Gras's freeness conjecture for maximal pro-p extensions unramified outside p

Let $K$ be a number field, let $S_p$ be the set of $p$-adic primes of $K$, and let $\Gamma_{S_p}=\operatorname{Gal}(K_{S_p}/K)$, where $K_{S_p}$ is the maximal pro-$p$ extension of $K$ unramified outside $S_p$. Let $r_2$ be defined by the condition that $2r_2$ is the number of complex embeddings of $K$. Gras's conjecture. For $p\gg 0$, the pro-$p$ group $\Gamma_{S_p}$ is free on $r_2+1$ generators. This conjecture predicts the eventual freeness and rank of the relevant Galois groups; the source attributes it to Gras, but the supplied text gives no evidence resolving its status.