Joint forecast of second-, third-, and fourth-order aperture statistics, with 1σ contours from the Fisher covariance matrix F⁻¹. The cloud of points in the two-dimensional distribution corresponds to the closest sets of cosmological parameters to the fiducial cSfid value, marked with a cross. The Figure of Merit (FoM) of the plotted ellipses, as derived in Appendix D.3, are: FoM(⟨M_ap²⟩) = 104 ± 15, FoM(⟨M_ap³⟩) = 72 ± 20, FoM(⟨M_ap⁴⟩_c) = 29 ± 11, FoM(⟨M_ap²⟩ + ⟨M_ap³⟩) = 652 ± 103, and FoM(⟨M_ap²⟩ + ⟨M_ap³⟩ + ⟨M_ap⁴⟩_c) = 680 ± 106. In the considered setting, the inclusion of fourth-order statistics leads to a nonsignificant improvement in the constraining power of the aperture statistics.