Interval-rank conjecture for finite simple groups

For a finite simple group $G$, consider the set of integers that occur as ranks of string C-group representations of $G$. A set of integers is an interval if it contains every integer between any two of its elements.

Interval-rank conjecture. The group $A_{11}$ is the only finite simple group whose set of ranks of string C-group representations is not an interval in the set of integers.

This conjecture predicts a strong interval property for the possible ranks of string C-group representations of finite simple groups, with $A_{11}$ as the unique exception. It was recalled from earlier work by Brooksbank and the author; the supplied text gives no resolution status.