A linear relation between galaxy-lensing cross-correlations to test the
  cosmological principle model-independently
  We discover a linear relation between two sets of galaxy-lensing
cross-correlations. This linear relation holds, as long as light follows the
geodesic and the metric is Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW).
Violation of the cosmological principle (and equivalently the FLRW metric) will
break this linear relation. Therefore it provides a powerful test of the
cosmological principle, based on direct observables and relied on no specific
cosmological models. We demonstrate that stage IV galaxy surveys and CMB-S4
experiments will be able to test this linear relation stringently and therefore
test the cosmological principle robustly.
