Calabi extension conjecture for Hamiltonian homeomorphisms of the disc

Let $D^2$ be the two-disc, with $[?]$ its area form, and let $Hameo(D^2,\partial D^2)$ be the subgroup of Hamiltonian homeomorphisms inside $Homeo^\Omega(D^2,\partial D^2)$. The Calabi homomorphism is defined on $Diff^\Omega(D^2,\partial D^2)$. Calabi extension conjecture. The homomorphism

$$\operatorname{Cal}: Diff^\Omega(D^2,\partial D^2)\to \mathbb R$$

extends continuously to $Hameo(D^2,\partial D^2)$ in the Hamiltonian topology. This is the main conjecture concerning nonsimplicity of the area-preserving homeomorphism group; the cited work explains how such an extension would contribute to the nonsimplicity proof.