Regular positroidal subdivision conjecture for the m=2 amplituhedron

A regular positroidal subdivision of $\mathcal{A}_{n,k,2}$ is a positroidal dissection of the form $\{S_{\hat{\pi}}\}$, where $\{S_{\pi}\}$ is a regular positroidal subdivision of $\Delta_{k+1,n}$. Regular subdivision conjecture. Every regular positroidal subdivision of $\mathcal{A}_{n,k,2}$ is a good dissection. Computational evidence verifies this in several small cases.