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. 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 archit
This paper offers a foundational mathematical proof, potentially preempting future arguments about AGI safety verifiability, positioning itself as a landmark ahead of widespread AGI deployment.
It fundamentally challenges the prevailing assumption that AGI alignment is a solvable engineering problem, instead positing it as an inherently unverifiable state, which dictates an entirely new approach to AGI development and regulation.
The pursuit of 'perfect' AGI alignment by engineering means becomes computationally intractable, shifting focus from verifiable safety to robust containment, control mechanisms, or alternative architectures.
- · Formal verification specialists
- · Hardware-based safety mechanism developers
- · AGI containment research
- · AGI alignment optimists
- · Pure software-based alignment strategies
- · Regulatory bodies assuming verifiable AGI safety
Research priorities for AGI safety will pivot from alignment verification to robust containment and control or entirely new architectural paradigms.
Public and government trust in achieveable AGI alignment may erode, leading to increased calls for extreme caution, slower development, or even moratoriums.
The development trajectory of AGI could fracture significantly, with some pursuing capabilities at all costs and others adopting fundamentally different, possibly capability-limited, approaches for 'safer' systems.
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Read at arXiv cs.AI