Purity conjecture for refined Gopakumar–Vafa invariants of flopping curves

Let $C$ be a flopping curve, let $r$ be a positive integer, and let $\operatorname{GV}_{C,r,0}$ be the associated monodromic mixed Hodge structure. Write $n_{C,r}(q^{1/2})$ for its refined numerical invariant and $n_{C,r}$ for its numerical dimension. Purity conjecture. The mixed Hodge structure $\operatorname{GV}_{C,r,0}$ is pure for every flopping curve $C$ and every $r$; equivalently,

$$n_{C,r}(q^{1/2})=n_{C,r}$$

for all $C$ and $r$. The conjecture asks whether the refined invariants contain information beyond the numerical Gopakumar–Vafa invariants; the paper states that it is open even for $r=1$.