Collective compensation and boundary selection in three interacting chiral active particles

The cost of suppressing collective motion depends on how the remaining degrees of freedom reorganize. We investigate this distinction in endpoint-conditioned rearrangements of three planar chiral active particles with smooth repulsion. Variational neural paths reveal competing close-encounter and wide configurations. An exact centroid decomposition and matched variational controls show that, at the baseline parameters, the wide configuration pays a much larger frozen-path penalty when centroid motion is removed, yet retains a smaller penalty after source-initialized reoptimization. It recovers about 91–92% of the initial projection penalty through coupled changes in propulsion balance and relative geometry, compared with 12–14% for the close-encounter configuration. An auxiliary centroid-control family exposes competition between distinct polarization configurations. In this controlled landscape, endpoint geometry changes the ordering of recovered configurations. Symmetric endpoints also organize several labeled paths into one symmetry orbit, and a boundary-response calculation predicts all sixteen tested rankings under small endpoint stretches. The results distinguish reorganization within a collective rearrangement from selection among configurations and their realizations, giving a particle-resolved account of competing weak-noise and auxiliary variational paths.