Is the electroweak vacuum absolutely stable if the SM holds to $M_{\mathrm{Pl}}$?
In plain words
If no new particles appear up to the Planck scale, the measured Higgs and top-quark masses seem to make our vacuum only long-lived instead of permanently stable. The verdict depends on the top mass to a fraction of a GeV.
Precise statement
In the SM with three-loop RG running and two-loop matching, determine whether the effective Higgs quartic stays positive for all field values up to and beyond $M_{\mathrm{Pl}}$. Absolute stability requires a top pole mass near $171.1\,\mathrm{GeV}$, about $1.5\,\mathrm{GeV}$ below the direct-measurement average $172.57 \pm 0.29\,\mathrm{GeV}$, or $\alpha_s(m_Z)$ near 0.1213 instead of 0.1180 (Hiller et al. 2024); the answer is the classification stable, metastable or unstable at $5\sigma$.
What would settle it
A top-quark pole mass determination with uncertainty $\sim 0.1\,\mathrm{GeV}$ (for example from a t-tbar threshold scan at an $e+e-$ collider) together with $\alpha_{s}(m_{Z})$ to $\sim 0.1\,\mathrm{percent}$.
Status in the literature
Unverified note
Hiller, Hohne, Litim and Steudtner (arXiv:2401.08811, revised 2026) find stability disfavored by $1.9\,\sigma$ with the cross-section pole mass $172.4 \pm 0.7\,\mathrm{GeV}$ and by $5.1\,\sigma$ if the template-fit mass $172.57 \pm 0.29\,\mathrm{GeV}$ is taken as the pole mass; reducing the $m_{t}$ and $\alpha_{s}$ errors by a factor of 2 to 3 would settle it at $5\,\sigma$.