The corner-peeling conjecture for extremal classes

Let $C$ be an extremal class. A concept $c\in C$ is a corner of $C$ if $C\setminus\{c\}$ is extremal. Corner-peeling conjecture. Every nonempty extremal class $C$ has at least one corner. The conjecture is proved for maximum classes and for several special cases, including extremal classes of VC dimension at most $2$, but remains open for general extremal classes.