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An answer is the set of n for which such numerators exist, with constructions and obstructions, and a statement of whether dimension-specific (for example 4D) numerators escape any obstruction.","problem_ref":null,"references":"","settled_by":"Explicit local numerators for all n, or a verified obstruction at a specific n.","status_note":"A September 2026 preprint (Sung, arXiv:2609.10693) reports that no dimension-independent, parity-even polynomial numerators multilinear in polarizations exist at $n = 6$; unrefereed and not independently checked; dimension-specific numerators are not excluded.","title":"Local color-kinematics duality for one-loop pure Yang-Mills 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