Conjecture on positive Thurston–Bennequin representatives of fibered knots

Let $K$ be a fibered knot, and let $\xi_K$ be the contact structure it supports in the sense of Giroux. Positive Thurston–Bennequin conjecture. In $\xi_K$, the knot type $K$ has Legendrian representatives with Thurston–Bennequin invariant greater than $0$.

This conjecture is motivated by known examples and by the partial result that a non-trivial fibered knot supporting $\xi_K$ has $\tbb(K)\geq 0$. The source gives no resolution status.