Non-Parametric Equation of State Reveals Non-Conformal Behavior Beyond Neutron Star Densities

We propose a non-parametric approach to construct the statistical equation of state (EOS) continuously from the nuclear crust to the asymptotic-freedom regime. Driven by the observationally required stiffening to support two-solar-mass neutron stars (NSs) with relatively small radii for low-mass NSs, this global thermodynamic constraint suggests a clear peak of squared sound speed ($c_s^2$) in massive NSs. To prevent overshooting perturbative QCD (pQCD) energy-density bounds, this early stiffening must be actively compensated by an extended density range of softening, with $c_s^2$ not approaching $1/3$ until $\sim\!30\,n_{\rm sat}$. Consistently, the trace anomaly $\Delta \equiv 1/3 - p/\epsilon$ becomes positive beyond NS densities and approaches the pQCD limit from above. This natural emergence of $\Delta > 0$ organically aligns with some anticipated microphysics, likely arising from the pressure dilution in a quark-hadron mixed phase, non-conformal pQCD corrections to quark-gluon interactions, or the symmetry-breaking effects of finite strange quark mass. By measuring the degree of this non-monotonic behavior in the posterior, we find evidence for a hadron-quark phase transition in the cores of the most massive neutron stars. This indicates that the non-perturbative quark matter is intrinsically soft, fundamentally distinguishing it from the stiff scenarios associated with the quark-star picture.