The amplituhedron form triangulation-independence conjecture

Let $Z\in\operatorname{Gr}_{>0}(k+m,n)$ and let $\mathcal{T}$ be a degree-one $Z$-triangulation. The amplituhedron form is the signed sum

$$\omega^{(\mathcal{T})}_{\mathcal{A}_{n,k,m}(Z)}:=\sum_{s=1}^N\omega_{Z(\Pi_{k+f_s}^{\mathbb C})}.$$

Amplituhedron form conjecture. The form $\omega^{(\mathcal{T})}_{\mathcal{A}_{n,k,m}(Z)}$ does not depend on the choice of triangulation $\mathcal{T}$. The form is intended to be an intrinsic differential form associated with the amplituhedron; the source reports numerical verification in several cases with $m=4$, but no general proof.