Higher-degree local-curve equivariant GW/DT4 conjecture

Let $C$ be a smooth projective curve, let $L_1,L_2,L_3$ be line bundles on $C$ satisfying

$$L_1\otimes L_2\otimes L_3\cong\omega_C,$$

and let $d\geq1$. Higher-degree local-curve conjecture. After substituting $\lambda_3=-\lambda_1-\lambda_2$,

$$\mathrm{GW}_{0,d[C]}=\sum_{k\mid d}\frac{1}{k^3}\mathrm{DT}_4\left(\frac{d}{k}[C]\right)\in\mathbb Q(\lambda_1,\lambda_2).$$

This extends the degree-two local-curve prediction to all positive degrees. It is conjectural in general; the paper reports verification only in limited cases.