The positive-diagram formula for the Rasmussen invariant in connected sums of $S^1\times S^2$

Let $D$ be a positive diagram for a null-homologous link $L$ in $\#^r(S^1\times S^2)$. Here $s_-(L)$ is the lower Rasmussen-type invariant, $n^+_D$ is the number of positive crossings of $D$, and $\varsigma(D)$ is the diagrammatic quantity defined in the paper.

Positive-diagram conjecture.

$$s_-(L)=n^+_D-\varsigma(D)+1.$$

This conjecture is motivated by the positive Whitehead-knot example and further examples in the paper. Its resolution is not indicated in the supplied text.