Submodularity conjecture for influence in social networks

Let a social network be equipped with the increasing diffusion process described in the paper. For an initial active set $S$, let $\sigma(S)$ denote the expected size of the set of active nodes at the end of the process. A set function is submodular when, for all sets $A\subseteq B$ and every node $v\notin B$, it satisfies

$$\sigma(A\cup\{v\})-\sigma(A)\geq\sigma(B\cup\{v\})-\sigma(B).$$

Influence submodularity conjecture. The function $\sigma$ is submodular.

Submodularity would yield strong approximation guarantees for the Influence Maximization Problem, allowing a near-optimal fixed-size initial set to be found efficiently. The cited results establish the algorithmic consequences if $\sigma$ is submodular, but the supplied text does not state whether this conjecture has been resolved.