Comparison of c vs. m_B − μ + αx₁, offset in bins of host galaxy mass, shown in the main plot. The SNe are colour-coded by their colour, c, for visual guidance. The slope (β value) for each mass bin is shown in red, alongside the fiducial beta in black dash-dotted line. The light grey dash-dotted vertical line shows the c = 0 point for each mass bin. Top: Colour histograms for each of the mass bins is shown, colour-coded according to c. Inset: β vs mass relationship for the fitted mass bins. The β values for the full sample are presented in brown points, the ZTF-only β values in teal triangle, and the high-redshift sample in olive triangle, with the fiducial β shown in grey dash-dotted line. See Sect. 4.3 for more details.