THE CHIROTROPICAL GRASSMANNIAN

Recent developments in particle physics have revealed deep connections between scattering amplitudes and tropical geometry. From the heart of this relationship emerged the chirotropical Grassmannian and the chirotropical Dressian, polyhedral fans built from uniform realizable chirotopes that encode the combinatorial structure of Generalized Feynman Diagrams. We prove that they agree for k = 3 and n = 6, 7, 8, and develop algorithms to compute these objects from their rays modulo lineality. Using these algorithms, we compute all chirotropical Grassmannians for k = 3 and n = 6, 7, 8 across all isomorphism classes of chirotopes. We prove that each chirotopal configuration for k = 3 and n = 6 is diffeomorphic to a polytope and propose an associated canonical logarithmic differential form. Finally, we show that the equality between chirotropical Grassmannian and Dressian fails for k = 4 and n = 8.