An Operational Definition of Coherence Transitions in Complex Systems (Paper 5, V1)

We present a domain-independent operational definition of internal coherence transitions in complex systems. The framework is designed to detect organizational structure without assumed mechanisms, parametric models, or scale-dependent constants. It formalizes the detector used in a series of empirical studies spanning geophysical, biological, oceanic, and cryospheric systems. The purpose of this paper is methodological: to provide a complete, reproducible specification of the coherence detector used to identify non-monotonic coherence transitions across domains.