Cao–Toda genus-one DT$_4$ descendent correspondence conjecture

Let $X$ be a Calabi–Yau $4$-fold, let $\beta$ be a curve class, and let $\tau_1(\gamma)$ be the first descendant insertion for $\gamma\in H^2(X,\mathbb Z)$. Write $n_{0,\beta}(\gamma^2)$ and $n_{1,\beta}$ for the genus-zero and genus-one Gopakumar–Vafa invariants, let $m_{\beta_1,\beta_2}$ be the meeting invariants, and use $(\gamma\mathbin{\cdot}\beta)$ for the intersection pairing.

Cao–Toda's genus-one descendent correspondence conjecture. Via some suitable choice of orientation on the moduli space, one has, for all $\gamma\in H^2(X,\mathbb Z)$,

$$\langle\tau_1(\gamma)\rangle_\beta=\frac{n_{0,\beta}(\gamma^2)}{2(\gamma\mathbin{\cdot}\beta)}-\sum_{\beta_1+\beta_2=\beta}\frac{(\gamma\mathbin{\cdot}\beta_1)(\gamma\mathbin{\cdot}\beta_2)}{4(\gamma\mathbin{\cdot}\beta)}m_{\beta_1,\beta_2}-\sum_{k\geq1,\,k|\beta}\frac{(\gamma\mathbin{\cdot}\beta)}{k}n_{1,\beta/k}.$$

This conjecture relates DT$_4$ descendant invariants to genus-one Gopakumar–Vafa invariants and meeting invariants; the supplied text gives no general resolution.