The combinatorial Stiefel map determines linkage matching fields

Let a linkage matching field be a collection of matchings satisfying the linkage conditions, and let its maximal tope linkage covectors be the maximal covectors associated to its topes. The combinatorial Stiefel map associates to each such covector a transversal matroid.

Stiefel-map determination conjecture. A linkage matching field is determined by the collection of transversal matroids associated to its maximal tope linkage covectors by the combinatorial Stiefel map.

This conjecture proposes that the transversal matroids obtained from maximal tope linkage covectors retain enough information to recover the entire linkage matching field. The source gives no resolution or evidence establishing the claim.