Phenomenological Reconstruction of Complex Systems (PRCS): A Method for Identifying Stable Patterns Without a Model.

In conditions of complexity, openness, and singularity of systems, the traditional paradigm of linear causality loses its predictive and explanatory power. Instead of searching for “causes,” an alternative approach is proposed — phenomenological reconstruction of complex systems (PRCS): a method aimed at identifying stable dynamic patterns directly from data, without prior specification of models or hypotheses. PRCS is based on the Takens embedding theorem, the analysis of spectral and geometric invariants (singular values, correlation dimension, coherence coefficients 𝐶 and flow balance 𝐽), and the construction of a phenomenological landscape of states. The method is verified on independent datasets — including the SPARC catalog (175 galaxies), where 88% of objects exhibit stable oscillations corresponding to the Feigenbaum constant with a significance of 13.25𝜎. PRCS is not a heuristic: it represents an operational projection of the general ontology of patterns, formally developed in the Tensor Model of Discrete Dynamics (TMDD) and rooted in Operational Set Theory (OST). The present work serves as a pilot publication in a series dedicated to the development and application of PRCS to technological, astrophysical, and social systems. In subsequent parts, the method will be applied to specific case studies — from the organizational collapse at the Fukushima-1 NPP to discrete dynamics within the TMDD framework, allowing us to trace a unified ontological framework from data to formal description.