  The amplituhedron Ank4 is a geometric object, introduced by Arkani-Hamed and
Trnka (2013) in the study of scattering amplitudes in quantum field theories.
They conjecture that Ank4 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.
