The vanishing conjecture for quasi-uneven motivic Lie elements

Let $\mathfrak{d}\mathfrak{g}_1$ be the depth-one part of the depth-graded motivic Lie algebra, let $\mathcal{U}\mathfrak{g}$ be its enveloping algebra, and let $gr^n_{\mathfrak{D}}\mathcal{U}\mathfrak{g}$ be its depth-$n$ graded part. Let

$$\gamma:\underbrace{\mathfrak{d}\mathfrak{g}_1\otimes\cdots\otimes\mathfrak{d}\mathfrak{g}_1}_{n}\longrightarrow gr^n_{\mathfrak{D}}\mathcal{U}\mathfrak{g}$$

be the natural map. Vanishing conjecture. For $n\geq3$, there are no quasi-uneven elements in $\operatorname{Im}\gamma$. This conjecture would identify the quasi-uneven obstruction to the totally odd part in higher depth. The paper does not report a resolution.