The long exact-sequence conjecture for depth-graded motivic multiple zeta values

Let $\mathcal{A}=\mathcal{H}/(\zeta^{\mathfrak{m}}(2))$, with depth-graded pieces $gr_r^{\mathfrak{D}}\mathcal{A}$, and let $\mathbb{P}^{\vee}$ be the weight-dual of the restricted even period-polynomial space. Long exact-sequence conjecture. For $r\geq4$, there is an exact sequence

$$0\longrightarrow\mathbb{P}^{\vee}\otimes gr_{r-4}^{\mathfrak{D}}\mathcal{A}\longrightarrow gr_r^{\mathfrak{D}}\mathcal{A}\longrightarrow gr_1^{\mathfrak{D}}\mathcal{A}^{odd}\otimes gr_{r-1}^{\mathfrak{D}}\mathcal{A}\longrightarrow\mathbb{P}^{\vee}\otimes gr_{r-2}^{\mathfrak{D}}\mathcal{A}\longrightarrow0.$$

This conjecture extends the known exact sequences in depths two and three and would give a general long exact sequence compatible with the motivic Broadhurst–Kreimer structure. The paper does not report a resolution.