The formal extended double shuffle conjecture for multiple zeta values

Let $\mathcal{Z}^f$ be the quotient of the shuffle algebra by the two-sided ideal generated by the formal extended double shuffle relations, and write $\zeta^f(k_1,\ldots,k_r)$ for the class of the corresponding word. Let $\mathcal{Z}$ be the algebra of multiple zeta values, with generators denoted $\zeta(k_1,\ldots,k_r)$. The formal extended double shuffle conjecture. The $\mathbb{Q}$-algebra homomorphism

$$\mathcal{Z}^f \longrightarrow \mathcal{Z},\qquad \zeta^f(k_1,\ldots,k_r)\longmapsto \zeta(k_1,\ldots,k_r)$$

is a $\mathbb{Q}$-algebra isomorphism. Equivalently, all $\mathbb{Q}$-linear relations among multiple zeta values are obtained from the extended double shuffle relations. This is the algebraic formulation of the extended double shuffle conjecture; the source gives no resolution.