Top: p-values from KS tests with trial Q_p comparing the eccentricity distributions of dynamically old and young planets across four representative iterations (out of 3000 total), distinguished by different line styles. In each curve, the minimum p-value among the trial Q_p values in the same iteration is marked with an “x.” Bottom three panels: histograms of Q_p corresponding to the locations of minimum p-values in each of the 3000 iterations, shown for (1) all planets, (2) planets above the median mass (M_p > 0.96 M_J), and (3) those below. In the first panel, we also overlay the case with a 3 Gyr offset applied to τ_cir, simulating the delay introduced by preceding processes such as eccentricity excitation. Dotted lines and blue shading indicate the constraints on Q_J, while dashed lines and orange shading show constraints on Q_p from S. N. Quinn et al. (2014).