Local PT/GV correspondence for irreducible one-cycles

Let $X$ be a Calabi–Yau threefold, let $\beta$ be an effective one-cycle class, and let $gamma \in \operatorname{Chow}_{\beta}(X)$ be an irreducible one-cycle. Denote by $P_{n,\gamma}^{\mathrm{loc}}$ the local stable-pair invariant and by $n_{g,\gamma}^{\mathrm{loc}}$ the local Gopakumar–Vafa invariant associated with $\gamma$. Local PT/GV correspondence. One should have the identity

$$\sum_{n\in\mathbb Z}P_{n,\gamma}^{\mathrm{loc}}q^n=\sum_{g\geq 0}n_{g,\gamma}^{\mathrm{loc}}(q^{1/2}+q^{-1/2})^{2g-2}.$$

This is the fixed-cycle form of the conjectural correspondence between stable-pair and Gopakumar–Vafa invariants; the source gives no resolution.