We present a probabilistic model for the QCD critical endpoint (CEP) and the equation of state (EOS) at $\beta$-equilibrium, constrained by neutron-star (NS) observations. Using a hybrid framework that combines the holographic V-QCD model with an effective van der Waals description of nuclear matter, we generate a large ensemble of EOS incorporating nuclear theory uncertainties. Constraining this ensemble with NS mass-radius data and tidal deformability measurements from gravitational waves, we identify a strong first-order deconfinement transition at zero temperature, with a transition strength $\mathrm{\Delta }{n}_{\mathrm{PT}}/n_0=3.89_{-0.60}^{+0.77}$ and onset density $n_{\mathrm{PT}}/n_0={5.4}_{-1.25}^{+1.41}$. The resulting posterior yields 95% credible intervals for the CEP location: ${\mu }_{\mathrm{crit}}=626_{-176}^{+91}\mathrm{MeV}$, $T_{\mathrm{crit}}=119_{-6}^{+14}\mathrm{MeV}$.

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• Equations of state of nuclear matter
• Nuclear matter in neutron stars
• QCD phenomenology
• Neutron stars & pulsars