Computed all-flavour neutrino background derived from an X-ray AGN population synthesis. The dark blue curves show the computed neutrino backgrounds for source populations integrated up to the distance of NGC1068 and redshift z = 5 (dash-dotted and dotted, respectively). A high-energy extrapolation up to 10⁷ GeV is added to the integrated spectrum for z = 5 and combined with the blazar neutrino background model by Padovani et al. (2015; dash-dotted grey curve) to highlight the structure of the combined AGN neutrino background flux (double-humped solid red curve). The estimated uncertainty on the integrated neutrino component from X-ray AGN is assumed to be 0.5 dex (dark blue band). We also show the current best-fit astrophysical diffuse neutrino flux and the segmented neutrino flux fit assuming an E⁻² energy spectrum in each bin (green area and black points: Naab et al. 2023), IceCube upper limits from stacking analyses for non-blazar AGN (solid grey line: Privon et al. 2023), and the point-source neutrino flux of NGC1068 (blue area: Abbasi et al. 2022).