Balogh–Tyson conjecture on polarizable Carnot groups

Let $\mathbb{G}$ be a Carnot group of homogeneous dimension $Q\geq 3$, and let $u$ be Folland's fundamental solution for the sub-Laplacian. The group is polarizable if $u^{1/(2-Q)}$ is infinity-harmonic away from the identity. A nascent H-type group is a step two Carnot group whose horizontal metric admits a compatible vertical metric making the resulting metric Lie algebra H-type. Balogh–Tyson's conjecture. If $\mathbb{G}$ is polarizable, then $\mathbb{G}$ has step two and is a nascent H-type group. The conjecture extends the known fact that H-type groups are polarizable and would characterize the polarizable groups, but the source gives no resolution.