Top: the stacked phase-space trajectories of all central halos. Middle: three representative cases of phase-space trajectories of halos around large-scale filaments. The starting point is marked as “formation,” and the pericenter is marked as “crossing.” The x- and y-axes are normalized by r ₀ and v _peak of each case, respectively, but note that this normalization is purely for representation, rather than by any physical meaning. The cases of “going for another orbit” and “escaping from potentional” are later called “bound” and “fly-by” objects. Bottom: the fraction (black dashed line) and number (blue solid line) of crossers (those denoted in green in the middle panel) that have passed the pericenter at least once at z = 0 as a function of distance to filaments at z = 0.