Integrated fluxes of the 68% confidence limit bands as shown in Fig. A.1 for the power-law assumption (purple diagonally hatched) and the pγ spectrum (green cross-hatched), for source TXS 0506+056. For the pγ spectrum, the flux is shown as a function of the peak energy. For the power-law spectrum, the flux is shown at the respective mean energy (cf. lower panel of Fig. A.3). This is the reason why the purple band covers a more limited energy range than in the lower panel of Fig. A.1, where the differential flux is shown in the full energy range of the analysis.