The Principle of Ontological Statistical Convergence: Physical Statistical Convergence Laws in Deterministic Causal Systems

Traditional physics often directly attributes the phenomenon of frequency convergence in large samples to the existence of intrinsic randomness at the fundamental physical level. However, the mathematical Law of Large Numbers (LLN) is merely a theorem within a formal axiomatic system and makes no ontological assertions regarding its physical origin. Equating frequency convergence with intrinsic randomness is an unverified logical extrapolation. Building upon the "Ontology-Information Dichotomy Framework," this paper proposes the Principle of Ontological Statistical Convergence: In a physical system with an underlying fully deterministic causal structure, the frequency of sample occurrences will progressively converge to the objective frequency ratio inherent in the ontological statistical truth set after numerous independent repeated physical samplings. This convergence behavior does not depend on object intrinsic randomness, information gap , or the existence of an observer. This paper designs a transparent visualized shaking experiment, a foreign object perturbation experiment, and a sample size-relative fluctuation experiment. Under the conditions of (complete information) and completely determined single-run physical results, the large-sample frequency convergence phenomenon is reproduced, and it is empirically demonstrated that the convergence target is entirely determined by the physical interaction structure. This paper strictly distinguishes the mathematical LLN from physical statistical convergence, corrects the traditional logical leap of attributing convergence to intrinsic randomness, and lays a solid foundation for a unified physical statistical theory across macro and micro scales.