Distributions of NS (purple) and non-NS (grey) events in log₁₀ t_E–log₁₀ θ_E space. All simulated events regardless of whether they passed the detectability cuts are plotted; shade denotes iso-density levels estimated with a Gaussian KDE. The black circles highlight the NS events that passed the detectability cuts. The NS distribution exhibits a characteristic spur feature that becomes stronger and more shifted leftwards with increasing v_kick, yielding more detectable NSs that are outliers from the main distribution.