The topology conjecture for the small-capacity Poisson-bracket limit

Let $(M,\omega)$ be a compact symplectic manifold, and let $\operatorname{pb}(c)$ be the Poisson-bracket function associated with ball capacity $c$. The topology conjecture. Assuming that there are only finitely many uncertainty phase transitions, the limit of $\operatorname{pb}(c)$ as $c$ tends to zero depends only on the topology of the symplectic manifold. The paper presents this as a conjectural universal property of the Poisson-bracket function and discusses its incompatibility in some situations with Polterovich's conjecture.