Morita's nontriviality conjecture for graph homology classes

For each integer $k\geq 1$, let $[\mu_k]$ denote the Morita homology class in

$$H\bigl(\mathsf{FG}_0^{2k+2\text{-loop}}(0)\bigr).$$

Morita's conjecture. The Morita homology classes $[\mu_k]\in H\bigl(\mathsf{FG}_0^{2k+2}(0)\bigr)$ are non-trivial for every $k\geq 1$. These classes are part of an infinite family in forested graph homology; the supplied text gives no evidence that nontriviality is known for every $k$.