Odd-order nilpotent Malle–Bhargava principle

Let $G$ be a nilpotent group, and let $c_{(H,\phi)}(G)$ be the leading constant in the constrained fair-counting asymptotic for $\operatorname{Epi}_{(H,\phi)}(G_{\mathbb{Q}},G)$. Odd-order Malle–Bhargava conjecture. If $|G|$ is odd, then $c_{(H,\phi)}(G)$ satisfies the Malle–Bhargava principle, namely it is an Euler product. This prediction concerns the factorization of the leading constant into local contributions and is distinct from the asymptotic conjecture itself.