Thermodynamic signatures do not uniquely identify deconfinement in neutron stars

Abstract

The smallness of polytropic index $Γ_\varepsilon \lesssim 1.75$ and near conformality of sound velocity $c_s^2 \approx 1/3$ in neutron star matter are usually referred to as signals of the emergence of quark matter. We construct a density-resolved nucleonic reference domain in the \((P/P_{\rm free},Γ_\varepsilon)\) plane using nucleonic EoSs jointly constrained by nuclear matter properties and neutron star mass, radius and tidal data, and found that the domain extends unambiguously below \(Γ_\varepsilon=1.75\). Crucially, the nucleonic domain becomes stable against the truncation order only after \(Z_0\) and \(Z_{sym}\) are included, showing that the higher-order density dependence controls the extrapolation from finite nuclei to neutron-star matter. These findings therefore provide concrete targets for finite-nucleus and heavy-ion experiments, while linking terrestrial nuclear physics directly to multimessenger observations. We compare the domain with smooth equations of state generated by neural networks without phase labels and represented by symbolic regression. Among these reconstructions, \(35.29\%\) have complete trajectories inside the nucleonic domain over \(0.5\leq n/n_0\leq8\). Within the EoS sample obtained after minimizing the multimessenger loss, the smallest value of \(\max_n c_s^2(n)\) is 0.38, above the conformal value $1/3$. In conclusion, we convert microscopic interpretation into a falsifiable, density-resolved null-hypothesis test and show quantitatively that current observations do not reject the nucleonic null over much of the admissible space of equation of state.