Relative Gromov–Witten invariant formula for plane curves satisfying (AL)

Let $B$ be the plane cubic from the preceding setup, let $m_d$ denote the number of degree-$d$ plane curves satisfying (AL) and meeting $B$ at a specified point of order $3d$, and let $[M_{3d}^B({\mathbb{P}^2},d)]^{\mathrm{virt}}$ be the virtual fundamental class of the corresponding relative stable-map locus. Relative invariant formula. The virtual class satisfies

$$[M_{3d}^B({\mathbb{P}^2},d)]^{\mathrm{virt}}=(3d)^2\sum_{k|d}(-1)^{d-d/k}m_{d/k}/k^4.$$

This proposal relates the enumerative invariants $m_d$ to relative Gromov–Witten invariants, accounting for the $(3d)^2$ torsion points and multiple covers. The source presents it as an expectation, and no resolution is supplied here.