce Type: new Abstract: Runtime guardrails act before irreversible tool calls, but their guarantees depend on what policy state is representable, what a judge observes, and whether intervention changes future behavior.
By Shawn Ray
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. 07316v2 Announce Type: replace-cross Abstract: Can a committee of LLM agents reach agreement that is certifiable at the level of meaning, not only at the level of a label?
By Haoran Xu, Lei Zhang, Iadh Ounis, Xianbin Wang
arXiv:2608. 15147v1 Announce Type: new Abstract: Machine intelligence has conquered the symbolic world but stalled at the physical one.
By Jiang Jiang (Persagy Science and Technology Co., Beijing, China), Yifu Sun (Persagy Science and Technology Co., Beijing, China), Qi Shen (Persagy Science and Technology Co., Beijing, China)
The paper introduces Rewindable Interactive Proofs (RIPs), a new model for scalable oversight where a weak verifier can rewind a powerful AI prover to an earlier state during interaction. RIPs enable efficient verification of computations whose outputs are robust to small changes in oracle answers, achieving near-linear verifier time without relying on cryptography. The authors implement the protocol, demonstrate a preliminary MNIST experiment, and show that an RIP can outperform a state‑of‑the‑art deployed proof system.
arXiv:2607. 29496v1 Announce Type: new Abstract: We study transcript management for fixed, finite-precision causal Transformers.
By Sergey Salishev
The paper introduces Rewindable Interactive Proofs (RIPs), a new model for scalable oversight where a weak verifier can rewind a powerful AI prover to an earlier state during interaction. RIPs enable verification of oracle‑aided computations that are robust to small changes in oracle answers, achieving near‑linear verifier time without relying on cryptography. The authors provide a construction, implement it on MNIST, and demonstrate that RIPs can outperform existing proof systems in practice.
By Ziyi Guan, Yael Tauman Kalai, Ron Rothblum, Zoe Xi