The low-degree GW 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. For $d<g$, set

$$\mathbf d=(d+1,g-d-1),\qquad \gamma=\emptyset.$$

Low-degree GW algorithm conjecture. Applying the localization vanishing to this data determines $N_{g,d}$ 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 is the proposed inductive mechanism for determining the low-degree initial GW invariants needed in the effective theory.