Width conjecture for complete graphs

Let $K_n$ be the complete graph on $n$ vertices, and let $w^1_{{\mathcal A}_3}(K_n)$ denote the width of the torsion in $H^{1,*}_{{\mathcal A}_3}(K_n)$. Width conjecture for complete graphs.

$$w^1_{{\mathcal A}_3}(K_n)=0.$$

The claim is suggested by calculations of complete graphs; the source gives no resolution.