Constituent-Tagged Transfer Linking Cluster Dynamics to Static Scaling

Abstract

Clusters that merge and split have no unique genealogy. Tracking the host size of a conserved constituent defines $q_*$ by $\langle(S_{t+τ}/S_t)^{q_*}\rangle=1$, with $q_*\ne0$. Across coupled map networks, coagulation-fragmentation dynamics, and Vicsek systems, $q_*\simeqα-2$ without fitting, where $c(s)\propto s^{-α}$ on the same size window. Radius scans locate the known Vicsek interaction radius and recover an independently specified clustering scale in experimental active rods. Local scale covariance yields the relation, while a tent map counterexample shows when reducing the stationary balance at each parent size to one moment fails.