Mathematical Models of Viability: Toward a Unified Computational Framework in Vitology

The development of Vitology as a formal interdisciplinary scientific framework requires the transition from conceptual definitions and quantitative indicators toward mathematical models capable of describing, comparing, predicting, and computationally investigating the viability of complex systems. Previous studies within the Vitology Scientific Series formulated the conceptual foundations of viability, proposed a research program for identifying universal regularities, introduced the Space of Harmony, outlined principles of formalization, and developed the basis for a formal metric system of viability. This article represents the next stage of that research program by proposing methodological foundations for mathematical models of viability. Rather than introducing a finalized mathematical theory, the study develops a conceptual framework for constructing multidimensional, dynamic, computationally implementable, and empirically verifiable models that integrate viability indicators into coherent representations of system states and developmental trajectories. Within this framework, the Space of Harmony is interpreted as a computational state space in which systems may be represented as multidimensional vectors or trajectories defined by indicators of integrity, harmony, coordination, adaptation, regeneration, resilience, development, and environmental interaction. Mathematical models of viability are therefore understood not as isolated equations but as structured representations of relationships among multiple dimensions of system organization. Artificial intelligence is considered an essential methodological instrument for constructing, testing, and refining such models. AI may support the identification of nonlinear relationships, classification of system states, simulation of developmental trajectories, detection of early signs of declining viability, and discovery of candidate universal regularities across interdisciplinary datasets. The proposed approach establishes a foundation for the future development of a unified computational framework in Vitology. Such a framework may support mathematical modeling, predictive diagnostics, simulation, decision support, and interdisciplinary research aimed at understanding, preserving, restoring, and increasing the viability of natural, biological, ecological, social, organizational, technological, and artificial systems. Keywords Vitology, viability, mathematical models, computational framework, Space of Harmony, Harmony Navigation, viability indicators, systems science, artificial intelligence, multidimensional modeling, dynamic systems, predictive diagnostics, empirical validation, interdisciplinary research.