Internal parameter correlations (Spearman rank coefficients, r) for the different attenuation-curve parameterizations under varying dust compositions. Each panel shows the correlations among free parameters for all three functional forms (Li+08, Salim+18, and the new model). For clarity, only the lower triangular portion of each symmetric correlation matrix is displayed. Similarly, we only print numerical values if ∣r∣ ≥ 0.2. The structure of the correlations differs across dust models, particularly for parameters associated with the UV bump (c₄, B, B₀, and B₂), indicating that no universal reparameterization can be defined across dust compositions.