Contextuality from Single-State Representations: An Information-Theoretic Principle for Adaptive Intelligence

Abstract: Adaptive systems often operate across multiple contexts while reusing a fixed internal state space due to constraints on memory, representation, or physical resources. Such single-state reuse is ubiquitous in natural and artificial intelligence, yet its fundamental representational consequences remain poorly understood. We show that contextuality is not a peculiarity of quantum mechanics, but an inevitable consequence of single-state reuse in classical probabilistic representations. Modeling contexts as interventions acting on a shared internal state, we prove that any classical model reproducing contextual outcome statistics must incur an irreducible information-theoretic cost: dependence on context cannot be mediated solely through the internal state. We provide a minimal constructive example that explicitly realizes this cost and clarifies its operational meaning. We further explain how nonclassical probabilistic frameworks avoid this obstruction by relaxing the assumption of a single global joint probability space, without invoking quantum dynamics or Hilbert space structure. Our results identify contextuality as a general representational constraint on adaptive intelligence, independent of physical implementation.