An Operational Definition of Coherence via Recursive Spectral Support

This work presents a model-independent, operational definition of coherence as a physically measurable quantity. Coherence is defined through the existence of non-zero spectral support in a functional constructed over recursive system activation. The formulation introduces a recursion parameter indexing repeated activation steps, a coherence functional derived directly from measured data, and a binary criterion for coherence detection based on spectral power. The framework makes no assumptions regarding time, geometry, dynamics, equilibrium, or physical substrate. Coherence is identified if and only if a finite-frequency spectral component is present in the coherence functional. Structural change is treated independently through a recursion sensitivity operator, allowing a strict separation between coherent regimes and structural transition regimes. All quantities are defined at the operator level and are directly computable from data without fitting, calibration, or interpretation. The resulting criterion is falsifiable, reproducible, and applicable across domains and scales. The work establishes coherence as a primary, experimentally testable physical property rather than a descriptive or model-dependent concept.