{We exploit the flag and Orlik-Solomon algebra to reconstruct the intersection number of twisted cocycles and results to the bi-adjoint amplitude. Through Studying the pairing of the special flag, we find it results to Cachao-He-Yuan represention of the bi-adjoint amplitude. We identify each standard basis flag with Feynman trivalent graph, one find the geometry interpretation of Bern-Carrasco-Johansson duality discovered by Mizera is the relation of flag with a gap. By define the flag simplex, we also construct the Z-amplitude in the α^ → 0 limit.
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Lili Yang (2024) studied this question.
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