Mutual arc presentation conjecture for fibered links

Let $L$ be a fibered link in $S^3$. A mutual arc presentation is the presentation defined in the paper that generalizes Cromwell's arc presentations. Mutual arc presentation conjecture. Every fibered link in $S^3$ admits a mutual arc presentation. A mutual arc presentation implies that the link satisfies Bode's braided open-book conjecture, so this conjecture would provide infinitely many further braided-open-book examples and a strengthening of the Harer theorem; the general assertion remains open.