{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:YJ7POO2ED65XWSKJBGEJYIVK5R","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"38b3d37bcefd43113474701f2c3a105985b8da29845c09ec184cdb86812af587","cross_cats_sorted":["hep-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-08-18T15:17:30Z","title_canon_sha256":"0db80297d165f77a67c725e1427f3c682efbc3c28b4ebfe47a12bb6a899e2c94"},"schema_version":"1.0","source":{"id":"1608.05291","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.05291","created_at":"2026-05-18T00:57:26Z"},{"alias_kind":"arxiv_version","alias_value":"1608.05291v3","created_at":"2026-05-18T00:57:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.05291","created_at":"2026-05-18T00:57:26Z"},{"alias_kind":"pith_short_12","alias_value":"YJ7POO2ED65X","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"YJ7POO2ED65XWSKJ","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"YJ7POO2E","created_at":"2026-05-18T12:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:40d043f4ca23494d43025ba1e2062a62831fd8775d5b66b879f66925e8dae219","target":"graph","created_at":"2026-05-18T00:57:26Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Tree-level $n$-point gauge-theory amplitudes with $n-2k$ gluons and $k$ pairs of (massless or massive) particles in the fundamental (or other) representation of the gauge group are invariant under a set of symmetries that act as momentum-dependent shifts on the color factors in the cubic decomposition of the amplitude. These symmetries lead to gauge-invariant constraints on the kinematic numerators. They also directly imply the BCJ relations among the Melia-basis primitive amplitudes previously obtained by Johansson and Ochirov.","authors_text":"Robert W. Brown, Stephen G. Naculich","cross_cats":["hep-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-08-18T15:17:30Z","title":"Color-factor symmetry and BCJ relations for QCD amplitudes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.05291","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:0bcc9080cf1a5812ab224090ae41428db60e4c834f2f1f8700b637b464f029dc","target":"record","created_at":"2026-05-18T00:57:26Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"38b3d37bcefd43113474701f2c3a105985b8da29845c09ec184cdb86812af587","cross_cats_sorted":["hep-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-08-18T15:17:30Z","title_canon_sha256":"0db80297d165f77a67c725e1427f3c682efbc3c28b4ebfe47a12bb6a899e2c94"},"schema_version":"1.0","source":{"id":"1608.05291","kind":"arxiv","version":3}},"canonical_sha256":"c27ef73b441fbb7b494909889c22aaec72bfaa15bafd29434f247a3d88233a3b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c27ef73b441fbb7b494909889c22aaec72bfaa15bafd29434f247a3d88233a3b","first_computed_at":"2026-05-18T00:57:26.443265Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:57:26.443265Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"D/LobFTlS2siXWLka1Ljo0svCcpDgDXQkMTguF/p5UkF/1d4apkd6g2IADdfsixNI7gHDWFB63i2OZlada/VAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:57:26.443820Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.05291","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0bcc9080cf1a5812ab224090ae41428db60e4c834f2f1f8700b637b464f029dc","sha256:40d043f4ca23494d43025ba1e2062a62831fd8775d5b66b879f66925e8dae219"],"state_sha256":"ba4dc11e508fc207dbfff4fabd6a2e807275fd13e76647d411c2b21f4229fb9d"}