Soprunov–Zvavitch extremizer conjecture for the Bezout ratio

Let $K\in\mathcal{K}_0^n$ be a convex body, where $\mathcal{K}_0^n$ denotes the convex bodies in $\mathbb{R}^n$ containing the origin in their interiors. Define

$$b_2(K):=\max_{A,B\in(\mathcal{K}_0^n)^2}\frac{V_n(A,B,K[n-2])V_n(K)}{V_n(A,K[n-1])V_n(B,K[n-1])}.$$

Here $V_n$ is the mixed-volume functional and $K[j]$ denotes $j$ repeated arguments. Soprunov–Zvavitch's conjecture. If $b_2(K)=1$, then $K$ is an $n$-simplex. The quantity $b_2$ is affine-invariant and satisfies $1\leq b_2(K)\leq 2$; the conjecture characterizes the equality case of the lower bound and is a reformulation of Conjecture 1.1 from Soprunov and Zvavitch's work on Bezout inequalities for mixed volumes.