  We study the gauge-independent observables associated with two interesting
stationary configurations of the Standard Model Higgs potential (extrapolated
to high energy according to the present state of the art, namely the NNLO): i)
the value of the top mass ensuring stability of the SM electroweak minimum, and
ii) the value of the Higgs potential at a rising inflection point. We examine
in detail and reappraise the experimental and theoretical uncertainties which
plague their determination, finding that: i) stability of the SM is compatible
with the present data at the 1.5 sigma level; ii) despite the large theoretical
error plaguing the value of the Higgs potential at a rising inflection point,
application of such configuration to models of primordial inflation displays a
3 sigma tension with the recent bounds on the tensor-to-scalar ratio of
cosmological perturbations.
