Amplituhedron facet-colooplessness conjecture

Let $S_{\pi^{(1)}}$ and $S_{\pi^{(2)}}$ be positroid cells in $Gr^+_{k,n}$ corresponding to coloopless permutations $\pi^{(1)}$ and $\pi^{(2)}$, with

$$\dim Z^\circ_{\pi^{(1)}}=\dim Z^\circ_{\pi^{(2)}}=2k$$

and $Z_{\pi^{(1)}}\cap Z_{\pi^{(2)}}=Z_{\pi^{(3)}}$, where $S_{\pi^{(3)}}\subset Gr^+_{k,n}$ and $\dim Z^\circ_{\pi^{(3)}}=2k-1$. Amplituhedron facet-colooplessness conjecture. The permutation $\pi^{(3)}$ is coloopless. This would ensure that common facets of top-dimensional amplituhedron cells remain in the domain of T-duality.