Geelen–Gerards–Whittle polynomial-time girth conjecture for proper minor-closed classes

Let $\mathcal{M}$ be a proper minor-closed class of binary matroids. Geelen–Gerards–Whittle's conjecture. There is a polynomial-time algorithm for computing the girth of matroids in $\mathcal{M}$. This conjecture connects the tractability of girth computation with structural restrictions on binary matroid classes; the paper studies an algorithmic result for perturbed graphic matroids, while the conjecture concerns every proper minor-closed class of binary matroids.