The pants invariant conjecture for connected sums of $S^2\times S^2$

Let $Y_m=\#^m(S^2\times S^2)$, and let $\mathcal{L}^*_3$ denote its trisection pants invariant.

Connected-sum pants-invariant conjecture. The $\mathcal{L}^*_3$-invariant of $Y_m$ is equal to $9m$.

The paper derives the lower bound $\mathcal{L}^*_3(Y_m)\geq 6m$ from minimal-genus trisections, but notes that those trisections can be reducible, so the available lower-bound results do not determine the invariant. Establishing the conjectured value requires new lower bounds for pants invariants of reducible manifolds.