T-duality conjecture for the momentum and ordinary amplituhedra

Let $m$ be even and let $\{S_{\pi}\}$ be a collection of cells of $Gr^+_{k+m/2,n}$. Generalized T-duality conjecture. The collection gives a triangulation, respectively dissection, of the momentum amplituhedron $\mathcal{M}_{n,k,m}$ if and only if the T-dual collection $\{S_{\hat{\pi}}\}$ in $Gr^+_{k,n}$ gives a triangulation, respectively dissection, of the amplituhedron $\mathcal{A}_{n,k,m}$. This extends the $m=2$ and $m=4$ correspondence conjectures to arbitrary even $m$.