Good T-duality correspondence for hypersimplex and amplituhedron

Let $\{S_{\pi}\}$ be a collection of cells of $Gr^+_{k+1,n}$, and let $\{S_{\hat{\pi}}\}$ be its T-dual collection. Good T-duality correspondence conjecture. The collection $\{S_{\pi}\}$ gives a good triangulation, respectively good dissection, of $\Delta_{k+1,n}$ if and only if $\{S_{\hat{\pi}}\}$ gives a good triangulation, respectively good dissection, of $\mathcal{A}_{n,k,2}$. The paper reports experimental confirmation of this correspondence.