Simulated effective spin χ_eff distribution used for mock catalog realizations (black) compared to effective spin PPDs recovered by two LVK analyses: the PPD implied by the B-spline analysis (blue), and the marginal PPD when directly modeling the population distribution of χ_eff and effective precessing spin χ_p as a bivariate Gaussian (orange; A. G. Abac et al. 2026b). Medians are denoted with solid lines and shaded regions enclose the 90% credible region.