Left: fractional difference between the analytical and numerical joint covariance matrix of the second- and third-order aperture mass statistics. The red lines divide the parts of the joint covariance matrix. The 3 × 3 matrix at the top left is the covariance matrix of ${\widehat{\mathcal{M}}}_{\mathrm{ap}}^2$ calculated in Linke et al. (2024). The 10 × 10 matrix at the bottom right is the covariance matrix of ${\widehat{\mathcal{M}}}_{\mathrm{ap}}^3$ from L+23. The non-square matrices at the top right and bottom left are the cross-covariance derived in this paper. Right: analytical S₈–Ω_m contours from the second- and third-order aperture mass statistics, shown separately and in combination.