Extended Data Fig. 1: Comparison of assumed shapes for Saturn’s composition gradient.

Helium distributions for our baseline linear composition profiles from Eq. (1) (a) are compared with those assuming sigmoid Z(r) and \(Y^{\prime} (r)\) in the transition region (b). The corresponding profiles of the heavy element mass fraction (c-d), mass density (e-f), and Brunt–Väisälä frequency (g-h) are also shown. 1,024 randomly selected models are shown for each sample, colored by log likelihood.