Annulus-twist invariance conjecture for the 4-ball genus

Let $K$ be a knot with a band presentation whose induced framing is $0$, and let $K_n$ be the knot obtained from $K$ by applying an annulus twist $n$ times.

Annulus-twist invariance conjecture. The 4-ball genera satisfy

$$g_{*}(K)=g_{*}(K_n).$$

This conjecture proposes that applying annulus twists preserves the 4-ball genus for knots admitting a band presentation with induced framing zero. The surrounding discussion presents it as a proposed relationship motivated by the study of shake genus and 4-ball genus; no resolution is given here.