Brown's even-part conjecture for the depth graded motivic Lie algebra

Let ${\mathfrak{d}}{\mathfrak{g}}$ be the depth graded motivic Lie algebra, let ${\mathfrak{s}}{\mathfrak{d}}{\mathfrak{g}}$ be the subalgebra generated by the non-exceptional elements, and define

$${\mathfrak{e}}:=\ker({\mathfrak{d}}{\mathfrak{g}}\to{\mathfrak{s}}{\mathfrak{d}}{\mathfrak{g}}).$$

Here ${\mathfrak{e}}$ is the ideal generated by the exceptional generators, and $\pi_e$ denotes projection to the totally even part. Even-part conjecture. Projection to the totally even part kills ${\mathfrak{e}}$ and induces an isomorphism ${\mathfrak{s}}{\mathfrak{d}}{\mathfrak{g}}\cong{\mathfrak{e}}{\mathfrak{g}}$; equivalently,

$$\ker\left(\pi_e:{\mathfrak{d}}{\mathfrak{g}}\to\bigoplus_{n\geq 1}\mathbb{Q}[z_0^2,\ldots,z_n^2]\right)={\mathfrak{e}}.$$

The conjecture is intended to identify the non-exceptional depth-graded Lie algebra with its totally even quotient and thereby explain the totally odd dimension conjecture.