Wrappingness and trunkenness additivity under fibered gluing

Let $Y_1$ and $Y_2$ be fibered 3-manifolds with boundary, with fibrations $\pi_1:Y_1\to S^1$ and $\pi_2:Y_2\to S^1$, and glue them along a fibered torus-boundary component to obtain a fibered 3-manifold $Y_1\cup_{T^2}Y_2$ with fibration $\pi:Y_1\cup_{T^2}Y_2\to S^1$. Let $L_1\subset Y_1$ and $L_2\subset Y_2$ be links, and regard $L_1\cup L_2$ as their disjoint union in $Y_1\cup Y_2$. Wrappingness and trunkenness additivity conjecture. One has

$$\operatorname{wrap}(L_1\cup L_2,\pi)=\operatorname{wrap}(L_1,\pi_1)+\operatorname{wrap}(L_2,\pi_2),$$

and

$$\operatorname{trunk}(L_1\cup L_2,\pi)=\max\left(\operatorname{trunk}(L_1,\pi_1)+\operatorname{wrap}(L_2,\pi_2), \operatorname{wrap}(L_1,\pi_1)+\operatorname{trunk}(L_2,\pi_2)\right).$$

This conjecture generalizes the stated additivity formula for the trunk of a disjoint union of links in $S^3$. It predicts that wrapping number is additive under this fibered gluing, while trunk is governed by the larger of the two mixed trunk–wrapping sums; the source provides no resolution, so the conjecture remains open.