Multiplicative Shear Calibration: From a Bias Parameter to an Amplitude Requirement

A multiplicative error m in a shear catalogue rescales every measured ellipticity correlation and propagates directly into the inferred amplitude. This paper tabulates the propagation: a bias of m equal to 0.01 biases the amplitude parameter S8 by 1.0 percent and the power by 2.0 percent, while m equal to 0.002 biases the amplitude by 0.2 percent. Requiring the calibration contribution to stay below one quarter of the Dark Energy Survey Year 3 statistical uncertainty demands that m be controlled to 0.0055; controlling the power to one percent requires m below 0.0050. Calibration at the few-times-10-to-the-minus-3 level is thus not an aspirational target but the entry requirement for the precision current surveys already claim. All numbers are computed from the stated propagation relations, not measured.