{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:TGJC2T5RQEVQDZQOUJWZGB7N3W","short_pith_number":"pith:TGJC2T5R","canonical_record":{"source":{"id":"2312.04319","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2023-12-07T14:21:33Z","cross_cats_sorted":["hep-ph"],"title_canon_sha256":"e868dad8bde020ab331a829ba9c75b95807730207df52a4c0d916a6bf8fb4b1e","abstract_canon_sha256":"11bff643625521e709fe8bda1ead3f06670b5d6bb3271ca288711bdff36f7eba"},"schema_version":"1.0"},"canonical_sha256":"99922d4fb1812b01e60ea26d9307eddda9d85dd6f884531aeaafc1260d3c9dda","source":{"kind":"arxiv","id":"2312.04319","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.04319","created_at":"2026-07-05T07:50:05Z"},{"alias_kind":"arxiv_version","alias_value":"2312.04319v2","created_at":"2026-07-05T07:50:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.04319","created_at":"2026-07-05T07:50:05Z"},{"alias_kind":"pith_short_12","alias_value":"TGJC2T5RQEVQ","created_at":"2026-07-05T07:50:05Z"},{"alias_kind":"pith_short_16","alias_value":"TGJC2T5RQEVQDZQO","created_at":"2026-07-05T07:50:05Z"},{"alias_kind":"pith_short_8","alias_value":"TGJC2T5R","created_at":"2026-07-05T07:50:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:TGJC2T5RQEVQDZQOUJWZGB7N3W","target":"record","payload":{"canonical_record":{"source":{"id":"2312.04319","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2023-12-07T14:21:33Z","cross_cats_sorted":["hep-ph"],"title_canon_sha256":"e868dad8bde020ab331a829ba9c75b95807730207df52a4c0d916a6bf8fb4b1e","abstract_canon_sha256":"11bff643625521e709fe8bda1ead3f06670b5d6bb3271ca288711bdff36f7eba"},"schema_version":"1.0"},"canonical_sha256":"99922d4fb1812b01e60ea26d9307eddda9d85dd6f884531aeaafc1260d3c9dda","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:50:05.655793Z","signature_b64":"56mTofVSmZDtqVZvVKWKJr3r1l7oCWST/QktD0Oy5OJrdI7Q8srHZKU19JmbQI1rq3GR4LYynR5HogoqyBJNCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"99922d4fb1812b01e60ea26d9307eddda9d85dd6f884531aeaafc1260d3c9dda","last_reissued_at":"2026-07-05T07:50:05.655264Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:50:05.655264Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2312.04319","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T07:50:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X0LKt1HJGpwpZwk6fEPl6E0vjkOhp/6me68XpfJPC9KAcshMjBNXxHPSxmOZPKUoaGuPY9fDCjJGq8Doj80WBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T18:22:40.658481Z"},"content_sha256":"004946abbb4217533363ecee45e9c1febc6dbd0eada759425c11edd470b24e05","schema_version":"1.0","event_id":"sha256:004946abbb4217533363ecee45e9c1febc6dbd0eada759425c11edd470b24e05"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:TGJC2T5RQEVQDZQOUJWZGB7N3W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Color-Kinematics Duality with Minimal Deformation: Two-Loop Four-Gluon Amplitudes in Pure Yang-Mills Revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-ph"],"primary_cat":"hep-th","authors_text":"Gang Yang, Zeyu Li","submitted_at":"2023-12-07T14:21:33Z","abstract_excerpt":"The conjectured duality between color and kinematics has significantly advanced our understanding of both gauge and gravitational theories. However, constructing numerators that manifest the color-kinematics (CK) duality, even for the two-loop four-gluon amplitude in pure Yang-Mills, has been challenging. In this paper, we revisit this amplitude and show that the difficulty of applying CK duality can be overcome by introducing a simple deformation. Our approach distinguishes itself from previous studies by maximizing the use of off-shell CK duality while maintaining a compact ansatz. In partic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.04319","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2312.04319/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T07:50:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WD8wPKKJwk+M98yp84B1xqVqpNe9QsD3WvUVfvTNtCQku1blBm1RdtcLF6ZWsaRLuNBRTX0mkL180WdPzeNQAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T18:22:40.659036Z"},"content_sha256":"63a913e5ce4c0f4848703bc3ab361e57cde7818f835358b528cd39f13d84f808","schema_version":"1.0","event_id":"sha256:63a913e5ce4c0f4848703bc3ab361e57cde7818f835358b528cd39f13d84f808"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TGJC2T5RQEVQDZQOUJWZGB7N3W/bundle.json","state_url":"https://pith.science/pith/TGJC2T5RQEVQDZQOUJWZGB7N3W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TGJC2T5RQEVQDZQOUJWZGB7N3W/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-12T18:22:40Z","links":{"resolver":"https://pith.science/pith/TGJC2T5RQEVQDZQOUJWZGB7N3W","bundle":"https://pith.science/pith/TGJC2T5RQEVQDZQOUJWZGB7N3W/bundle.json","state":"https://pith.science/pith/TGJC2T5RQEVQDZQOUJWZGB7N3W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TGJC2T5RQEVQDZQOUJWZGB7N3W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:TGJC2T5RQEVQDZQOUJWZGB7N3W","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":"11bff643625521e709fe8bda1ead3f06670b5d6bb3271ca288711bdff36f7eba","cross_cats_sorted":["hep-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2023-12-07T14:21:33Z","title_canon_sha256":"e868dad8bde020ab331a829ba9c75b95807730207df52a4c0d916a6bf8fb4b1e"},"schema_version":"1.0","source":{"id":"2312.04319","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.04319","created_at":"2026-07-05T07:50:05Z"},{"alias_kind":"arxiv_version","alias_value":"2312.04319v2","created_at":"2026-07-05T07:50:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.04319","created_at":"2026-07-05T07:50:05Z"},{"alias_kind":"pith_short_12","alias_value":"TGJC2T5RQEVQ","created_at":"2026-07-05T07:50:05Z"},{"alias_kind":"pith_short_16","alias_value":"TGJC2T5RQEVQDZQO","created_at":"2026-07-05T07:50:05Z"},{"alias_kind":"pith_short_8","alias_value":"TGJC2T5R","created_at":"2026-07-05T07:50:05Z"}],"graph_snapshots":[{"event_id":"sha256:63a913e5ce4c0f4848703bc3ab361e57cde7818f835358b528cd39f13d84f808","target":"graph","created_at":"2026-07-05T07:50:05Z","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/2312.04319/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The conjectured duality between color and kinematics has significantly advanced our understanding of both gauge and gravitational theories. However, constructing numerators that manifest the color-kinematics (CK) duality, even for the two-loop four-gluon amplitude in pure Yang-Mills, has been challenging. In this paper, we revisit this amplitude and show that the difficulty of applying CK duality can be overcome by introducing a simple deformation. Our approach distinguishes itself from previous studies by maximizing the use of off-shell CK duality while maintaining a compact ansatz. In partic","authors_text":"Gang Yang, Zeyu Li","cross_cats":["hep-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2023-12-07T14:21:33Z","title":"Color-Kinematics Duality with Minimal Deformation: Two-Loop Four-Gluon Amplitudes in Pure Yang-Mills Revisited"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.04319","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":"sha256:004946abbb4217533363ecee45e9c1febc6dbd0eada759425c11edd470b24e05","target":"record","created_at":"2026-07-05T07:50:05Z","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":"11bff643625521e709fe8bda1ead3f06670b5d6bb3271ca288711bdff36f7eba","cross_cats_sorted":["hep-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2023-12-07T14:21:33Z","title_canon_sha256":"e868dad8bde020ab331a829ba9c75b95807730207df52a4c0d916a6bf8fb4b1e"},"schema_version":"1.0","source":{"id":"2312.04319","kind":"arxiv","version":2}},"canonical_sha256":"99922d4fb1812b01e60ea26d9307eddda9d85dd6f884531aeaafc1260d3c9dda","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"99922d4fb1812b01e60ea26d9307eddda9d85dd6f884531aeaafc1260d3c9dda","first_computed_at":"2026-07-05T07:50:05.655264Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:50:05.655264Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"56mTofVSmZDtqVZvVKWKJr3r1l7oCWST/QktD0Oy5OJrdI7Q8srHZKU19JmbQI1rq3GR4LYynR5HogoqyBJNCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T07:50:05.655793Z","signed_message":"canonical_sha256_bytes"},"source_id":"2312.04319","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:004946abbb4217533363ecee45e9c1febc6dbd0eada759425c11edd470b24e05","sha256:63a913e5ce4c0f4848703bc3ab361e57cde7818f835358b528cd39f13d84f808"],"state_sha256":"1e07eec4e174f642e3af368b537b2c2106f483160a61525c7699c8d50412a953"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VDdzoDJ7TX4Pg2E5YfnqSOmMlhsmIoRf/kGSL1pXzgvhmPeME9/iRAPJIf5SZCt3nZFeoHYVwJBE4MDBTpjaCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T18:22:40.663398Z","bundle_sha256":"ddaf58eb7a487756c47e919851077b54472aea1898e12bde682461962804c4c0"}}