a lower and not an upper bound on the lightest neutrino mass. In particular we find that the lightest neutrino must have $m_{\nu} \geq 1.6 \, \text{meV}$. We can combine this bound with the results in [@IMV1; @2toro] to conclude that, if both conjectures are true, the SM with inverse hierarchy would be in the Swampland. Normal hierarchy is therefore another non-trivial prediction that arises from the conjecture. It is interesting that present data already show a slight preference for the normal hierarchy.

Constraints on the SM Higgs mass
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Independently of the above 3D constraints on the SM, one can consider possible SSWGC constraints directly in 4D. Here the natural candidate to give rise to interactions weaker than gravity at some scale is the Higgs field. The bound in eq(\[ours\]) is a bound on the mass of a scalar (for all $\phi$). Since the mass is suppressed by a $1/M_{\text{p}}$ factor one may expect that it will trivially be obeyed by any particle physics model. In fact this is not necessarily the case. It may happen that for some particular value of $\phi$ the term in the left hand side cancels exactly. In other words, defining () =  2(V”’)\^2 