The spun-lens-space conjecture for the trisection pants invariant

Let $X_p$ be a $4$-manifold obtained by spinning a lens space. Denote its trisection pants invariant by $\mathcal{L}^*_3$.

Spun-lens-space conjecture. The $\mathcal{L}^*_3$-invariant of spun lens spaces is equal to $18$.

The paper establishes the bounds $12\leq \mathcal{L}^*_3(X_p)\leq 18$ for the spun lens spaces under discussion. The conjecture proposes that the upper bound is sharp; the precise value is otherwise left open.