Existence of embracing exchange sequences in oriented matroids

Determine whether every pair of e-embracing bases in an oriented matroid admits an e-embracing exchange sequence, regardless of the sequence length.

Background

In ordinary matroids, the basis exchange axiom guarantees a sequence of exchanges between any two bases. The oriented setting imposes the additional requirement that every intermediate basis remain e-embracing.

The paper emphasizes that, for general oriented matroids, it is not known whether such a sequence exists at all, even without imposing the conjectured upper bound of r exchanges. This is a distinct unresolved existence question underlying the distance conjecture.