Common algebraic condition across projective rigidity minors

Establish whether the determinants of different maximal minors of an isostatic projective rigidity matrix are equivalent up to simple factors and signs, as in the corresponding theory for ordinary rigidity matrices.

Background

The paper notes that, for ordinary rigidity matrices, determinants associated with different choices of deleted columns or tie-downs are closely related. It asks whether the same algebraic uniformity holds for projective rigidity matrices.

References

For the usual rigidity matrix, there is an analysis which shows that all the polynomials for different minors are, up to simple factors and signs, ``the same".

— Counting for rigidity under projective transformations in the plane  (2503.07228 - Berman et al., 10 Mar 2025) in Section "Open problems and future work," subsection "The pure conditions"