Geometry and Dynamics of Complex Systems: From Empiricism to Fundamental Ontology

This work establishes a complete connection between three levels of description for complex systems: the method of phenomenological reconstruction (PRCS), the Tensor Model of Discrete Dynamics (TMDD), and Mazein Mechanics (MM). We demonstrate that key objects of the applied model—the state tensor 𝒳(ℓ)𝑎𝑘 , the logics matrix 𝐿(𝑡), and the structural risk coefficient Φ(𝑡) = rank 𝐿(𝑡)/𝑘—are natural projections of fundamental TMDD objects: the wave function Ψ and the evolution operator 𝑈. Stable patterns revealed by PRCS (using the accident at the Fukushima Daiichi NPP as an example) are interpreted as attractors in the TMDD state space, and their dynamics—as a consequence of variational principles in MM. The resulting synthesis forms a closed ontological triad “empiricism–formalism–dynamics” and paves the way for creating proactive systems of structural risk diagnostics through monitoring the parameter Φ(𝑡)