The paper presents a comprehensive analysis of the Standard Model (SM) Higgs potential at next-to-next-to-leading order (NNLO). The authors compute the two-loop QCD and Yukawa corrections to the relation between the Higgs quartic coupling ($\lambda$) and the Higgs mass ($M_h$), reducing the theoretical uncertainty in determining the critical value of $M_h$ for vacuum stability to 1 GeV. They find that while $\lambda$ at the Planck scale is close to zero, absolute stability of the Higgs potential is excluded at 98% confidence level for $M_h < 126$ GeV. The paper discusses the implications of the near-zero $\lambda$ at the Planck scale, including the possibility of the Higgs field playing a role during inflation. The authors explore scenarios where the Higgs field could have caused inflation by non-minimal coupling to gravity or by being trapped in an unstable minimum near the Planck scale. They conclude that these possibilities are not favored by current data unless the top quark mass is below about 172 GeV or new-physics threshold corrections modify the SM potential. The paper provides a detailed derivation of the two-loop corrections to the Higgs mass and the Higgs quartic coupling, and presents numerical results for the stability condition in the $M_h$-$M_t$ plane.The paper presents a comprehensive analysis of the Standard Model (SM) Higgs potential at next-to-next-to-leading order (NNLO). The authors compute the two-loop QCD and Yukawa corrections to the relation between the Higgs quartic coupling ($\lambda$) and the Higgs mass ($M_h$), reducing the theoretical uncertainty in determining the critical value of $M_h$ for vacuum stability to 1 GeV. They find that while $\lambda$ at the Planck scale is close to zero, absolute stability of the Higgs potential is excluded at 98% confidence level for $M_h < 126$ GeV. The paper discusses the implications of the near-zero $\lambda$ at the Planck scale, including the possibility of the Higgs field playing a role during inflation. The authors explore scenarios where the Higgs field could have caused inflation by non-minimal coupling to gravity or by being trapped in an unstable minimum near the Planck scale. They conclude that these possibilities are not favored by current data unless the top quark mass is below about 172 GeV or new-physics threshold corrections modify the SM potential. The paper provides a detailed derivation of the two-loop corrections to the Higgs mass and the Higgs quartic coupling, and presents numerical results for the stability condition in the $M_h$-$M_t$ plane.