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Nima Arkani-Hamed has another hedron for the theory: the Cosmohedron: https://arxiv.org/abs/2412.19881.
He makes you go back to 2017 to begin figuring out what he means by "cosmological wavefunction" and what it might have to do with the theory. The story is not very clear.
This topic was moved here from #theory: category theory > Amplituhedron, associahedron, and related approaches by Matteo Capucci (he/him).