The S8 Offset Between Lensing Surveys and the Microwave Background: Size, Significance and the Suppression It Would Require

Combining the published cosmic shear amplitudes of KiDS-1000, DES Year 3 and HSC Year 3 as fixed inputs gives a weighted mean S8 of 0.770 plus or minus 0.012, against a microwave-background value of 0.832; the offset corresponds to a tension of 3.5 sigma under the stated treatment of the uncertainties, and would require the matter power spectrum, at the scales and redshifts lensing probes, to be suppressed by -14.5 percent in power, or -7.5 percent in amplitude, relative to the microwave-background-normalised expectation. For DES Year 3 alone the required power suppression is -13.0 percent. These numbers define the target for any proposed explanation, whether astrophysical, systematic or cosmological: a mechanism that cannot produce a suppression of this size, at the right scales, is not a candidate. All quantities are computed from the cited published values, not measured.