This paper presents a study of the QCD critical endpoint (CEP) using multi-point Padé approximations. The authors locate Lee-Yang edge singularities of the QCD pressure in the complex baryon chemical potential plane by analyzing singularities in the net baryon-number density calculated in $ N_f = 2+1 $ lattice QCD at physical quark mass and purely imaginary chemical potential. They extrapolate these singularities to real baryon chemical potential to estimate the CEP position. The results are $ T^{CEP} = 105_{-18}^{+8} $ MeV and $ \mu_B^{CEP} = 422_{-35}^{+80} $ MeV, which are consistent with recent estimates in the literature. The slope of the transition line at the critical point is found to be $ -0.16(24) $. The study uses a multi-point Padé resummation method to construct a Padé approximation to the logarithm of the QCD grand partition function for complex $ \mu_B $. Singularities of the approximant are used to estimate the CEP location. The authors consider temperature-like and magnetization-like couplings $ t $ and $ h $ near the CEP and apply the Lee-Yang theorem to the universal theory $ (3-d~Z(2)) $, where zeroes of $ Z_{QCD} $ in the complex $ h $-plane that approach the real axis in the thermodynamic limit correspond to phase transitions. The authors find that the location of $ T^{CEP} $ must be searched below the chiral transition temperature $ T_{c}^{chiral} \approx 132 $ MeV. They extend their calculations down to $ T = 120 $ MeV. The results are summarized in Fig. 1, which shows the probability distribution of the QCD critical point from extrapolating Lee-Yang singularities to the real domain using universal scaling. The lattice simulations are performed on $ N_\sigma^3 \times N_\tau $ lattices with $ N_\sigma = 36 $ and $ N_\tau = 6 $, using $ N_f = 2+1 $ dynamical highly improved staggered quarks (HISQ). The simulations run at $ \mathcal{O}(10) $ pure imaginary $ \mu_B $ in the range $ \mu_B/T \in [0, i\pi] $ to avoid the sign problem. The authors measure the first- and second-order cumulants of the net baryon-number density and use these to construct rational approximations of the cumulants. The poles of these approximations are used to estimate the CEP location. The authors estimate the CEP location using a scaling ansatz motivated by the temperature scaling of theThis paper presents a study of the QCD critical endpoint (CEP) using multi-point Padé approximations. The authors locate Lee-Yang edge singularities of the QCD pressure in the complex baryon chemical potential plane by analyzing singularities in the net baryon-number density calculated in $ N_f = 2+1 $ lattice QCD at physical quark mass and purely imaginary chemical potential. They extrapolate these singularities to real baryon chemical potential to estimate the CEP position. The results are $ T^{CEP} = 105_{-18}^{+8} $ MeV and $ \mu_B^{CEP} = 422_{-35}^{+80} $ MeV, which are consistent with recent estimates in the literature. The slope of the transition line at the critical point is found to be $ -0.16(24) $. The study uses a multi-point Padé resummation method to construct a Padé approximation to the logarithm of the QCD grand partition function for complex $ \mu_B $. Singularities of the approximant are used to estimate the CEP location. The authors consider temperature-like and magnetization-like couplings $ t $ and $ h $ near the CEP and apply the Lee-Yang theorem to the universal theory $ (3-d~Z(2)) $, where zeroes of $ Z_{QCD} $ in the complex $ h $-plane that approach the real axis in the thermodynamic limit correspond to phase transitions. The authors find that the location of $ T^{CEP} $ must be searched below the chiral transition temperature $ T_{c}^{chiral} \approx 132 $ MeV. They extend their calculations down to $ T = 120 $ MeV. The results are summarized in Fig. 1, which shows the probability distribution of the QCD critical point from extrapolating Lee-Yang singularities to the real domain using universal scaling. The lattice simulations are performed on $ N_\sigma^3 \times N_\tau $ lattices with $ N_\sigma = 36 $ and $ N_\tau = 6 $, using $ N_f = 2+1 $ dynamical highly improved staggered quarks (HISQ). The simulations run at $ \mathcal{O}(10) $ pure imaginary $ \mu_B $ in the range $ \mu_B/T \in [0, i\pi] $ to avoid the sign problem. The authors measure the first- and second-order cumulants of the net baryon-number density and use these to construct rational approximations of the cumulants. The poles of these approximations are used to estimate the CEP location. The authors estimate the CEP location using a scaling ansatz motivated by the temperature scaling of the