Erhart, Jim: The Structural Operator

This paper develops a structural, operator‑geometric framework for classifying dynamical systems under coarse‑grained evolution. The central proposal is that many physically and conceptually distinct systems—ranging from stochastic processes and dissipative flows to causal mechanisms and transport semigroups—exhibit recurrent large‑scale geometric behaviors that can be captured through a finite family of structural modes. Trajectories are lifted into probability‑measure space, where their induce