The heaviness–SH-heaviness conjecture

Let $(M,\omega)$ be a closed symplectic manifold and let $K\subset M$ be a compact subset. The subset $K$ is SH-heavy in the sense of the quantum cohomology ideal-valued quasi-measures introduced by Dickstein, Ganor, Polterovich, and Zapolsky. Heaviness–SH-heaviness conjecture. The subset $K$ is heavy if and only if it is SH-heavy. The source introduces SH-heaviness as a newer notion and reports this conjecture, but does not state its resolution in the supplied text.