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."
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.
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).
arXiv:2607. 13070v1 Announce Type: cross Abstract: Safety claims on self-improving agent runtimes are almost always self-graded: a policy file, a guardrail, or a README commitment.
The paper introduces a semantic elevation operator that transforms static semantic questions about a program into dynamic questions about whether a property is preserved after the program rewrites itself. It proves that for intensional transformations the elevated property remains undecidable, showing that the class of non‑verifiable properties is closed under this operator and that repeated application climbs the arithmetical hierarchy to Υ02‑completeness. The work also demonstrates that no finite tower of verifiers can provide an unconditional certificate of preservation, and suggests a categorical perspective for future exploration.
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.
arXiv:2607. 13070v2 Announce Type: replace-cross Abstract: Safety claims for self-improving agent runtimes are almost always self-graded: a policy file, a guardrail, a promise in a README.
arXiv:2602. 20064v2 Announce Type: replace-cross Abstract: Large language models are increasingly deployed as agents: they plan, call tools, read untrusted data, and act on the results.
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.
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...
The paper demonstrates that safety mechanisms for autonomous large language model agents fail to compose across iterative loops, as trajectory‑scoped monitors cannot detect attacks whose evidence is spread over multiple iterations. It introduces LoopHarness, a system that maintains a persistent, non‑decaying safety state across loops, bounding unauthorized actions with a constant that does not grow with the number of iterations. The authors provide a comprehensive evaluation protocol, including attacks that require cross‑iteration evidence, module ablations, and adaptive white‑box red‑team testing.
The paper introduces a formal framework for agent harnesses that guarantees termination, prevents drift, and enforces spend limits through bounded loops, gates, and repair relations. It proves that these guarantees hold even with repair budgets and demonstrates the effectiveness of the system by identifying vacuous gates and achieving low false‑accept rates in a 69‑loop catalogue. The authors provide an instrumented implementation and a held‑out mutant corpus to validate gate correctness.
arXiv:2606. 26406v1 Announce Type: cross Abstract: We propose a complete architectural blueprint for safe artificial general intelligence based on a closed reentry loop (D I cycle).