The Drinfeld-associator generation conjecture for unramified Tate periods

Let $P$ be the algebra of periods, let $P_{\mathbb{Z},\mathrm{Tate}}$ be the subalgebra generated by $(2\pi i)^{\pm1}$ and periods of mixed Tate motives unramified over $\mathsf{Spec}(\mathbb{Z})$, and let $I_{\epsilon_1,\dots,\epsilon_n}$ denote the integrals occurring in Drinfeld's associator. The Drinfeld-associator generation conjecture. $P_{\mathbb{Z},\mathrm{Tate}}$ is the subalgebra of $P$ generated by $(2\pi i)^{\pm1}$ and by periods whose evaluations are the integrals $I_{\epsilon_1,\dots,\epsilon_n}$ appearing in Drinfeld's associator. The source motivates this with dimension counts and computer experiments, but gives no proof or resolution.