The winding-number lower-bound conjecture for satellite knots

Let $K$ be a satellite of a nontrivial knot, and let the pattern have winding number $p$. The unknotting number $u(K)$ is the minimum number of crossing changes needed to transform $K$ into the unknot.

Winding-number lower-bound conjecture.

$$u(K) \geq p+1.$$

This would generalize the result of Scharlemann and Thompson that a nontrivial satellite with nonzero winding number has unknotting number at least $2$. The conjecture proposes a stronger lower bound in terms of the pattern's winding number; its status is not resolved in the source.