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Is the MHV gravity numerator adjoint to a positive geometry?

Determine whether the numerator of MHV gravity amplitudes is adjoint to a positive geometry, i.e., whether there exists an “amplituhedron” for MHV amplitudes whose adjoint hypersurface equals this numerator.

References

Except for some small cases, this description remains conjectural. It is natural to ask whether this numerator is adjoint to a positive geometry -- an ``amplituhedron'' for MHV amplitudes.

What is Positive Geometry? (Ranestad et al., 18 Feb 2025) in Section 3: (Semi-)algebraic subsets of the Grassmannian; paragraph after equation (adjA5)