The Amplituhedron BCFW Triangulation

The amplituhedron $\mathcal{A}_{n,k,4}$ is a geometric object, introduced by Arkani-Hamed and Trnka (2013) in the study of scattering amplitudes in quantum field theories. They conjecture that $\mathcal{A}_{n,k,4}$ admits a decomposition into images of BCFW positroid cells, arising from the Britto--Cachazo--Feng--Witten recurrence (2005). We prove that this conjecture is true.