Trace anomaly and isospin splitting in inverse-mapped relativistic mean-field theory
Trace anomaly and sound speed provide EOS-level probes of dense-matter nonconformality, but do not by themselves identify the microscopic channels responsible for the response. We study this question with a uniform-matter inverse-mapped relativistic mean-field ensemble constrained by chiral effective field theory, heavy-ion flow information, and neutron-star mass-radius data. The ensemble reproduces the flow-based trace trend in symmetric nuclear matter, while beta-equilibrated matter approaches the neutron-star trace bands more slowly. The resulting splitting, \(Δ_{\SNM}-Δ_{\betaeq}\), remains positive over \(2--5\nzero\) and is most strongly correlated with the density derivative of the isovector-vector coupling, with bootstrap-stable Spearman coefficients \(r_s\simeq0.91--0.92\) at \(2--3\nzero\). Its correlation with the beta-equilibrium proton fraction is much weaker. The sound-speed splitting changes sign near \(3.38\nzero\), and the derivative term \(-\ddΔ/\dd\ln\varepsilon\) becomes sensitive to both scalar-vector and isovector responses above \(4\nzero\). Data-combination and controlled-isovector tests show that this channel separation is resolved only when laboratory and astrophysical projections are combined. Thus, within the present inverse-mapped RMF space, the SNM--beta trace splitting acts as a thermodynamic probe of the high-density symmetry sector rather than as a unique signal of exotic degrees of freedom. A finite-nucleus-calibrated extension will be needed to test how much of this channel diagnostic survives in predictive covariant density functionals.