Conjecture on the weak saturation number of unbalanced complete bipartite graphs

Let $K_{s,t}$ be the complete bipartite graph with $2<s\leq t$, and let $j$ satisfy $2\leq j\leq t-3$. Write $\mathrm{wsat}(n,K_{s,t})$ for the weak saturation number of $K_{s,t}$. The weak saturation conjecture. For all such $s,t,j$,

$$\mathrm{wsat}(s+t+j,K_{s,t})=\binom{s+t+j}{2}-j(s+t)-2t+O(j).$$

The exact value remains unknown in the range $s+t+2\leq n\leq 3t-3$. The conjecture gives the proposed asymptotic form of the weak saturation number, while the paper establishes upper and lower bounds differing by an additive term.