Signature and Rasmussen invariant conjecture for thin non-alternating knots

Let $K$ be a thin non-alternating knot, and let $\sigma(K)$ and $s(K)$ denote its signature and Rasmussen invariant, respectively. Signature–Rasmussen conjecture. Their absolute values coincide:

$$|\sigma(K)|=|s(K)|.$$

The source notes that this holds for many classes of non-alternating knots, but the general assertion is presented without a proof.