The Links-Quivers Correspondence for colored HOMFLY-PT polynomials

Let $L$ be a link, and let $\widehat{P}(L)$ denote its rescaled generating function of antisymmetric-colored HOMFLY-PT polynomials. For a symmetric quiver $Q_L$ with adjacency matrix $Q$, let $P_{Q_L}$ be its cohomological Hall algebra generating function, and let $S$ and $A$ be linear forms on a free $\mathbb{Z}$-module whose dimension is the number of vertices of $Q_L$.

Links-Quivers Correspondence. For every link $L$, there is a symmetric quiver $Q_L$ such that

$$\widehat{P}(L)=P_{Q_L}(\overline{x})\bigg|_{x_i\mapsto (-1)^{Q_{ii}-S_i}q^{S_i-1}a^{A_i}x}.$$

Here $Q$ is regarded as a quadratic form and $S,A$ as linear forms on the corresponding free $\mathbb{Z}$-module. This conjecture proposes a universal quiver description of colored HOMFLY-PT generating functions and is the polynomial form of the Links-Quivers Correspondence; the supplied text does not give evidence that it has been resolved.