Caustic radii measured from total (black), T₁ (red), and T₃ (blue) profiles as functions of formation time in different halo mass bins, as indicated in each panel. Error bars are calculated using the two-level (100 × 1000) bootstrap samples. We note that some profiles have multiple local minimums, and therefore multiple caustic radii. The shaded areas from light to dark indicate the regions where the first, second, and third caustics are located, respectively.