Pressure-energy density prior distributions for the PP (left panel) and CS (right panel) extensions with Bayesian χEFT uncertainties up to 1.5 n₀ (GP-N³LO, blue regions) and uniformly sampled in the previous N³LO range (N³LO, black dashed lines). The dark (light, lighter) blue regions and dashed black (gray, lighter gray) lines encompass the 68% (95% and 99.7%) credible intervals for the GP-N³LO and N³LO cases, respectively. The pink region shows all EOSs excluded from the prior for their unphysical behavior above 1.5ε₀, indicated by the vertical thin dotted line.