Jang–Lee prime-knot conjecture for Whitehead doubles

Let $K$ be a prime knot, let $c(K)$ denote its crossing number, and let $W(K)$ be its Whitehead double. Jang–Lee's conjecture. The crossing number of any prime knot coincides with the canonical genus of its Whitehead double:

$$g_c(W(K))=c(K).$$

This modifies Tripp's conjecture after the discovery of composite counterexamples. The source proves the corresponding equality for all prime alternating $3$-braid knots and for several larger families, but leaves the assertion for arbitrary prime knots open.