The universal linear stick-number bound for knots

Let $K$ be a knot type, let $c[K]$ denote its crossing number, and let $\operatorname{stick}[K]$ denote its stick number. Universal linear stick-number conjecture. Every knot with crossing number at least $12$ satisfies

$$\operatorname{stick}[K]\leq c[K].$$

This is slightly stronger than the asymptotic conjecture $\beta_*\leq 1$. It is motivated by the authors' computations, including large random knots, for which they found embeddings using fewer sticks than the crossing number; no counterexample is known.