Effect of a finite radial integration range on the fourth-order aperture statistics. (Top) Aperture statistics for varying radial integration ranges, computed on a grid with a logarithmic bin width of Δ(lnϑ) = 0.07 and Δ_ψ = 0.07 rad alongside the considered ground truth (see text). Dash-dotted lines show the effect of E- and B-mode mixing in the second-order aperture statistics for a radial integration range ϑ ∈ [e⁻² ′,e⁵ ′], propagated to the fourth-order with Eqs. (39)–(43). Parity violating modes are, in all cases considered here, below 10⁻²⁰. The discrepancies found on the pure B-mode arise from the combination of inaccurate complex aperture measures, and remain on all considered scales and cases smaller than 0.1% of the E-mode, thus well below noise levels for Stage III or Stage IV surveys. (Bottom) Relative difference for ⟨M_ap⁴⟩(θ) to the considered ground truth. The dash-dotted line shows the impact of a finite integration range on 3⟨M_ap²⟩², and the other lines on ⟨M_ap⁴⟩. Gray regions show the 1% and 2% regions.