Polystability conjecture for polarised fibrations and optimal symplectic connections

Let $(X,H)\to(B,L)$ be a polarised fibration, meaning a fibration equipped with relatively ample polarisation $H$ and a polarisation $L$ on the base. An optimal symplectic connection is the canonical differential-geometric connection considered for such a polarised fibration. Polystability conjecture. The polarised fibration $(X,H)\to(B,L)$ is polystable if and only if it admits an optimal symplectic connection.

This conjecture proposes an equivalence between an algebro-geometric stability condition for fibrations and the existence of a canonical symplectic connection. Its resolution is not specified in the source.