The trunk additivity conjecture for knots

Let $K_1$ and $K_2$ be knots, and let $trunk(K)$ denote the minimum, over Morse positions of $K$, of the maximum intersection number with a level sphere.

Trunk additivity conjecture. It holds that

$$trunk(K_1\# K_2)=\max\{trunk(K_1),trunk(K_2)\}.$$

Its status is not resolved in the supplied text.