Invariant of Vital Regulation (IVR): A Scale-Aggregated Measure of Dynamic Coherence

We introduce the Invariant of Vital Regulation (IVR), a generic and scale-aggregated quantity designed to measure the dynamic coherence of observed processes. The IVR is defined through a family of local variation operators evaluated across multiple temporal scales and aggregated into a single invariant descriptor. This construction is deliberately abstract and implementation-independent, allowing application to deterministic or stochastic systems, discrete or continuous signals, learning dynamics, and neural or physical processes. We show that the IVR provides a robust contrast between structured dynamics and surrogate or noise-driven controls, while remaining independent of specific architectures or optimization schemes. The proposed framework establishes a unifying metric for analyzing regulation, stability, and coherence across complex dynamical systems.