Persistent Sullivan Minimal Models of Metric Spaces

We extend classical tools from rational homotopy theory to topological data analysis by introducing persistent Sullivan minimal models of persistent topological spaces. Our main result establishes that the interleaving distance between such models in the homotopy category of CDGAs is stable with respect to the homotopy interleaving distance of the underlying spaces. For Vietoris-Rips filtrations of metric spaces, this yields new persistent invariants that are more discriminative than persistent homology. We further show that these models provide sharper lower bounds for the Gromov-Hausdorff distance than those obtained from persistent homology or persistent rational homotopy groups.