Left panel: PM distribution of orbital points derived from the integration of the trajectories of stars associated with nearby halo substructures, with each colour corresponding to a different object (see legend). The larger red triangles are observed members of the HAC. The smaller vertical and horizontal diagrams show the (normalised) KDE (bandwidth = 0.2 mas yr⁻¹) for each substructure and for the observed HAC members. Right panel: as in the left panel but showing the galactocentric distance vs. V_GSR. The KDEs were computed using a 0.5 kpc and 10 km s⁻¹ bandwidth.