Neguț's stable-basis realization conjecture for the quantum affine quiver algebra

Let $\mathcal A$ be the algebra defined by the action-product map from the shuffle-algebra construction, and let $U_q(\widehat{\mathfrak g}^Q)$ be the Hopf algebra obtained from the stable-basis construction for Nakajima quiver varieties. Neguț's stable-basis realization conjecture. The map defined by the action product should yield an isomorphism

$$\mathcal A\cong U_q(\widehat{\mathfrak g}^Q).$$

This is proposed as an algebraic-geometric identification of the shuffle-algebra realization with the stable-basis quantum affine algebra. The text notes that choices of chambers, alcoves and polarization must be arranged so that the map lands in the target, and gives no resolution status.