Homological q-holonomicity of colored HOMFLY homologies

A sequence of chain complexes of filtered graded vector spaces is said to be homologically $q$-holonomic when it satisfies the proposed notion of homological $q$-holonomicity. For a knot $K$ in $S^3$, let $\{{[\![K]\!]}_{S^r}\}_{r\geq 1}$ denote the sequence of $S^r$-colored HOMFLY homologies. Homological $q$-holonomicity conjecture. For each knot $K$ in $S^3$, the sequence

$$\{{[\![K]\!]}_{S^r}\}_{r\geq 1}$$

is homologically $q$-holonomic. This conjecture proposes a categorified analogue of the known $q$-holonomicity of colored HOMFLY polynomials, extending recurrence relations from Euler characteristics to HOMFLY homology. The source does not state any cases in which the conjecture is proved or disproved.