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Develop a systematic procedure to extract full correlators from the correlahedron geometry

Develop a systematic, general method to extract complete cosmological correlators from the cosmological correlahedron, including precise rules for associating singularities and computing canonical forms for arbitrary n.

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Background

The correlahedron extends the cosmohedron by one dimension and is intended to encode both wavefunction and correlator contributions. While the geometry and facets have been sketched and examples embedded for small n, a general, systematic extraction procedure for correlators has not been fully developed.

The authors note that beyond initial checks and embeddings, codifying an algorithmic pipeline analogous to amplitude extraction from associahedra remains future work.

References

For general $n$, we expect an interesting relation between $\epsilon_{T,B}$ to produce the correct combinatorics. We leave an exploration of this question, as well as the systematics of extracting the correlator from the geometry, to future work.

— Cosmohedra (2412.19881 - Arkani-Hamed et al., 27 Dec 2024) in Section “Cosmological correlahedra”