The stable invariant Albanese cohomology conjecture for Torelli groups

Let $\mathcal{I}_g$, $\mathcal{I}_{g,1}$ and $\mathcal{I}_g^1$ be the Torelli groups of a closed surface, a surface with one boundary component, and a surface with one marked point, respectively. The invariant Albanese cohomology conjecture. Stably, there are isomorphisms of graded algebras

$$H_A^*(\mathcal{I}_g,\mathbb{Q})^{\operatorname{Sp}(2g,\mathbb{Z})}\cong H_A^*(\mathcal{I}_{g,1},\mathbb{Q})^{\operatorname{Sp}(2g,\mathbb{Z})}\cong\mathbb{Q}[y_1,y_2,\ldots],$$ $$H_A^*(\mathcal{I}_g^1,\mathbb{Q})^{\operatorname{Sp}(2g,\mathbb{Z})}\cong\mathbb{Q}[z,y_1,y_2,\ldots],$$

where $\deg y_i=4i$ and $\deg z=2$. The source presents this as a conjecture closely related to, but distinct from, the Kawazumi–Morita conjecture; it remains open.