The positive-density weak property PT conjecture for hyperbolic knots

Let a knot have weak property PT when it satisfies the property defined in the paper. Positive-density weak property PT conjecture. There exist $\varepsilon>0$ and $N>0$ such that, for all $n>N$, the percentage of knots with weak property PT among all hyperbolic knots with at most $n$ crossings is at least $\varepsilon$. This is presented as an additional conjectural condition related to the weak property PT conjecture and is not resolved in the paper.