The collider landscape: which collider for establishing the SM instability?

Capabilities of future colliders are usually discussed assuming specific hypothetical new physics. We consider the opposite possibility: that no new physics is accessible, and we want to learn if the unnatural Standard Model is part of a vast landscape. We argue that a main step in this direction would be establishing the possible instability scale of the Higgs potential. This primarily needs reducing the uncertainty on the strong coupling and on the top quark mass. We show that the top quark mass can be measured well enough via a $t \bar t$ threshold scan with low $10^{33}\,{\rm cm}^{-2}{\rm sec}^{-1}$ luminosity, that seems achievable at a `small' $e^+ e^-$ collider in the LEP tunnel, or at the first low-energy stage of a muon collider.