Which covariance estimator actually works for weak lensing surveys

Covariance matrices tell cosmologists how much to trust their measurements, so errors there propagate directly into parameter constraints. Using simulated convergence fields with the actual Hyper Suprime-Cam Year 3 survey mask, three analytical estimators were benchmarked against direct simulation. The improved Narrow Kernel Approximation, despite accurately capturing diagonal structure in harmonic space, produces significant errors once transformed to real-space angular correlations via Legendre projection — the off-diagonal leakage is the culprit. A weighted quartic-counts method handles survey geometry more faithfully and matches simulations better, pointing to where future lensing pipelines should focus.