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Neutrosophic environments have gained significant relevance across diverse disciplines. Neutrosophic Over Supra Exterior Modal Topological Structure is introduced, demonstrating the generation of two distinct structures through traditional Neutrosophic Over supra topological operations, denoted as ... (closure) and ... (interior), along with novel Neutrosophic Over Supra Exterior Modal Operations, expressed as ... (modal closure) and ... (modal interior). This exploration delves into the essential properties and characteristics of these structures, illuminating their behavior and implications. To illustrate the practical relevance, a numerical example is presented, demonstrating the identification of disease types using a score function. The study conclusively shows that the Neutrosophic Over Supra Exterior Modal Topological Structure effectively classifies diseases such as tuberculosis (bacterial), malaria (parasitic), swine flu (viral), and ringworm (fungal). This dual approach ensures a holistic understanding of the topic, appealing to both theoretical and practitioners seeking practical solutions in the neutrosophic over environment. [ABSTRACT FROM AUTHOR]

The empirical correlation system serves as a crucial tool for unveiling the linear interconnections between two variables. Its significance lies in providing a prominent approach to depict a straightforward relationship without explicitly indicating a causal link between the sets involved. In the current research, an innovative concept of correlations is introduced specifically for Neutrosophic Over Soft Sets (NSO-sets). This novel framework involves a meticulous examination of basic definitions and operations associated with Neutrosophic Over Soft Sets. Furthermore, the study extends to the introduction of a groundbreaking concept: a topological space integrated with Neutrosophic Over Soft Sets (NSO-sets). This addition aims to broaden the scope of understanding and application in mathematical contexts.The research does not merely establish theoretical foundations; it also explores various properties and theorems related to the introduced concepts. This is complemented by a series of numerical examples designed to provide clarity and facilitate a comprehensive grasp of the material. To demonstrate the practical application of these concepts, the research utilizes the correlation framework to present a numerical illustration. Specifically, it is applied to determine the top-performing student at GFC School for the academic year 2022-2023, showcasing the real-world relevance and applicability of the proposed methodologies. [ABSTRACT FROM AUTHOR]