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.
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:2608. 15147v1 Announce Type: new Abstract: Machine intelligence has conquered the symbolic world but stalled at the physical one.
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: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).
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:2605. 09045v2 Announce Type: replace Abstract: Agentic frameworks are the software layer through which AI agents act in the world.
arXiv:2606. 03019v1 Announce Type: cross Abstract: Copyleft, as implemented in licenses such as the GNU General Public License, was a legal hack that used copyright to guarantee user freedom by tying the availability of source code to every act of distribution.
arXiv:2607. 04505v1 Announce Type: new Abstract: We advance the hypothesis that human mathematical reasoning, constrained by both the undecidability and the computational intractability of even modest logical fragments, relies fundamentally on pattern matching from domains external to pure deduction.
arXiv:2607. 24243v1 Announce Type: new Abstract: Mainstream AI research emphasises capability growth and tolerates low failure rates when average-case performance is high.
arXiv:2603. 25414v4 Announce Type: replace-cross Abstract: A prevailing assumption in machine learning is that model correctness must be enforced after the fact.
arXiv:2303. 04203v4 Announce Type: replace Abstract: The theory of computation was built to answer Turing's question: what is effectively calculable by an unbounded, immortal, disembodied agent following rules?
arXiv:2605. 24727v2 Announce Type: replace Abstract: While large-scale models such as LLMs and diffusion models have achieved practical success, public institutions have emphasized the importance of explainability in AI.