Modified Kähler-equation formula for Gromov–Witten correlators

Let $P_g$ be the set of partitions of $g$, let $S(\sigma_g)$ be the partition coefficient defined by the generating function in the paper, let $\tilde{L}^{N,k,d_i}_{1+(k-N)d_i}$ be the indicated virtual structure constants, and let $w(\cdots)_{d-g}$ be the quantity obtained from associativity and the modified Kähler equation. Modified Kähler-equation conjecture.

$$\left\langle {\cal O}_{e^{N-2-m}}{\cal O}_{e^{m-1-(k-N)d}}{\cal O}_{e}\right\rangle_d=\sum_{g=0}^{d-1}(-1)^{l(\sigma_g)}\sum_{\sigma_g\in P_g}S(\sigma_g)\left(\prod_{i=1}^{l(\sigma_g)}\frac{\tilde{L}^{N,k,d_i}_{1+(k-N)d_i}}{d_i}\right)w\left({\cal O}_{e^{N-2-m}}{\cal O}_{e^{m-1-(k-N)d}}{\cal O}_{e}\prod_{i=1}^{l(\sigma_g)}{\cal O}_{e^{1+(k-N)d_i}}\right)_{d-g}.$$

The source calls this the main result rather than explicitly giving it a conjectural status; the supplied status is unresolved.