Top: Overall shape of the lensing κ-PDF, smoothed with a top-hat filter of radius 469 and including shape noise. The fiducial cosmology is shown in gray as predicted from large deviation theory (line) and measured in the DUSTGRAIN-pathfinder simulations (data points with error bars indicating the standard deviation across the 256 realizations). Derivatives of the κ-PDF with respect to the CPs are shown in color, with theoretical predictions using nonlinear variances predicted by Halofit shown as solid lines. The markers represent the derivatives obtained from the simulations using finite differences based on larger and smaller increments (points and stars, respectively). Bottom: Fisher forecast constraints on Ω_m and σ₈ for a Euclid-like survey from the κ-PDF shown above. Numerically measured (orange) and theoretically predicted (pink) derivatives find good agreement, with differences in the final 1σ parameter constraints of approximately 20%.