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Dovetail believes that many of the core arguments about AI danger can be formalized as precise mathematical theorems, and that doing so would provide clearer safety guidance, improve coordination among researchers, and legitimize policy interventions. Their two key bets are: (1) that conceptual arguments about existential risk from AI can be converted into rigorous mathematical statements, eliminating ambiguity and enabling better coordination; and (2) that safety-relevant properties of AI systems can be understood through general architectural properties · such as optimizer strength and proximity to ideal agent designs · using mathematical tools rather than purely empirical exploration. By establishing foundational paradigms for agent theory and deconfusing researchers about the nature of AI agents, Dovetail aims to enable downstream safety research to be more targeted and effective.