Eventual destabilization of low-Thurston–Bennequin Legendrian representatives

Let $K$ be a null-homologous smooth knot type in a tight contact manifold $(M,\xi)$. A Legendrian representative of $K$ has a Thurston–Bennequin invariant $\tb$. Low-Thurston–Bennequin destabilization conjecture. There is an integer $n$ such that every Legendrian representative of $K$ with $\tb<n$ destabilizes. The conjecture would provide a broad criterion for recognizing destabilizable Legendrian representatives and would substantially aid the classification of Legendrian knots; it remains open in general.