  The knowledge of the stability condition of the electroweak (EW) vacuum is of
the greatest importance for our understanding of beyond Standard Model (BSM)
physics. It is widely believed that new physics that lives at very high energy
scales should have no impact on the stability analysis. This expectation has
been recently challenged, but the results were controversial as new physics was
given in terms of non-renormalizable higher order operators. Here we consider
for the first time a renormalizable (toy) UV completion of the SM, and
definitely show that such a decoupling does not take place. This result has
important phenomenological consequences, providing a very useful test for BSM
theories. In particular, it shows that speculations based on the so called
"criticality" do not appear to be well founded.
