The Non-parametric Equation of State Realizes a Generalized Quark-Hadron Crossover

We propose a non-parametric approach to construct the statistical equation of state (EOS) continuously from the nuclear crust to the asymptotic-freedom regime. The combined requirement of supporting two-solar-mass neutron stars (NSs) with relatively small radii at low masses and of reaching the asymptotically soft pQCD boundary forces a squared-sound-speed ($c_s^2$) peak followed by extended softening, with $c_s^2$ returning toward $1\mathrm{/}3$ near $\sim \text{\hspace{0.17em}⁣}30n_{\mathrm{s}\mathrm{a}\mathrm{t}}$. Correspondingly, the trace anomaly $\mathrm{\Delta }\equiv 1\mathrm{/}3-p\mathrm{/}\epsilon$ becomes positive beyond NS densities and approaches the pQCD limit from above. By quantifying the degree of this softening in the posterior, we find evidence for a hadron-quark transition in the cores of the most massive neutron stars. More importantly, this shows that the thermodynamic structure of a complete crust-to-pQCD statistical EOS naturally realizes a generalized quark-hadron crossover. The quark EOS above NS densities is therefore soft and non-perturbative, in contrast to the stiff quark EOS underlying the quark-star picture.