Mean offsets (points) and corresponding standard deviations (error bars, showing ±1σ centred on zero for clarity) of RA (blue) and Dec (orange) between cross-matched LoTSS-DR3 mosaics and FIRST sources are shown as a function of LoTSS-DR3 S_P/σ_SP for the declination range 40–50°. The green line shows the ideal standard deviations derived from modelled noise-like offsets in FIRST and LoTSS positions, including an additional systematic offset of 0.24″. The shaded light grey region shows the range of standard deviations across the full declination range of the cross-matched catalogue (−2°–65°), while the darker grey region shows the corresponding range of mean offsets.