Injectivity conjecture for modular-form classes in rank-two assembly

Let $\mathcal{X}_{2m,0}$ be the space appearing in the modular-form construction, and let

$$\chi:\bigoplus_{0\leq i<m}\left(\bigwedge^2\mathcal{X}_{2m,i}\right)\longrightarrow H_{4m+2}\bigl(\operatorname{Out}(F_{2m+3})\bigr)$$

be the map obtained by gluing two rank-$2$ graphs along all their leaves. Injectivity conjecture. The restriction of $\chi$ to the summand $\bigwedge^2\mathcal{X}_{2m,0}$ is injective. The first potentially nontrivial target is $H_{42}(\operatorname{Out}(F_{23}))$; the conjecture appeared previously as a question, and injectivity is regarded as plausible for small indices.