p-adic Artin integrality conjecture

Let $k$ be a totally real number field and let $\chi:G_k\to\overline{\mathbb Q}_p$ be an even $p$-adic Artin character. Let $G_\chi(T)$ be its Iwasawa power series. p-adic Artin conjecture. There exists an integer $l$ such that

$$p^lG_\chi(T)\in\mathbb Z_{p,\chi}[[T]].$$

The paper states that this integrality is known for odd $p$ and conjectural for $p=2$ in the relevant construction. It is needed to ensure convergence and well-definedness of the associated $p$-adic $L$-function.