Visualisation of the Bayesian ensemble EPM fit. The upper panel presents the combined EPM regressions for all SNe, with θ/v_ph values scaled by the Hubble-free luminosity distance D_L(z_cosmo)H₀, placing them on a uniform absolute scale. Each spectrum contributes one measurement to this plot, with the median of the fit indicated by a dashed line. The 68% and 95% confidence intervals are shown in light and dark grey, respectively. Each SN is colour-coded for clarity. The error bars include the inferred additional uncertainty σ_int. In the bottom panel, we complement this visualisation with a plot similar to a classical Hubble diagram, where D_L values, derived by solving Eq. (5), are plotted against their redshifts. Unlike traditional Hubble diagrams, each point represents one epoch of an SN, with all spectra for a given SN appearing at the same redshift. Special care is needed when interpreting the error bars. In the EPM-like visualisation, the y-errors include both θ/v_ph and peculiar velocity uncertainties, whereas in the Hubble-diagram-like visualisation, they include both θ/v_ph and time of explosion uncertainties. The time of explosion and peculiar velocity uncertainties are completely correlated for all epochs of an SN, introducing correlations in the y-error bars that cannot be captured in this figure. The situation is even worse for the uncertainties in the x-direction, which are solely the time of explosion and peculiar velocity uncertainties, and thus are 100% correlated. The data points are thus not independent, making it more difficult to assess aspects like the dispersion around the fit. It is important to remember, however, that we do not use the plotted data points for the fit; instead, we use the θ/v_ph values directly.