Finiteness conjecture for finitely generated d-maximal pro-2 groups

Let $G$ be a finitely generated pro-$2$ group, and write $d(G)=\dim_{\mathbb{F}_2}G/G^{2}[G,G]$. Call $G$ $d$-maximal if $d(H)<d(G)$ for every proper closed subgroup $H<G$. The pro-2 finiteness conjecture. Every finitely generated $d$-maximal pro-$2$ group is finite.

The source presents this as a weaker version of the conjecture that the nilpotency class of an $r$-generated finite $d$-maximal $2$-group is bounded in terms of $r$. The supplied text gives no evidence of a resolution.