Conjecture on irreducible fibered knots and negative Thurston–Bennequin invariant

Let $K$ be a fibered knot in $S^3$ with irreducible monodromy, and suppose that $K$ does not support the standard contact structure $\xi_{std}$. Irreducible-monodromy conjecture. Then

$$\tbb(K)\leq -1.$$

The conjecture asserts that the known positive Thurston–Bennequin examples outside the supported contact structure arise from reducible monodromy. The source gives no resolution status.