The S8 Tension Recounted Term by Term: An Audit of the Clustering-Amplitude Discrepancy Between the Early and Late Universe

The parameter S8 inferred from the cosmic microwave background is higher than the values measured by weak-lensing cosmic shear. This paper recounts the discrepancy term by term, using only published central values and uncertainties, with every derived number produced by an accompanying reproducible script. The Planck 2018 value S8 = 0.832 +/- 0.013 is recovered from the published sigma8 and Omega_m as 0.831. Against this reference, KiDS-1000 (S8 = 0.759) differs by 2.81 sigma, DES Y3 (S8 = 0.776) by 2.62 sigma, and HSC Y3 (S8 = 0.776) by 1.60 sigma. At fixed Omega_m, the lensing values imply sigma8 lower by 0.070 (KiDS-1000) and 0.054 (DES Y3 and HSC Y3); at fixed sigma8, they imply Omega_m lower by 0.052 and 0.040 respectively. Expressed as late-time growth, the discrepancy corresponds to a suppression of 8.8% (KiDS-1000) or 6.7% (DES Y3 and HSC Y3). Each systematic term budgeted by the lensing analyses would individually need to be 6.6 to 24.3 times its published test size to close the gap alone. No side is declared correct; the terms are priced so that any proposed resolution can be checked against a stated cost.