Composition Inference from Published Shower-Maximum Distributions by the Superposition Method

Published mean shower-maximum depths are converted into a mean logarithmic mass by the superposition method, using a proton reference line rising at 55 g per square centimetre per decade and an iron line 96.2 g per square centimetre shallower. The conversion constant is 2.389e+01 g per square centimetre per unit of natural-log mass. Applied to representative Auger mean depths, the inferred logarithmic mass rises from 6.280e-01 at 1e18 eV to 2.093e+00 at 1e19 eV and 3.977e+00 at 1e20 eV, corresponding to effective mass numbers of 1.874e+00 and 5.337e+01. The trend toward heavier composition at the highest energies is therefore recovered from the published depths by arithmetic transparent enough to audit, and it agrees in direction with the observatory's own analyses. No density-bound effect enters the conversion, because shower development is unaffected by the bound at atmospheric densities; the composition trend is a property of the sources or of propagation, not of the detector physics. This study is simulated and computed from stated assumptions; it is not a measurement.