Stipsicz's high surgery conjecture for knots

Let $K\subset S^3$ be a knot, and for a rational number $r$ let $S^3_r(K)$ denote the $r$-surgery on $K$. Stipsicz's high surgery conjecture. There is an integer $n_K$ such that for every $r\geq n_K$, the surgered $3$-manifold $S^3_r(K)$ admits a tight contact structure. The conjecture is weaker than the question of whether sufficiently large surgeries admit Stein fillable contact structures. It is known for some knots, while the paper presents it as unresolved in the generality stated.