Posterior predictive distribution (PPD) of the black hole spin tilts of the low-mass population (﹩{m}_{1}\,\lesssim \,\tilde{m}=44.{3}_{-4.6}^{+8.6}\,{M}_{\odot }﹩) in our parametric Gaussian + Isotropic + Cut model (blue). The PPD is constructed by taking the quantiles (median indicated by dashed lines, 90% interval by shaded envelope) across MCMC samples (thin lines). The left panel shows the PPD of only the low-mass Gaussian component, and the right panel includes the low-mass isotropic component. The green color shows the nonparametric B-spline model of The LIGO, Virgo, and KAGRA Collaborations (2025a, 2025e ). In both panels, the dotted blue lines indicate the prior bounds (90%), i.e., they show the PPDs if all hyperparameters are drawn from their priors. The red line shows simulation outcomes of binary black hole mergers, which are caused by the Lidov–Kozai effect in hierarchical triples (F. Antonini et al. 2018). The orange lines show simulation outcomes of binary black hole mergers from isolated binary-star evolution (A. Olejak et al. 2024) assuming high natal kicks at black hole formation that are drawn from a Maxwellian velocity distribution with σ = 133 km s⁻¹ (dashed–dotted) or natal kicks lowered by fallback (C. L. Fryer et al. 2012) with σ = 265 km s⁻¹ (solid). Since we cut the y-axis, the small inset (linear axes) shows that the orange models are strongly concentrated at ﹩\cos \,\approx \,1﹩. In the right panel, the binary black hole sketch depicts a merger with ﹩\cos {\theta }_{1(2)}\approx 0﹩, where, for visualization purposes, we pick near-opposite in-plane directions.