Hypermodular Matroid Conjecture

A matroid is hypermodular if every pair of two distinct maximal proper flats is modular. A matroid is a restriction of another matroid if it is obtained by restricting that matroid to a subset of its ground set. Hypermodular Matroid Conjecture. Any hypermodular matroid of sufficiently large rank is a restriction of a modular matroid of the same rank. The conjecture holds in rank $3$. If it holds in rank $4$, the sticky matroid conjecture follows. It is presented as a weakening of Kantor's conjecture.