Universal-enveloping-algebra conjecture for the local line Quot CoHA module

Let $Q$ be the three-loop quiver obtained from $Q_r$ by removing the framing vertex and all arrows containing it. For framing vector $\mathbf f=1$ and stability parameter $\zeta_{\underline\infty}=-1$, let

$$\mathcal N_{Q_{\operatorname{fr}},\mathbf f}^{\zeta}=\bigoplus_{n\geq 0}\operatorname{H}(Q_L^n,\phi^{\operatorname{mon}}_{\operatorname{Tr}(W_r)}\underline{\mathbb Q}_{\mathcal N^{\circ\circ}_n})\otimes\mathbb T^{-n-n^2}$$

be the resulting graded mixed Hodge structure, identified with the vanishing-cycle cohomologies of the Quot schemes $Q_L^n$. Universal-enveloping-algebra conjecture. The graded mixed Hodge structure $\mathcal N_{Q_{\operatorname{fr}},\mathbf f}^{\zeta}$ is a universal enveloping algebra. This conjecture proposes an algebraic structure on the local line Quot vanishing-cycle module; the source mentions a cocommutative coproduct and a candidate compatible product, but does not establish the universal-enveloping-algebra identification.