Dimension-W as Cognitive State Space: A Formal Foundation for Mathematical Psychology

Abstract Psychology has historically lacked a well-defined state space comparable to phase space in physics, limiting its ability to function as a fully formal, predictive science. This paper proposes Dimension-W as the latent state space underlying cognition, defined as the manifold of possible constraint configurations prior to semantic interpretation, behavior, or neural instantiation. We formally describe the mathematical structure of this space, its elements, invariants, and lawful dynamics, and show how cognitive states, meaning, and psychological phenomena emerge as trajectories within it. By identifying the correct object of study—constraint dynamics rather than mental content—this framework enables psychology to be treated as an applied dynamical systems science without reduction to neurobiology or behaviorism.