Pillay–Yao conjecture on definably amenable NIP groups

Let $G$ be a definably amenable NIP group. An fsg group is a group with finitely satisfiable generics, and a dfg group is a group with definable f-generics. Pillay–Yao's conjecture. $G$ is an extension of an fsg group by a dfg group, כלומר there is a short exact sequence

$$1\to H\to G\to C\to 1$$

where $H$ is dfg and $C$ is fsg.

This conjecture concerns the structure of definably amenable NIP groups and would generalize the corresponding decomposition known for definably amenable groups in o-minimal expansions of real closed fields. The cited source does not provide evidence that the conjecture has been resolved.