1.4 GHz luminosity function of radio-excess AGN in (NUVrJ) SFGs (AGN RLF) at different redshifts (increasing from left ro right). The grey shaded area encloses the ±2σ locus (i.e. ±0.44 dex) around the luminosity corresponding to the IRRC. All data points below the +2σ boundary (dotted black line) are conservatively disregarded to minimise incompleteness. (Top panels): Former AGN RLF (grey squares) corrected for AGN classification purity according to (see Sect. 3.2 and Fig. 2). This step lowers Φ(L) at the faint end (red stars). (Bottom panels): -corrected AGN RLF (grey stars) further corrected for AGN luminosity purity at 1.4 GHz, based on . This step mildly steepens Φ(L) at the faint end (black circles), while the brightest bins remain unchanged. The dashed magenta line indicates the luminosity corresponding to 90% AGN completeness (L_90%) in each z-bin. After applying the above corrections, the final numbers and fractions relative to the parent VLA-COSMOS 3GHz sample are reported in each z-bin. See the text for details.