Inference of the Mass Composition of Cosmic Rays with Energies from 10$^{18.5}$ to 10$^{20}$ eV Using the Pierre Auger Observatory and Deep Learning

We present measurements of the atmospheric depth of the shower maximum X$_{max}$ , inferred for the first time on an event-by-event level using the surface detector of the Pierre Auger Observatory. Using deep learning, we were able to extend measurements of the X$_{max}$ distributions up to energies of 100 EeV (1020 eV), not yet revealed by current measurements, providing new insights into the mass composition of cosmic rays at extreme energies. Gaining a 10-fold increase in statistics compared to the fluorescence detector data, we find evidence that the rate of change of the average X$_{max}$ with the logarithm of energy features three breaks at 6.5$\pm$0.6(stat)$\pm$1(syst) EeV, 11$\pm$2(stat)$\pm$1(syst) EeV, and 31$\pm$5(stat)$\pm$3(syst) EeV, in the vicinity to the three prominent features (ankle, instep, suppression) of the cosmic-ray flux. The energy evolution of the mean and standard deviation of the measured X$_{max}$ distributions indicates that the mass composition becomes increasingly heavier and purer, thus being incompatible with a large fraction of light nuclei between 50 and 100 EeV.