The FJRW effective-algorithm conjecture for quintic singularities

Let $\Theta_{g,k}$ denote the genus $g$ FJRW invariant of the Fermat quintic with $k$ many $\frac{2}{5}$-insertions. Let $\gamma$ be a tuple of markings from the narrow sectors, and consider the localization relations with $d_0=0$.

FJRW effective-algorithm conjecture. The polynomial relations among the FJRW invariants $\Theta_{g,k}$ obtained from these localization relations, with

$$\gamma\in(\boldsymbol{\mu}_5^{\mathrm{nar}})^{\times\ell},$$

can effectively evaluate all $\Theta_{g,k}$.

This proposes using nontrivial marking data to determine the complete collection of FJRW invariants, beyond the ranges already covered by the stated theorems.