Rationality conjecture for weak saturation limits

Let $F$ be a graph, and let $w_F$ denote its weak saturation limit. Rationality conjecture. For any graph $F$, $w_F$ is rational. This asks whether all weak saturation limits are rational; the source notes that rationality is known when $w_F<\delta_F/2$, while the case between $\delta_F/2$ and $\delta_F-1$ may still allow irrational values.