The Growth Tension Is Mostly a Projection: S8, fσ8, and the Histories That Lower One Without Touching the Other

Weak-lensing surveys measure the clustering amplitude S8 below the value the Planck microwave-background analysis infers, by margins of 2.59 sigma for DES Year 3, 2.94 sigma for KiDS-1000, and 1.79 sigma for HSC Year 3 under the published errors. This paper asks how much of that discrepancy is a disagreement about the growth of structure and how much is an artefact of the parameter combination S8 itself, by computing S8 and the redshift-space-distortion observable fσ8 for three expansion histories: the Planck standard history; the small-ruler combination that adopts the SH0ES expansion rate at fixed physical matter density (matter fraction 0.268); and the same combination with its clustering amplitude adjusted to match DES exactly. The small-ruler combination, with the Planck clustering amplitude held fixed, already yields S8 = 0.767 — slightly below the DES central value of 0.776 — purely because S8 divides by the square root of the matter fraction; matching DES exactly within that history would require raising σ8 by 1.2 percent, not suppressing growth at all. Against four published fσ8 measurements, all three histories are statistically acceptable (chi-squared 4.92, 4.34, and 4.05 for four points), and none reproduces the high eBOSS quasar point at redshift 1.48. The growth tension, at its present size, is therefore mostly a statement about the matter fraction entering a derived parameter, not evidence that structure grows more slowly than the standard history predicts — and any resolution of the Hubble tension that lowers the matter fraction inherits a growth-tension remedy as a by-product, whether it wants one or not. This study is computed from published values and stated assumptions; it is not a measurement.