{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:ZBQV6NPAPNNXB7TTHKK3NUJIGH","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":"bd9d418a222a898bde2ec8bc54143a6014fce6311f66bf91f490e46d06391181","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2021-09-29T14:51:25Z","title_canon_sha256":"e4004500ad54b21434d460519b29980acee6a37da18ce719dd6f91d847656d77"},"schema_version":"1.0","source":{"id":"2109.14462","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.14462","created_at":"2026-07-05T03:56:50Z"},{"alias_kind":"arxiv_version","alias_value":"2109.14462v2","created_at":"2026-07-05T03:56:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.14462","created_at":"2026-07-05T03:56:50Z"},{"alias_kind":"pith_short_12","alias_value":"ZBQV6NPAPNNX","created_at":"2026-07-05T03:56:50Z"},{"alias_kind":"pith_short_16","alias_value":"ZBQV6NPAPNNXB7TT","created_at":"2026-07-05T03:56:50Z"},{"alias_kind":"pith_short_8","alias_value":"ZBQV6NPA","created_at":"2026-07-05T03:56:50Z"}],"graph_snapshots":[{"event_id":"sha256:eace8e5eb71d976a2e7385f7b9f4b751ced3d977e518b53ded431e1ea4cc52bc","target":"graph","created_at":"2026-07-05T03:56:50Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2109.14462/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Tree-level color-ordered Yang-Mills (YM) amplitudes can be decomposed in terms of $(n-2)!$ bi-scalar (BS) amplitudes, whose expansion coefficients form a basis of Bern-Carrasco-Johansson (BCJ) numerators. By the help of the recursive expansion of Einstein-Yang-Mills (EYM) amplitudes, the BCJ numerators are given by polynomial functions of Lorentz contractions which are conveniently described by graphic rule. In this work, we extend the expansion of YM amplitudes to off-shell level. We define different types of off-shell extended numerators that can be generated by graphs. By the use of these e","authors_text":"Konglong Wu, Yi-Jian Du","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2021-09-29T14:51:25Z","title":"Off-shell extended graphic rule and the expansion of Berends-Giele currents in Yang-Mills theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.14462","kind":"arxiv","version":2},"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:f0ce780d9e52de8af4f33550bbd1521b6451c1a62adfe8703abbdd36d14dccd3","target":"record","created_at":"2026-07-05T03:56:50Z","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":"bd9d418a222a898bde2ec8bc54143a6014fce6311f66bf91f490e46d06391181","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2021-09-29T14:51:25Z","title_canon_sha256":"e4004500ad54b21434d460519b29980acee6a37da18ce719dd6f91d847656d77"},"schema_version":"1.0","source":{"id":"2109.14462","kind":"arxiv","version":2}},"canonical_sha256":"c8615f35e07b5b70fe733a95b6d12831c53fb546e73c3cc1464762d3aa29453d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c8615f35e07b5b70fe733a95b6d12831c53fb546e73c3cc1464762d3aa29453d","first_computed_at":"2026-07-05T03:56:50.380459Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:56:50.380459Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gAzuqvF1mIXxdXvxs+h3skU/l6+kVrdaTuLRI4HOqK0366duRGyj2QrPJFmGGI7yazgRmjnI6m/5F/qT7DgXCg==","signature_status":"signed_v1","signed_at":"2026-07-05T03:56:50.380951Z","signed_message":"canonical_sha256_bytes"},"source_id":"2109.14462","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f0ce780d9e52de8af4f33550bbd1521b6451c1a62adfe8703abbdd36d14dccd3","sha256:eace8e5eb71d976a2e7385f7b9f4b751ced3d977e518b53ded431e1ea4cc52bc"],"state_sha256":"7ed36c93feb3728a42529e209d60b3f4472e39ea4afc6bec43f54991ab0f777e"}