The Links-Quivers Correspondence for colored HOMFLY-PT homology

Let $L$ be a link with the exponential growth property. Let $\widehat{\mathcal{P}}(L)$ be the rescaled generating function of its colored HOMFLY-PT Poincaré polynomials. Let $Q$ be a symmetric quiver with $m$ vertices, and let $S,A,T\in\mathbb{Z}^m$ be grading vectors; write $Q$ for its adjacency matrix and $(q^2;q^2)_{d_i}$ for the $q$-Pochhammer symbols.

Links-Quivers Correspondence for homology. The colored HOMFLY-PT homologies of $L$ may be represented by chain complexes such that

$$\widehat{\mathcal{P}}(L)=\sum_{\mathbf d=(d_1,\ldots,d_m)\in\mathbb{N}^m}\frac{q^{S\cdot\mathbf d+\mathbf d\cdot Q\cdot\mathbf d^T}a^{A\cdot\mathbf d}t^{T\cdot\mathbf d}}{\prod_{i=1}^m(q^2;q^2)_{d_i}}x^{d_1+\cdots+d_m},$$

where $T=(t_1,\ldots,t_m)\in\mathbb{Z}^m$ satisfies $t_i=-Q_{ii}$. This extends the Links-Quivers Correspondence from colored HOMFLY-PT polynomials to their triply graded homologies; the supplied text identifies it as a reformulation of an earlier conjecture but gives no resolution.