Lalonde–McDuff c-splitting conjecture for Hamiltonian fiber bundles

Let $(M,\omega)$ be a closed symplectic manifold, and let $(M,\omega)\rightarrow P\rightarrow B$ be a Hamiltonian fiber bundle, meaning that its structural group can be reduced to the group of Hamiltonian diffeomorphisms. Lalonde–McDuff conjecture. Every Hamiltonian fiber bundle c-splits, in the sense that there is an additive isomorphism

$$H^{*}(P)\cong H^{*}(B)\otimes H^{*}(M).$$

The conjecture concerns the collapse of the cohomological structure of Hamiltonian bundles. In this paper, the abstract states that the author proves c-splitting when the fiber is a nilmanifold; the general conjecture is not resolved by the supplied passage.