The unknotting-number conjecture for the family $\mathcal{K}_n$

For each integer $n\geq 1$, let $\mathcal{K}_n$ be the knot represented by the positive diagram $D_n$ in the paper's infinite family. The family unknotting-number conjecture.

$$u(\mathcal{K}_n)=2+7n.$$

The preceding proposition proves only the bounds $2+5n\leq u(\mathcal{K}_n)\leq 2+7n$. Thus the conjecture would determine the exact unknotting number for every knot in this family and extend the proposed counterexample at $n=1$.