Researchers have significantly refined the estimation of the color-flavor locked (CFL) pairing gap in dense neutron star matter, a crucial parameter for understanding their internal structure. Using Bayesian inference and current astrophysical observations, the study establishes a value for the CFL pairing gap $\Delta_{\rm CFL}^{*}$ of $28^{+23}_{-20}$ MeV, with a 95% credibility upper limit of approximately 51 MeV. This new bound is three times more restrictive than previous ones and challenges most existing microscopic models, suggesting that pairing power corrections contribute only a small percentage to 2.6 GeV.

The equation of state (EOS) model employed combines a Gaussian process parametrization with sampled hyperparameters for neutron star densities, and a feed-forward neural network representation with boundary constraints extending to perturbative quantum chromodynamics (pQCD) densities. This approach maintains non-parametric flexibility and allows for efficient nested sampling. The matching with the pQCD+CFL prediction at a baryonic chemical potential $\mu_B = 2.6$ GeV was key to obtaining these estimates.

In addition to the CFL pairing gap, the study has also established a limit for the N$^3$LO constant $c_0$ in pQCD, a value previously poorly known. It has been determined that $c_0 = -28^{+5}_{-7}$, using a loose prior derived from the convergence analysis of the N$^3$LO pressure. These results are fundamental for improving our understanding of dense matter under extreme conditions and for refining theoretical models of neutron stars, opening new avenues for future research in the physics of compact nuclear matter.