Qualitative estimators, as defined in the main text, for the UHECR fit as a function of injection Z. The shaded regions illustrate our expectations from cosmic ray data (top left from Heinze et al. 2016; top right and bottom left from Aab et al. 2017; and bottom right from Kampert & Unger 2012). The different curves correspond to different values of L_γ , as illustrated in the legend. In the upper right panel, the maximal energy following the Peters cycle (rigidity dependent maximal energy) is illustrated for two examples. The production radius is fixed to R ≃ 10^8.3 km in this figure.