The adelic Lehmer conjecture for hypersurface heights

Let $V$ be a hypersurface in $\mathbb{G}_m^n$ defined over $\mathbb{Q}(T_1,\ldots,T_d)$, and let $\widehat{h}_S(V)$ denote its normalized height. Suppose that $V$ is not a union of torsion subvarieties.

Adelic hypersurface Lehmer conjecture. There exists a positive constant $c(n)$, depending only on $n$, such that

$$\widehat{h}_S(V)\geq c(n).$$

This is the hypersurface analogue of the adelic Lehmer problem: it predicts a uniform positive lower bound for normalized heights away from torsion geometry. The source proposes it as a conjecture for future investigation, with no resolution stated.