Evolving the Loeb Scale

We develop a differential formulation of the Loeb Scale that extends the original static framework into a radially evolving, real time classification scheme for interstellar objects. By promoting each anomaly metric to a function of heliocentric distance and introducing a relaxation equation for the effective score, our method incorporates memory, hysteresis and predictive capability. This allows us to have early, stable forecasts of an object's eventual Loeb level based on sparse data obtained at large distances, which is more helpful to quantify its true nature when near Earth.