We investigate dynamical constraints on the population of large interstellar objects (ISOs) by combining encounter rate analysis, Eddington inversion, and Liouville mapping. Encounter rate scaling demonstrates that detections of kilometer-scale ISOs require flux enhancements beyond natural Maxwellian expectations. Using Eddington inversion, we show how steep density profiles imply phase-space biases consistent with strong gravitational focusing and we then develop a Liouville mapping formalism that propagates the interstellar velocity distribution inward under conservation of energy and angular momentum, revealing that low-angular momentum anisotropies can reproduce the observed size dependent detection rates. These results provide a self consistent dynamical framework for interpreting the observed population of ISOs and for assessing whether the required anisotropies arise from natural or artificial origins. The main results are framed in the context of the parameters for 3I/ATLAS, but the implications are general and go on to sharpen the distinction between natural dynamical mechanisms and potential artificial origins for ISOs.
Trivedi et al. (Mon,) studied this question.