The GW effective-algorithm conjecture for quintic threefolds

Let $N_{g,d}$ be the genus $g$, degree $d$ Gromov–Witten invariant of the quintic threefold, and let $\Theta_{g,k}$ be the genus $g$ FJRW invariant of the Fermat quintic with $k$ many $\frac{2}{5}$-insertions. Let $d_0$ and $d_\infty$ be positive integers, and let the relations be those obtained from the localization vanishing.

GW effective-algorithm conjecture. By choosing $d_0$ and $d_\infty$ positive, these relations provide an effective algorithm to determine all genus GW invariants $N_{g,d}$, provided that

$$N_{g',d'}\text{ are known for }g'<g,\ d'\leq d,$$

and

$$\Theta_{g',k'}\text{ are known for }g'\leq g,\ k'<7g-2.$$

This strengthens the preceding effective algorithm by asserting that suitable positive choices of the two degrees remove the need for same-genus lower-degree GW initial values.