Finite Operational Distinguishability as a Structural Condition for Predictive Physical Law

Foundational result: predictive physical laws require finite operational information. Physical prediction presupposes that physical states can be operationally distinguished and manipulated within finite regions of space and time. Continuum descriptions, however, appear to admit infinitely detailed microscopic configurations, raising a tension between infinite descriptive structure and finite predictive capacity. This work identifies a structural resolution of this tension. Under minimal operational assumptions — finite operational capacity, operational stability, and autonomy of prediction — we prove that only finitely many operationally distinguishable states can be physically relevant in any bounded region. Finite operational structure thus emerges as a necessary consequence of the conditions required for predictive physical law. The result provides a general structural constraint on physical theories and suggests that continuum descriptions should be understood as effective representations of an underlying finite operational structure.