Comparison of the predicted wavelet ℓ₁ -norm to the simulations at different scales. Top panel: predicted (solid) ℓ₁ -norm as compared to measurements in simulation (dots) for different inner radii θ₁ = 15′, 18′, and 20′ and a single source redshift z_s = 1.43, displayed with blue, orange, and green lines, respectively. The dash-dotted red lines show the Gaussian prediction for reference. The vertical dotted and dot-dashed lines correspond to the 1σ and 2σ regions around the mean of the $w_{{\theta }_1}$ for each of the case considered. Bottom panel: residual of the prediction relative to the simulation (dotted lines). For reference, the dash-dotted plots illustrate the residual of the ℓ₁ -norm derived from the Gaussian PDF with the same mean and variance as the simulation PDF. The shaded region indicates the 3σ region around the error bars for each inner radius. The prediction agrees well with the measurements up to approximately 2σ and remains within percent levels.