Top left panel: the muon number obtained by direct measurements at Auger (A. Aab et al. 2020a, 2021) compared to the predictions with and without the application of ΔX_max. Note that in case of the SIBYLL 2.3d model, only the predictions at energy 10¹⁹ eV were at our disposal. Top right panel: the ratio of the muon signal in the data and the signal predicted from air-shower simulations with (filled markers) and without (open markers) application of ΔX_max. The results from A. Abdul Halim et al. (2024a) are displayed by triangles. Bottom panels: the X_max distribution of Auger data (A. Aab et al. 2014a) compared to the prediction for the heavy-metal scenario (Gauss × exp.) using QGSJET II-04 + ΔX_max (left) and SIBYLL 2.3d + ΔX_max (right) in the energy bin 10^18.0−18.5 eV. For visualization purposes, the fits to the tail of the predicted X_max distributions (Λ_η), corrected for detector acceptance, are shown.