The finitely generated subgroup embedding conjecture for Thompson's group F

Let $G\leq \mathrm{PL}_+ I$ be a finitely generated subgroup. An $F$-obstruction is a pair of elements of $G$ forming an $F$-obstruction in the sense of Theorem. Embedding conjecture. If $G$ does not contain an $F$-obstruction, then $G$ embeds into Thompson's group $F$. This is the proposed converse to Theorem; its status is not resolved in the source.