The amplituhedron positive geometry conjecture

Let $\mathcal{A}_{n,k,m}(Z)$ be the amplituhedron in $\operatorname{Gr}_{k,k+m}(\mathbb{C})$. The amplituhedron positive geometry conjecture. The pair

$$(\operatorname{Gr}_{k,k+m}(\mathbb{C}),\mathcal{A}_{n,k,m}(Z))$$

should be a positive geometry. This would extend the positive-geometry structures of cyclic polytopes and the positive Grassmannian to general amplituhedra and would provide a canonical form for the amplituhedron; the conjecture is presented here without a resolution.