Bounded branch-width conjecture for excluded minors of frame matroids

A matroid $M$ is a frame matroid if there is a matroid $M'$ with a basis $V$ such that

$$M=M'\backslash V$$

and, for each $e\in E(M)$, the unique circuit in $V\cup\{e\}$ has size at most $3$. An excluded minor for a minor-closed class is a matroid not in the class whose every proper minor is in the class; the branch-width of a matroid is its standard connectivity-width parameter. Bounded branch-width conjecture. There exists an integer $k$ such that all excluded minors for the class of frame matroids have branch-width at most $k$. The paper constructs infinitely many pairwise non-isomorphic excluded minors for frame matroids, while the asserted uniform branch-width bound remains open.