Sleep Transition-Coordinate Theory: State Closure and Path Dependence in Sleep Dynamics

Sleep Transition-Coordinate Theory (STCT) is a proposed physical state-closure theory of path-dependent sleep. It models sleep as a physical transition process in which a brain-body actuator enters sleep in a pre-sleep state, follows a realized sleep trajectory, and exits in a post-sleep actuator state from which later measurable outputs are produced. The manuscript defines the exact output-relevant transition statistic T_Y(H): c ↦ L(Y | C=c,H), where Y is a target vector and C is the measured conditioning state. It separates this exact conditional-law object from the applied empirical claim that, in useful sleep regimes, the statistic may admit a finite-dimensional reconstructable coordinate J_Y. The theory is presented as a proposed, testable physical theory. Existing sleep and adjacent physical evidence motivate the model class but do not prove the compact coordinate. Empirical instantiation requires frozen held-out prediction beyond measured state C, post-sleep actuator-probe mediation, negative-control nulls, enriched-state absorption, and trajectory-steering intervention tests.