The generalized Malle conjecture for linear group actions

Let $K$ be a number field and let $G$ act faithfully and linearly on $V=\mathbb{A}_K^d$, with the associated map $\overline{V}\to\overline{X}=\overline{V}/G$ étale in codimension one. Let $N(G,V,B)$ count $G$-fields with extended $V$-discriminant at most $B$, and let $\operatorname{age}(G)$ be the minimum age of a nontrivial element of $G$. Let $\upsilon(G)$ be the number of youngest $K$-conjugacy classes. The generalized Malle conjecture. If $K$ is sufficiently large, then

$$N(G,V,B)\sim CB^{1/\operatorname{age}(G)}(\log B)^{\upsilon(G)-1}.$$

This extends Malle's predicted exponent from permutation representations to general faithful linear actions; the source gives no resolution status.