Solution space distribution (a) and contour of the distribution (b) for Uranus. The left panel a shows the weighted distribution of all successful uncorrelated Uranus density profiles. The inset shows a zoomed-in view of the outermost region, from r/R=1 to r/R=0.7. Note that the zoom is not aspect-preserving. The colour scale shows the relative frequency over all distributions of a certain density value at a given radius. Coloured lines show density profiles from previous studies for comparison. Solid and dashed lines correspond to models U1 and U2 from Nettelmann et al. (2013) (orange); U1 and U3 from Morf & Helled (2025) (green); and V2 and V3 from Vazan & Helled (2020) (blue), respectively. The colour scale in the right panel b shows the percentile intervals in 10% increments, except the last interval, where a 95% interval was added. The black line shows the median. The dashed lines show the 16th (lower) and 84th (upper) percentiles.