Illustration of our mock spectrum. Panel (a) displays the mock spectrum of the. In this case, the continuum is hard to detect. Panel (b) presents the fit to the [O III] emission line doublet. The mock spectrum and the uncertainty are shown as a black histogram and a gray-shaded region. The best-fit model is shown as a blue line. Panel (c) shows the fit to the Hα+[N II] emission complex. Similar to Figure B1, the top subpanel displays the data (black histogram), the total best-fit model (blue line), the broad Hα component (red-dashed line), and the narrow-line template derived from the [O III] profile (green dotted line). The lower two subpanels show the fit residuals. The middle subpanel confirms the quality of the total fit, while the bottom subpanel demonstrates that a model lacking the broad Hα component provides a significantly poorer fit to the data. This mock observation was generated for a BH with a mass of ﹩\mathrm{log}{M}_{{\rm{BH}}}/{M}_{\odot }=5.99﹩ and a magnification of μ = 3.0, located at a redshift of z = 5.8656.