definiteness and simplicity here we focus on the simplest type-I seesaw mechanism in which only one right-handed neutrino, $n=1$, is added to the [[Standard Model ]{}]{}particle content, the scenario called (3,1) in [@Schechter:1980gr]. Since at least two light neutrino masses are required to explain the current neutrino oscillation data, the minimal (3,1) seesaw scheme is not phenomenologically viable by itself. However, it gives us a good starting point since it provides a clear picture of the impact of seesaw extensions on the Higgs vacuum stability in the simplest possible setting. Moreover, it provides an adequate template for the formulation of a fully realistic scotogenic dark matter completion [@Rojas:2018wym], to be discussed in latter sections.

Let us start by looking at the impact of the right-handed neutrinos on the stability of the Higgs vacuum. As we discussed at length in Section \[sec:sm-vac\], the [[Standard Model ]{}]{}RG running of the Higgs quartic scalar coupling $\lambda$ is dominated by the top Yukawa, which is the largest coupling present in the theory. As we saw, in this case the [[Standard Model ]{}]{}$\lambda$ coupling becomes negative around the scale $\mu\sim 10^{10}$ GeV. However, within the seesaw completion, the neutrino Yukawa couplings $Y_\nu$ of can completely 