Cabling conjecture for bridge spectra of knots

Let $J$ be a knot with bridge spectrum

$${\mathbf b}(J)=(b_0(J),\ldots,b_g(J),0),$$

and let $K={\mathsf {cable}}(T_{m,n},J)$ be a cable of $J$. The bridge-spectrum cabling conjecture.

$${\mathbf b}(K)=\left(m\cdot b_0(J),m\cdot b_1(J),\ldots,m\cdot b_{g-1}(J),m\cdot b_g(J),b_{g+1}(K),0\right).$$

The conjecture expresses the observed regularity of cabling: all listed existing bridge numbers should be multiplied by $m$, with only the final new term left unspecified. The source explicitly calls for either counterexamples or a proof, and gives no resolution.