The analogue of the Deligne–Ihara conjecture for once-punctured CM elliptic curves

Let $I$ be the index set of multi-indices used to define the characters $\kappa_{\boldsymbol{m}}$, let $g$ be the associated graded Lie algebra, and let $\chi^{\boldsymbol{m}}$ denote the corresponding isotypic character. For every $\boldsymbol{m}\in I$, choose $\sigma_{\boldsymbol{m}}$ in the $\chi^{\boldsymbol{m}}$-isotypic component of $g_{|\boldsymbol{m}|}$ such that $\kappa_{\boldsymbol{m}}(\sigma_{\boldsymbol{m}})\in\mathbb{Z}_p(\boldsymbol{m})$ is nonzero and generates $\kappa_{\boldsymbol{m}}(g_{|\boldsymbol{m}|})$. Analogue of the Deligne–Ihara conjecture. The graded Lie algebra $g\otimes\mathbb{Q}_p$ is freely generated by $\{\sigma_{\boldsymbol{m}}\}_{\boldsymbol{m}\in I}$. This is the paper's proposed analogue for the pro-$p$ outer Galois representation associated with a once-punctured CM elliptic curve; the supplied text does not state whether it is known or open.