Genus bound for reconstructing non-separable matroids from Tutte polynomials

Let $M$ be a non-separable matroid. Let $C$ be a largest circuit of $M$, let $D$ be a largest cocircuit of $M$, and let $\mathcal{B}(M)$ denote the set appearing in the genus bound. Genus reconstruction conjecture. Then $M$ can be reconstructed from its Tutte polynomial of genus $|\mathcal{B}(M)|-\max\{|C|,|D|\}+3$. The paper presents this as an open problem that the authors believe can be proved, extending the policy used in the proof of the main theorem.