Euclideaness under connected sum

Establish whether Euclideaness is preserved by the connected-sum construction for oriented matroids described by Richter-Gebert.

Background

The paper surveys operations known to preserve Euclideaness and proves preservation for several constructions, including direct sums, unions, lexicographic extensions, and certain mutation-flips. It conjectures preservation under Richter-Gebert's connected sum but does not prove it in general.