{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"54c376002dd2bbdd4121b31dc3de141cb12bad1c9d87f6fe1f4eba039aaf8523","created":"2026-10-03T07:18:09Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"5b9825d8c6f06ae90cde52efdb8fbc6fe883e92350602e45a46093b4ab33d758","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"yes-no","assisted_by":[],"external_id":"qft.double-copy.five-loop-bcj","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"The squaring trick needs the gauge-theory answer arranged so that its momentum-dependent parts obey the same algebra as its color (charge) parts. At five loops nobody has found such an arrangement for four-gluon scattering in the most symmetric gauge theory.","posed_since":"","precise":"Determine whether the five-loop four-point integrand of $N=4$ super-Yang-Mills admits a representation on cubic graphs with local numerators $n_i$ satisfying every kinematic Jacobi relation $n_i + n_j + n_k = 0$ that mirrors a color Jacobi identity (a BCJ representation). An answer is an explicit representation verified on all unitarity cuts, or a proof that none exists with polynomial numerators of the allowed power counting.","problem_ref":null,"references":"","settled_by":"An explicit BCJ representation checked on all cuts, or an exhaustive ansatz no-go proof.","status_note":"The 2018 five-loop $N=8$ supergravity integrand was built with the generalized double copy, which does not require a BCJ form; no BCJ form of the five-loop four-point amplitude is reported as of 2026.","title":"Color-kinematics dual form of the five-loop $N=4$ super-Yang-Mills amplitude","topic_ref":"1423f8d1d6c45d6696107efe735144c4230462c57b3f02acac8489226faee33e"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"c7b4576e75b1a627334bcc4e122874e3b119e2dc98b9b82c854a549e1320cce1","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"8183b4e57c867ddc61c0c706e89eb124c37ac044e97663fbcb393b59b2e63a30","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"Td84C7BZLb0oGwYhcg3HWoNrGEsUoK6ti3FT04LWPEirJu7CMYsPBSa4sXBPRqFaiJJmuq2_HAV-GAuQsAS6Cw"},"schema":"pubphys.envelope/1"},"record_hash":"c7b4576e75b1a627334bcc4e122874e3b119e2dc98b9b82c854a549e1320cce1","leaf_index":1906}