The Cohen–Lenstra–Martinet heuristic for Arakelov class groups

Let $K$ be a number field, let $\bar K$ be an algebraic closure, let $G$ be a finite group, let $P$ be a set of primes, and let $V$ be the prescribed rational $G$-module. Let $\Lambda=\Z_{(P)}[G]$, let $\cF$ be the infinite family of pairs $(F,i)$ described in the setup, and for $B>0$ let $\cF_{c\leq B}$ be the subfamily with ramification norm at most $B$. For a reasonable function $f$ on the corresponding module-isomorphism space, write $\bE_{\cM_V}(f)$ for its expected value.

Cohen–Lenstra–Martinet conjecture. If $P$ is finite, then

$$\lim_{B\to\infty}\frac{\sum_{(F,i)\in\cF_{c\leq B}}f(\Lambda\otimes_{\Z[G]}\Ar_F)}{\#\cF_{c\leq B}}=\bE_{\cM_V}(f).$$

This is a refined distributional conjecture for Arakelov class groups in families of Galois extensions, proposed in the cited work as a version of the Cohen–Lenstra–Martinet heuristics. The supplied text does not give a resolution status.