Left panel: scheme used to explain the difference between KERRBB and AGNSED results. The observed AD luminosity is dimmer than the intrinsic one by a factor α because a compact corona (located in the innermost part of the disk) scatters part of the disk radiation (C). The optical part of the disk (A, i.e., the emission produced by the most distant annuli of the AD) is fixed because the corona does not cover its radiation. The intrinsic disk emission can be approximately reconstructed by taking into account the factor α and by fixing the low-frequency emission; the peak of the emission (B) is produced by the AD parts closer to the corona. Right panel: comparison between AGNSED BH mass solutions (thick lines) as a function of the spin, and KERRBB ones (dashed lines) for NGC 5548 (blue) and MRK 509 (red). All these solutions describe the same SED plotted in Fig. C.1 for θ_v = 45°. For NGC 5548, the results of both models are consistent while for MRK 509, masses differ by a factor ≲0.2 dex. The shaded area represents the uncertainty of ∼0.1 dex (on average) linked to the spectrum peak position (see Sect. 5.1).