Properness conjecture for Hamiltonian homeomorphisms

Let $(M,c9)$ be a closed symplectic manifold. Write $Hameo(M,c9)$ for the group of Hamiltonian homeomorphisms and $Sympeo_0(M,c9)$ for the identity component of the group of symplectic homeomorphisms. Properness conjecture. The group $Hameo(M,c9)$ is a proper subgroup of $Sympeo_0(M,c9)$.

The conjecture extends the known cases in which the mass flow homomorphism is nontrivial or a symplectic diffeomorphism without fixed points exists. Its general validity for closed symplectic manifolds is not resolved in the supplied source.