Coning circuits in cofactor matroids

Prove or disprove that coning preserves circuits in cofactor matroids.

Background

The construction applies coning to pass from dimension d to dimension d+1. Independence is known to be preserved under coning for cofactor matroids, but preservation of circuits is required for the authors’ acceptability argument and remains unresolved. Resolving this question would determine whether the construction can extend to dimensions in which rigidity and cofactor matroids differ.

References

However, it is currently not known whether coning preserves circuits for cofactor matroids (although coning does preserve independence for cofactor matroids Thm 11.3.3), and so we cannot extend the result into values of $d$ where $\mathcal{R}{d,n} \neq \mathcal{C}{d,n}$.

— Constructing pathological symmetric abstract rigidity matroids  (2610.12036 - Dewar et al., 8 Oct 2026) in Section 4, “Open problems,” subsection “Extending main results to hyperconnectivity and cofactor matroids”