Parity stability conjecture for the top cohomology of $\operatorname{Aut}(F_n)$

Let $F_n$ be the free group of rank $n\geq 2$, let $\operatorname{Aut}(F_n)$ be its automorphism group, and let $H^*(-;\mathbb{Q})$ denote rational group cohomology. Parity stability conjecture. For each $i\geq 0$ the group $H^{2n-2-i}(\operatorname{Aut}(F_n);\mathbb{Q})$ only depends on the parity of $n$ for $n\gg i$. This is a more speculative analogue of the stable instability conjectures for arithmetic and mapping class groups, and the source states that it remains open even for $i=0$.