To further generalize the identifiability results, various other types of manifolds and geometric structures can be explored. For instance, considering non-compact manifolds, such as Euclidean spaces or certain types of Lie groups, could provide insights into the behavior of interacting particle systems in less constrained environments. Additionally, exploring manifolds with singularities or boundaries, such as stratified spaces or manifolds with corners, could reveal new challenges and opportunities for identifiability analysis. Furthermore, the study of more complex geometric structures, such as Riemannian foliations or symplectic manifolds, may yield richer interaction dynamics and broaden the applicability of the results to fields like robotics and control theory. Investigating the impact of curvature and topology on the identifiability of interaction kernels could also lead to novel findings, enhancing our understanding of how geometric properties influence collective behaviors in interacting systems.