Independence conjecture for rational 2-Selmer prime conditions

Let $n=2m$, let $S$ be a finite set of primes, let $T$ be a finite set of primes (or an infinite set when $n>2$) disjoint from $S$, and let $X_{S,T}$ be the set of $S_n$-number fields for which every $p\in S$ lies in $\operatorname{Sel}_2^{\mathbb{Q}}(F)$ and every $q\in T$ does not. The rational 2-Selmer independence conjecture. As $F$ varies over $S_n$-number fields of degree $2m$ with signature $(r_1,r_2)$ ordered by absolute discriminant,

$$\operatorname{Prob}(F\mid F\in X_{S,T})=\prod_{p\in S}\left(\frac{c(m,p)}{c(2m,p)}\cdot\frac{1}{p^m}\right)\prod_{q\in T}\left(1-\frac{c(m,q)}{c(2m,q)}\cdot\frac{1}{q^m}\right).$$

This asserts independence of the prime-by-prime rational 2-Selmer conditions and is used to predict rationally imprimitive types; it remains open.