{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"3e3eb26d811d42276bf4a25403256ce275593e69b1f3aa290144df3d558b3bcc","created":"2026-10-03T07:18:09Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"31bf6378614e2406da5a779378fa527818036606f141733c5c5d54a522e909f0","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"classification","assisted_by":[],"external_id":"qft.double-copy.one-loop-local","kind":"well-posed","literature_status":"partially-resolved","n":"1","parents":[],"plain":"Even at one loop it is unclear whether gluon amplitudes of ordinary Yang-Mills theory, with no supersymmetry, can be put in the special form using simple polynomial numerators.","posed_since":"","precise":"Determine for which multiplicities n the one-loop n-gluon amplitude of pure Yang-Mills admits BCJ numerators that are local (polynomial in momenta and polarization vectors) and valid in arbitrary spacetime dimension D. 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 amplitudes","topic_ref":"1423f8d1d6c45d6696107efe735144c4230462c57b3f02acac8489226faee33e"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"1b298fbab539c70e8875badea633c176605a68796525c6d37b513b07dc965433","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"4e7654f80120e0fe29c7d708d1e6eeb610a86a64f79da3407180cc3632a9e5e5","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"wFVJ5EGk_RCCd5n2G84I6ta8zddaHFgReSK8HSLaiiUh8Ga7H9E145Nmiw6zoraWjLCKDTOAjOoT-danzKRLBQ"},"schema":"pubphys.envelope/1"},"record_hash":"1b298fbab539c70e8875badea633c176605a68796525c6d37b513b07dc965433","leaf_index":1909}