The conjecture that all finite-index subgroups of Thompson group F are 2-generated

Let $F$ denote Thompson group $F$, and let a group be 2-generated if it has a generating set with two elements. The finite-index generation conjecture. Every finite-index subgroup of $F$ is $2$-generated. Finite-index subgroups of $F$ can have generating sets of this size in known examples, but the assertion for all finite-index subgroups is presented as a conjecture and remains open.