Determine representability properties of the matroid N over skew fields and related theories

Determine whether the matroid N obtained by relaxing the basis {11,12,13} in the matroid M is representable over a skew field, multilinear, or algebraic.

Background

The matroid N is defined by taking the matroid M associated with the 13-point configuration and relaxing the set {11,12,13}; its non-bases are exactly the collinearity conditions in Theorem 1.7. The paper states that N is not realizable over any field, but its behavior in broader representability frameworks remains unresolved. The remark also identifies a possible computational route to proving that N is not skew-linear, but that proposed certification is not itself an established result.