  We perform a manifestly gauge-independent analysis of the vacuum stability in
the Standard Model (SM) including two-loop matching, three-loop renormalization
group evolution, and pure QCD corrections through four loops. All these
ingredients are exact, except that light-fermion masses are neglected. We in
turn apply the criterion of nullifying the $\overline{\mathrm{MS}}$ Higgs
self-coupling and its beta function and a recently proposed consistent method
for determining the true minimum of the effective Higgs potential that also
avoids gauge dependence. Exploiting our knowledge of the Higgs-boson mass, we
derive an upper bound on the pole mass of the top quark by requiring that the
SM be stable all the way up to the Planck mass scale and conservatively
estimate the theoretical uncertainty. This bound is compatible with Monte Carlo
mass quoted by the Particle Data Group at the $1.3\sigma$ level.
