Traditional methods for analyzing complex systems rely on a priori physical models, which creates an epistemological circle: we see in the data only what has been embedded in the model. This paper presents the Phenomenological Reconstruction of Complex Systems (PRCS) method - a model-independent computational pipeline that transforms arbitrary time series into a reconstructed phase space with the extraction of stable dynamical patterns. The key object of analysis is the structural risk index K(t), dened as the fraction of the tail of the singular spectrum of the trajectory matrix (SVD). High values of K(t) are interpreted within the TMDD ontology as phases of increased ontological decoherence of the θ-network, where the system realizes higher-dimensional and more complex congurations. We derive the ontological threshold Kthr ≈ 0.301 from fundamental mathematical constants (e, π, ϕ) and its relation to the eective inertia Me(V ), providing cross-domain normalization for high-energy physics, fusion plasma, and biosystems. The pipeline is validated on open CMS Dimuon (LHC) and LHD bolometry data: high-risk phases are statistically signicantly concentrated in narrow kinematic windows (M ≈ 6578 GeV, pT > 40 GeV, |η| < 1.0 for CMS; four stable patterns with Lk ≈ 1.0 and a frequency of 1.08 Hz for plasma). The work demonstrates a methodological shift from searching for static classes to dynamic segmentation of phase space, oering a reproducible tool for diagnostics, early warning of transient events, and onto-management of complex systems.
Sergey Aleksandrovich Mazein (Sun,) studied this question.