Evidence for a Continuous Hadron--Quark Transition in Cold Dense Matter

Statistical evidence for a continuous hadron-quark transition is found in this work. Confronting microscopic descriptions connecting the Parity Doublet Model and the Nambu--Jona-Lasinio model with observationally constrained non-parametric equations of state, Bayesian model comparison decisively favors a boundary-free crossover over the conventional first-order Maxwell construction (Δ Z about +7.20) and fixed-boundary crossover (Δ Z about +5.16). The preferred crossover decouples the intermediate stiffening from the intrinsic stiffness of each phase, allowing both sectors to exhibit physical self-consistency. The chiral-invariant nucleon mass is large, M 0 = 834+28-92 MeV, as expected for a substantial baryon mass surviving chiral restoration. While the quark sector accommodates a small pairing gap Δ CFL = 88+83-59 MeV consistent with perturbative QCD limits, avoiding the excessively large gaps Δ CFL 200 MeV required by the other constructions. These results demonstrate that a realistic unified description represents a continuous transition deviating substantially from isolated effective models of hadrons and quarks. Exploring genuine phase boundaries is therefore necessary through the emergence of spinodal instabilities within unified frameworks.