COM ample-completion conjecture

Let a complex of oriented matroids (COM) be a set family of VC-dimension $d$, and let an ample completion be an ample partial cube containing it. COM ample-completion conjecture. Any COM of VC-dimension $d$ has an ample completion of VC-dimension $d$. This stronger completion property would support the sample compression conjecture, a central open problem in learning theory; the supplied text does not state that it has been proved or disproved.