Morita's non-vanishing conjecture for the Morita classes of free-group automorphisms

For each integer $i\geq1$, let

$$\mu_i\in H_{4i}(\operatorname{Out}F_{2i+2};\mathbb Q)$$

be the homology class constructed from Kontsevich's graph-homology construction. Morita's conjecture. The classes $\mu_i$ are non-trivial for all $i=1,2,\ldots$. The cases $i=1$ and $i=2$ were known to be non-trivial at the time of the paper, while non-triviality for all $i$ remains open.