large $\phi$ but one must change to $e^{\phi/M_{\text{p}}}$ for $\phi \rightarrow - \infty$, and there is no single function which includes both behaviours simultaneously. We propose that the above formulated SWGC needs to be modified in such a way that both issues may be circumvented. Furthermore we will insist that our new SWGC applies to any scalar in the theory. The latter possibility was termed [*Super SWGC*]{} in [@Palti].

We propose the formulation of a Strong version of a Scalar Weak Gravity Conjecture (SSWGC) for the case of a single scalar as follows:

[*i) The potential of any canonically normalized real scalar $V(\phi)$ in the theory must verify for any value of the field the constraint:*]{}

\[ours\]

with primes denoting derivation with respect to $\phi$. Compared to eq.(\[palti\]) here there is a new term $V^{\prime \prime \prime \prime}$ associated to the quartic interaction of the scalars. Such a term was not present in the SWGC bound in the previous paragraph because such an interaction among the $H$ fields is not mediated by $\phi$ and hence it should not be included. In our case it is different because our condition applies to any scalar, including massive mediators. In our conjecture there 