Width conjecture for triangle-square chain graphs

Let $G_{t,s^k}$ be the graph obtained by gluing a triangle and $k$ squares in a sequence along edges, and let $w^1_{{\mathcal A}_3}(G)$ denote the width of the torsion in $H^{1,*}_{{\mathcal A}_3}(G)$. Width conjecture for $G_{t,s^k}$.

$$w^1_{{\mathcal A}_3}(G_{t,s^k})=k.$$

The claim is based on computations in the paper; no resolution is stated.