Carnot tangent characterization of biLipschitz rectifiability

Let $(X,d)$ be a complete metric space, let $\mathbb G$ be a Carnot group of homogeneous dimension $Q$, and let $E\subseteq X$ be a Borel subset such that $0<\mathcal{H}^Q(E)<+\infty$. Write $\Theta^Q_*(\mathcal{H}^Q\llcorner E,x)$ for the lower $Q$-density of $\mathcal{H}^Q\llcorner E$ at $x$, and call a metric space biLipschitz $\mathbb G$-rectifiable if it is covered, up to a set of zero $Q$-dimensional Hausdorff measure, by countably many subsets biLipschitz equivalent to subsets of $\mathbb G$. A pointed measured Gromov--Hausdorff tangent (pmGH tangent) is a pointed measured Gromov--Hausdorff limit obtained by rescaling $(X,d,\mathcal{H}^Q\llcorner E)$ at a point.

Carnot tangent characterization. The following are equivalent:

1. $\Theta^Q_*(\mathcal{H}^Q\llcorner E,x)>0$ for $\mathcal{H}^Q$-almost every $x\in X$, and, for $\mathcal{H}^Q$-almost every $x\in X$, there exists a constant $K_x$ such that all the pmGH tangents of $(X,d,\mathcal{H}^Q\llcorner E)$ at $x$ are supported on metric spaces that are $K_x$-biLipschitz equivalent to $\mathbb G$.
2. $(E,d)$ is biLipschitz $\mathbb G$-rectifiable.

This conjecture seeks a characterization of biLipschitz rectifiability in terms of metric-measure tangents modeled on a non-Abelian Carnot group. Its resolution would connect the authors' differentiability-space framework with geometric measure theory; the supplied text does not state whether it is known or open.