Why Azimuthal Averaging Works in Halo Lensing: Symmetry and Power Counting for Nonlinear Shear and Magnification

Cluster weak-lensing analyses often compress two-dimensional lensing fields into azimuthally averaged radial profiles and evaluate nonlinear observables from the averaged convergence and shear. However, the ring average of a nonlinear observable generally differs from the mean-field prediction forme