Mutation-flip distance from Euclidean oriented matroids

Determine whether Mandel oriented matroids can have mutation-flip distance greater than one from every Euclidean oriented matroid.

Background

The paper proves that several non-Euclidean Mandel oriented matroids arise from Euclidean oriented matroids by one mutation-flip. It does not determine whether all Mandel oriented matroids are within mutation-flip distance one of the Euclidean class.

References

Are there Mandel oriented matroids with more mutation-flip distance than $1$ to a Euclidean oriented matroid?

— Mutations and (Non-)Euclideaness in oriented matroids  (2501.12951 - Wilhelmi, 22 Jan 2025) in Concluding remarks, Section concluding remarks