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Probing hadronic interactions with measurements at ultra-high energies with the Pierre Auger Observatory

The characteristics of an extensive air shower derive from both the mass of the primary ultra-high-energy cosmic ray that seeds its development and the properties of the hadronic interactions that feed it. With its hybrid detector design, the Pierre Auger Observatory measures both the longitudinal development of showers in the atmosphere and the lateral distribution of particles arriving at the ground, from which a number of parameters are calculated and compared with predictions from current hadronic interaction models tuned to LHC data. At present, a tension exists concerning the production of muons, in that the measured abundance exceeds all predictions. This discrepancy, measured up to center-of-mass energies of $\sim$ 140 TeV, is irresolvable through mass composition arguments, constrained by measurements of the depth of the electromagnetic-shower maximum. Here, we discuss a compilation of hadronically-sensitive shower observables and their comparisons with model predictions and conclude with a brief discussion of what measurements with the new detectors of the AugerPrime upgrade will bring to the table.