Threat as a Formal Representation of Classificatory Primacy: A Re-foundation of Game-Theoretic Abstraction

This paper introduces the Tᵢ-framework, a classification-based decision architecture in which threat functions serve as the primitive formal object. Instead of deriving behavior from utility maximization, the framework models decision-making through classificatory primacy: outcomes are evaluated according to threat levels, including non-Archimedean regimes. The paper develops the formal structure of the threat operator Tᵢ, its induced preference relation, regime decomposition, and dynamic update mechanisms. It also introduces institutional transformation operators acting directly on the outcome space. The framework is presented as a re-foundation at the level of game-theoretic abstraction, not as an empirical model but as a formal architectural alternative to utility-based representations. Version: v7.2.6