Shao-Peng Tang, Yong-Jia Huang, Yi-Zhong Fan

We probe the color-flavor locked (CFL) pairing gap ($Δ_{\rm CFL}^{*}$) and the unknown N$^3$LO constant $c_0$ in perturbative QCD (pQCD) with Bayesian inference of flexible dense-matter equations of state (EOSs) informed by current astrophysical observations. Our EOS model combines a Gaussian process parameterization with sampled hyperparameters at neutron star densities and a boundary-constrained feed-forward neural network representation extending to pQCD densities, retaining nonparametric flexibility while supporting efficient nested sampling. Matching to the pQCD$+$CFL prediction at $μ_B=2.6$ GeV, we obtain $Δ_{\rm CFL}^{*}=28^{+23}_{-20}$ MeV (90% credibility), corresponding to a 95% credible upper limit of $\approx 51$ MeV, which is a factor of $\sim 3$ tighter than previous record and challenges most microscopic models. The pairing power corrections thus contribute at most a few percent at $μ_B = 2.6~\mathrm{GeV}$, and are not a major source of uncertainty for neutron-star matter inference. We also set a bound on the poorly-known N$^3$LO constant $c_0=-28^{+5}_{-7}$, using a loose prior from convergence analysis of the N$^3$LO pressure.