Stochastic Neutrosophic Probability Fields for Modeling Temporal Uncertainty in Digital System for Ethnic Music Education and Inheritance

In this paper, we introduce a novel mathematical framework called Stochastic Neutrosophic Probability Fields (SNPF) designed to model the evolution of truth, indeterminacy, and falsity in time-varying cultural knowledge systems. While classical neutrosophic theory treats uncertainty as a static triplet of degrees, the SNPF approach redefines these components as stochastic functions of time, governed by differential and probabilistic dynamics. This allows for the modeling of how collective truth, ambiguity, and rejection shift in response to temporal, social, and cognitive fluctuations, particularly relevant in domains such as the international transmission of traditional Chinese ethnic music through digital media. We present formal definitions, derive foundational equations, prove theoretical properties, and illustrate the utility of the model in capturing the dynamic interplay between belief systems and cultural symbols. This work establishes a mathematically rigorous and application-driven expansion of neutrosophic logic.