This work presents a framework for detecting collective regimes in coupled dynamical systems through observational, informational, and predictive metrics. The model proposes a hierarchical structure composed of four main operators: LCR (Local Collective Resonance), CCI (Coupling Coherence Index), DIG (Dynamical Independence Gap), and RCO (Regime Coherence Operator). The conceptual core of the framework is the Shared Dynamical Coordinate System (SDCS), defined as a lower-dimensional latent manifold capable of describing the joint evolution of interacting systems with greater predictive power than decomposed subsystem models. The purpose of the framework is not to infer collective consciousness or metaphysical emergence, but to detect effective collective structures associated with shared dynamical compression, statistical redundancy, and latent stability. The document integrates concepts from dynamical systems theory, mutual information, manifold learning, synchronization, and coordination dynamics, proposing operational criteria for identifying collective regimes in human-AI interactions and other dissipative systems. The framework includes: statistical coherence metrics; complexity-penalized predictive gain measures; surrogate data tests; latent manifold stability analysis; statistical validation and experimental falsifiability criteria. Conceptual simulations illustrate the expected behavior of the operators in independent, synchronized, and coordinated systems. The work is presented as an operational and observational formalism without ontological commitment to strong emergence theories. Keywords: collective regimes; dynamical systems; mutual information; predictive compression; latent manifold; coordination dynamics; dissipative systems.
Taotuner (Wed,) studied this question.