Distribution of the halo spin orientation angle, θ_Jz, with respect to the simulation z-axis, shown for three mass bins at redshift z = 0.5 in our S¹ × ℝ²ΛCDM simulation. We only used halos with N_part > 100 in this analysis to reliably measure the angular momentum vectors. The histogram uses equal-area binning on the unit sphere, so that an isotropic spin distribution implies equal expected counts per bin. Each panel is annotated with the one-sample Kolmogorov-Smirnov test on $u=\frac{1}{2}(1+cos({\theta }_{\mathit{Jz}}))\in [0,1]$ against the uniform null. The three mass bins show no departures from the isotropic expectation. We found similar distributions in all other output redshifts and mass bins with no clear signs of anisotropy.