Ontology of quantum correlation: hidden parameter for a pair or an ensemble?

The article is dedicated to the analysis of the ontological status of the hidden parameter λ in the context of Bell's theorem and quantum correlations. In the standard formulation of Bell's inequalities, the hidden parameter is attributed to an individual pair of entangled particles: it is assumed that λ determines the measurement outcomes for each specific pair and, therefore, serves as the carrier of correlation at the level of a single event. This interpretation gives rise to a well-known dilemma: the violation of Bell's inequalities in an experiment is interpreted as evidence of the impossibility of any local realistic theory, leading to conclusions about the non-locality of nature or a rejection of realism. The subject of this study is the very legitimacy of attributing the hidden parameter to an individual pair of particles. The question is posed: is λ a property of a single pair or a characteristic of a statistical ensemble? The problem is considered in the context of the classical philosophical opposition between the singular and the general, as well as the mereological relationship between parts and the whole in relation to the quantum-mechanical description of reality. A conceptual analysis of the mathematical structure of Bell's theorem is employed, along with a comparison of the ontological assumptions of the standard and ensemble interpretations, as well as a philosophical analysis of the levels of realization of correlation. The scientific novelty of the work lies in the explicit formulation of the question regarding the level of ontological belonging of the hidden parameter—a question that is typically not addressed in standard discussions around Bell's theorem. It is shown that attributing λ to an individual pair of particles represents not an experimentally justified fact, but an ontological assumption embedded in the formalism at the stage of its construction. This assumption predetermines the interpretation of the results: the violation of Bell's inequalities is perceived as a collapse of local realism only under the condition that correlation must be realized at the level of a single pair. If the correlation is realized at the level of the ensemble—through the structure of the distribution ρ(λ)—then the violation of Bell's inequalities indicates not non-locality, but the inadequacy of an individual ontology of the hidden parameter. The conclusion is that the standard interpretation of Bell's theorem conflates two ontological levels of description, and a correct delineation of these levels removes the necessity of choosing between non-locality and a rejection of realism.