Bhargava–Shankar's average $n$-Selmer size conjecture

Let $n$ be any positive integer. For elliptic curves $E$ over $\mathbb{Q}$ ordered by height, let $\operatorname{Sel}_n(E/\mathbb{Q})$ denote the $n$-Selmer group, and let $\sigma(n)$ be the sum of the divisors of $n$. Bhargava–Shankar's conjecture. The average size of $\operatorname{Sel}_n(E/\mathbb{Q})$ is $\sigma(n)$. The conjecture has been verified for $n=2,3,4,5$, yielding partial results toward the rank distribution conjecture; it is not stated as fully resolved for arbitrary positive integers here.