Representation stability for graded Torelli Lie algebras of surfaces

Let $\mathcal{I}_{g,1}$ be the Torelli group of a genus-$g$ surface with one boundary component, and let $\operatorname{gr}(\mathcal{I}_{g,1})$ be the graded rational Lie algebra associated to its lower central series; write $\operatorname{gr}(\mathcal{I}_{g,1})^i$ for its $i$th graded piece. For $g\geq 6$, the source recalls a presentation of this Lie algebra as an $\operatorname{Sp}_{2g}(\mathbb{Q})$-representation. Stability of the Malcev Lie algebra conjecture. For each fixed $i\geq 1$, the sequence $\{\operatorname{gr}(\mathcal{I}_{g,1})^i\}$ of $\operatorname{Sp}_{2g}\mathbb{Q}$-representations is uniformly representation stable. This is described as the infinitesimal counterpart of the Torelli-group homology conjecture; the source gives no resolution.