The elliptic Deligne–Ihara conjecture for complex multiplication

Let $X$ be the once-punctured elliptic curve under consideration, let $K$ be its complex multiplication field, let $I_K$ be the specified index set, and let $\boldsymbol{m}$ range over $I_K$. Write $\mathfrak{g}_{X,|\boldsymbol{m}|}$ for the component of degree $|\boldsymbol{m}|$, and let $\mathbb{Q}_p(\boldsymbol{m})$ denote the corresponding isotypic representation. The elliptic Deligne–Ihara conjecture. The Lie algebra $\mathfrak{g}_{X} \otimes \mathbb{Q}_{p}$ is a free bigraded Lie algebra with one generator in the $\mathbb{Q}_{p}(\boldsymbol{m})$-isotypic component of $\mathfrak{g}_{X, |\boldsymbol{m}|} \otimes \mathbb{Q}_{p}$ for each $\boldsymbol{m} \in I_{K}$. This is the elliptic analogue of the Deligne–Ihara conjecture for the thrice-punctured projective line; the source says it was conjectured in previous work, and the supplied text does not establish its resolution.