Photometric Redshift Mean Shifts and the Resulting Bias in Cosmic Shear Amplitudes

An error in the mean redshift of a shear source sample displaces its lensing kernel and biases the inferred amplitude. Computing the convergence power at multipole 300 while shifting the source distribution by known amounts, this paper finds a bias in the amplitude parameter S8 of -0.72 percent for a mean shift of 0.01 and -1.44 percent for a shift of 0.02, corresponding to a sensitivity of -0.72 percent per 0.01 of shift. A one-percent amplitude bias is produced by a mean shift of only 0.014. Redshift calibration is therefore not a secondary correction but a first-order term in the amplitude budget: current surveys, which calibrate mean redshifts to roughly 0.01, carry an irreducible contribution of order one percent to their amplitude uncertainty from this term alone, comparable to the statistical precision of the largest samples. All values are computed from stated assumptions, not measured.