Residuals of the predicted versus observed comparison, ﹩\mathrm{ln}({Y}_{{\rm{obs}}}/{Y}_{{\rm{pred}}})﹩, for a_2,int, a_3,int, b₂, b₃, as a function of T_eff, ﹩\mathrm{log}g﹩, and [Fe/H] were included in the adopted model, for the full sample. The black line shows a running median; the shaded band indicates the ±2σ region. Top row (a)–(d): full sample, color coded by evolutionary phase. Bottom row (e)–(h): the same residuals separated into individual RGB (top), pRC (middle), and sRC (bottom) subpanels, with the running median computed independently within each evolutionary phase