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We formalize this boundary through two central impossibility results: the Unverifiability Theorem of Alignment and the Theorem of Finite Structural Unverifiability of AGI Alignment. We ground this boundary at Trakhtenbrot's Wall, demonstrating that contemporary engineering defenses relying on finite hardware or halting architectures fail to escape logical obstructions. This failure manifests as an inescapable triad of containment failures: open domains yield fundamental undecidability (Rice and G\\\"odel); universal finite verification collapses into algorithmic incomputability (Trakhtenbrot); and particular bounded environments trap the supervisor within intractable bounds in the worst case. As a direct structural cor","title":"The Undecidability of Artificial General Intelligence (AGI) Alignment","url":"https://arxiv.org/abs/2606.28639","vendor":"arxiv_cs_ai"},"summary":"arXiv:2606.28639v1 Announce Type: cross \nAbstract: 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. We formalize this boundary through two central impossibility results: the Unverifiability Theorem of Alignment and the Theorem of Finite Structural Unverifiability of AGI Alignment. We ground this boundary at Trakhtenbrot's Wall, demonstrating that contemporary engineering defenses relying on finite hardware or halting architectures fail to escape logical obstructions. This failure manifests as an inescapable triad of containment failures: open domains yield fundamental undecidability (Rice and G\\\"odel); universal finite verification collapses into algorithmic incomputability (Trakhtenbrot); and particular bounded environments trap the supervisor within intractable bounds in the worst case. 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