Maulik–Pandharipande determination conjecture for quintic threefold invariants

Let $Q$ be the quintic threefold in $\boldsymbol{^4}$. Let $N_{g,d}$ denote its Gromov–Witten invariants, and let the degeneration formula for $(V,W)=(\mathbb{P}^4,Q)$ relate the relative theories of $(\mathbb{P}^4,Q)$ and $(\mathbb{P}(N_{Q/\mathbb{P}^4}\oplus\mathcal{O}_Q),D_0)$ to the absolute theory of $\mathbb{P}^4$. Maulik and Pandharipande's algorithm determines the relative theory of $(\mathbb{P}(N_{Q/\mathbb{P}^4}\oplus\mathcal{O}_Q),D_0)$ from the absolute invariants of $Q$. Maulik–Pandharipande's conjecture. The resulting system of equations can be used to determine both the relative theory of $(\mathbb{P}^4,Q)$ and all Gromov–Witten invariants $N_{g,d}$ of $Q$. This extends the recursive determination known for genera at most one and proposes an all-genus procedure; the paper establishes related results for genera $2$ and $3$, while the general claim remains open.