Predicted muon neutrino energy flux (left) and number flux (right) for the two UHE neutrino source candidates discussed in the main text. The emission of neutrinos above 1 PeV is led by interactions with broad line photons (orange) and above 10 PeV by interactions with the thermal photons from the dust torus (purple). The dashed gray curves show the neutrino emission expected without external photons (corresponding to a true BL Lac). In the upper panel, we show in green the 68% CL limits on the ten-year point-source flux from the direction of TXS 0506+056 under the assumption of a hard signal spectrum (Rodrigues et al. 2024b) and in red the latest IceCube ultra-high-energy flux limits (4π νF_ν/3, where νF_ν is the all-flavor diffuse flux in erg s⁻¹sr⁻¹cm⁻², Abbasi et al. 2025). The pink band in the bottom panel is the energy range of the KM-230213A muon detected by KM3NeT (Aiello et al. 2025).