We introduce an observer‑projection framework for assessing similarity among descriptions of coupled dynamical systems. Collective regimes emerge as operational classes in the resulting observer space. The framework projects system descriptions onto three observer‑dependent metrics: Projection Metric Status Statistical redundancy CCI (Coupling Coherence Index) Definitional at theoretical level; empirical estimation is estimator‑dependent Model sensitivity DIG‑proxy (Dynamical Independence Gap – proxy) Provisional operationalization (cross‑correlation) – no canonical estimator Projection stability LMS (Latent Manifold Stability) Linear proxy (PCA autocorrelation) – collapses for nonlinear manifolds RCO (Regime Coherence Operator) is an arbitrary aggregation functional – a scalar projection for visualization only (appendix/post‑processing). It is not part of the core pipeline. Classification is multivariate based on the 3D vector (CCI, DIG‑proxy, LMS), independent of RCO thresholds. Operational regime classes are defined by a distance metric in (CCI, DIG‑proxy, LMS) space. The implementation uses Euclidean distance as a convenience metric; it has no privileged theoretical status. Alternative observer embeddings (mutual information graph space, spectral embedding, etc.) are possible and yield different class structures. SDCS (Shared Dynamical Coordinate System) is a meta‑theoretical selection criterion over families of models – not a latent object. The present implementation does not demonstrate that DIG‑proxy and LMS constitute sufficient statistics for parsimony assessment; they are treated as heuristic indicators motivating future direct implementations of SDCS (e.g., via cross‑validated prediction error, MDL, or Bayesian model comparison). Regime is a property of the description under the operator (CCI, DIG‑proxy, LMS), not an intrinsic system property. A collective regime is hypothesized when the observer projections indicate that a lower‑dimensional description may provide a more parsimonious account than independent subsystem descriptions. Epistemological core: This is a framework for assessing similarity of descriptions of dynamical systems under projective observers. Regimes correspond to operational classes of descriptions in the observer projection space. The topology of the regime space depends on the chosen observer embedding. No claim of collective consciousness or strong ontological emergence is made.
Taotuner (Wed,) studied this question.