Oberdieck–Pandharipande multiple-cover conjecture for K3 surfaces

Let $S$ be a K3 surface, let $\beta$ be a primitive curve class, let $m$ be a positive integer, and let $\gamma_1,\ldots,\gamma_n$ be cohomology insertions. Let $\tau_{a_i}(\gamma_i)$ denote descendant insertions, let $\deg$ have the meaning used in the source, and let $\varphi_{d,m}$ be the cohomological map appearing in the multiple-cover formula. Oberdieck–Pandharipande's multiple-cover conjecture.

$$\left\langle \tau_{a_1}(\gamma_1)\ldots\tau_{a_n}(\gamma_n)\right\rangle_{g,m\beta}=\sum_{d\mid m}d^{2g-3+\deg}\left\langle \tau_{a_1}(\varphi_{d,m}(\gamma_1))\ldots\tau_{a_n}(\varphi_{d,m}(\gamma_n))\right\rangle_{g,\varphi_{d,m}\left(\frac{m}{d}\beta\right)}.$$

This formula is intended to compute imprimitive K3 Gromov–Witten invariants from primitive ones and is the multiple-cover formula invoked to explain the higher-divisibility holomorphic anomaly equation.