2 problems

The graph-product conjecture. The free product $\ast_{v\in V}\Gamma_v$ is weakly sofic, and, more generally, $G_X$ is weakly sofic for every graph $X=(V,E)$ on $V$.

The graph-product conjecture. The free product $\ast_{v\in V}\Gamma_v$ is $\mathbb{K}$-linear sofic, and, more generally, $G_X$ is $\mathbb{K}$-linear sofic for every graph…