  In \cite{arkani2018unwinding}, Arkani-Hamed, Thomas and Trnka formulated two
conjectural descriptions of the tree amplituhedron $\ampli$ depending on the
parity of $m$. When $m$ is even, the description involves the winding number
and when $m$ is odd the description involves the crossing number. In this
paper, we prove that if a point of the amplituhedron is in the image of the
positive Grassmannian by the amplituhedron map, then it satisfies the winding
or crossing descriptions depending on the parity of $m$. When $m=2$, we also
prove the other direction: a point satisfying the winding description is inside
the amplituhedron.
