Toward the Formalization of Viability Research: A Mathematical and Computational Framework for Vitology.

The increasing complexity of modern scientific research requires rigorous mathematical and computational approaches capable of integrating knowledge across multiple disciplines. Although systems science, cybernetics, complexity science, resilience research, and artificial intelligence have significantly advanced the study of complex systems, no unified formal framework has yet been developed for investigating viability as a universal scientific object. This article proposes the first conceptual foundations for the formalization of viability research within the framework of Vitology. Rather than introducing a finalized mathematical theory, the study outlines a methodological program for developing formal quantitative, qualitative, computational, and interdisciplinary models capable of describing, comparing, and predicting the viability of complex systems. The proposed framework considers formalization as a multilevel process involving conceptual definitions, mathematical representation, computational modeling, comparative analysis, empirical validation, and artificial intelligence–assisted discovery. Within this approach, the Space of Harmony is introduced as a multidimensional computational environment in which viable system states and candidate universal regularities may be systematically investigated. Artificial intelligence plays a central methodological role by enabling comparative analysis of large interdisciplinary datasets, multidimensional pattern recognition, computational simulation, hypothesis generation, and iterative refinement of formal models. At the same time, the article emphasizes that AI supports scientific discovery but does not replace theoretical reasoning, mathematical proof, or empirical verification. The study argues that the formalization of viability research represents an essential step toward establishing Vitology as a rigorous interdisciplinary scientific framework. It provides methodological foundations for future mathematical models, computational algorithms, empirical investigations, and the identification of universal regularities governing the preservation, restoration, and development of viability across natural, biological, ecological, social, organizational, technological, and artificial systems. Keywords Vitology, viability, formalization, mathematical modeling, computational modeling, artificial intelligence, systems science, interdisciplinary research, Space of Harmony, Harmony Navigation, computational framework, empirical validation.