Globality conjecture for dual pairs of Malcev algebras and Moufang loops

Let $(M,\mathcal{L})$ be a dual pair of Malcev algebras and their corresponding Moufang loops. A dual pair is global if, for every local analytic loop $G$ in the variety $\mathcal{L}$, there exists a global analytic loop $\tilde G$ in $\mathcal{L}$ that is locally isomorphic to $G$.

Globality conjecture. Every dual pair $(M,\mathcal{L})$ of Malcev algebras and their corresponding Moufang loops is global.

This conjecture concerns the passage from local analytic Moufang loops to globally defined analytic loops in the same variety. The surrounding discussion notes that not all varieties of Moufang loops are smooth, but gives no resolution of the conjecture.