Integral Rasmussen invariant conjecture for Whitehead doubles of consecutive torus knots

Let $T(a,b)$ denote the $(a,b)$-torus knot, let $W_+(J,t)$ denote the positive $t$-twisted Whitehead double of $J$, and let $\overline{K}$ denote the mirror of $K$. For a knot, $s^{\mathbb{Z}}(K)$ is the integral Rasmussen invariant recorded as the relevant ordered pair.

Consecutive-torus-knot conjecture. For every integer $n\geq 2$, if

$$K=W_+\bigl(T(n,n+1),n^2-1\bigr),$$

then

$$s^{\mathbb{Z}}(\overline{K})=(0,n).$$

This extends the preceding prime-parameter prediction from field coefficients to the integral invariant and to all integers $n\geq2$. The source gives no evidence that it has been proved or refuted.