Morita's conjecture on the graded Lie algebras of the Torelli group

Let $g$ be the genus, let $\mathfrak{t}_g$ be the relevant graded Lie algebra associated to the Torelli group, and let $\mathfrak{m}_g$ be the Lie algebra of symplectic derivations. Write $\mathfrak{t}_g(k)$ and $\mathfrak{m}_g(k)$ for their degree-$k$ parts, and let $\mathrm{Gr}\,\mathfrak{t}_g\twoheadrightarrow\mathfrak{m}_g$ be the natural surjection. Morita's conjecture. For any $k\not=2$, the equality

$$\mathfrak{t}_g(k)\cong\mathfrak{m}_g(k)$$

holds so that

$$\mathrm{Ker}(\mathrm{Gr}\,\mathfrak{t}_g\twoheadrightarrow\mathfrak{m}_g)\cong\mathbb{Q}.$$

This conjecture concerns the relationship between the graded Lie algebra of the Torelli group and the Lie algebra of symplectic derivations, and is also formulated in terms of characteristic classes of the mapping class group. The source presents it as an open conjecture and cites Morita's Problem 6.2 as prior context.