Conclusions about properties of high-energy cosmic-rays drawn with limited recourse to hadronic models

Determining the energy and mass of the highest energy cosmic rays requires knowledge of features of particle interactions at energies beyond those reached at the LHC. Inadequacies of the model predictions set against a variety of data are summarised and it is clear that firm statements about primary mass are premature. Nonetheless, conclusions of significance about the origin of the highest-energy cosmic rays can be deduced from the data. This paper is dedicated to my great friend and colleague, Jim Cronin, who died suddenly on 25 August 2016, without whom the Auger Collaboration would not have happened.