Căldăraru's conjecture for the ribbon graph complex in genera at least two

Let $\mathsf{RGC}^g$ be the genus-$g$ part of the ribbon graph complex, with altered differential $\delta+\Delta$, where $\Delta$ is the Bridgeland differential, and let ${\rM}_g$ be the moduli space of curves of genus $g$ without marked points.

Căldăraru's conjecture. For every genus $g\geq 2$, there is a natural identification

$$H(\mathsf{RGC}^{g},\delta+\Delta)\cong H_c({\rM}_g)[-1].$$

This conjecture is presented as a consequence of the proposed comparison between the twisted hairy graph complex and the ribbon graph complex. The source gives no resolution status.