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Two-loop amplituhedron A^{(2)}_4 as a weighted positive geometry

Show that the two-loop amplituhedron A^{(2)}_4 defines a weighted positive geometry by carrying out the necessary residue computations.

References

Show that the two-loop amplituhedron $\mathcal{A}{(2)}_4$ is a weighted positive geometry. Following Section 5.2, some residues need to be computed.

What is Positive Geometry? (Ranestad et al., 18 Feb 2025) in Section “Open questions”: Problem [Dian]