{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:5TIUKYUATQMNNQ7WGGD5H5KLE3","short_pith_number":"pith:5TIUKYUA","canonical_record":{"source":{"id":"2208.05519","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-08-10T18:29:09Z","cross_cats_sorted":[],"title_canon_sha256":"4b2f759b615925a3f30031ee39c20d29eecd6c865db796a29b58cad5d6e57541","abstract_canon_sha256":"f8a23ee899419908d3eeb6a2fa51d5026b858ce2eb4def40d7927edfa7de3e3e"},"schema_version":"1.0"},"canonical_sha256":"ecd14562809c18d6c3f63187d3f54b26f47ffda52572419bfbeb5d286d76eeef","source":{"kind":"arxiv","id":"2208.05519","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2208.05519","created_at":"2026-07-05T06:03:25Z"},{"alias_kind":"arxiv_version","alias_value":"2208.05519v2","created_at":"2026-07-05T06:03:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2208.05519","created_at":"2026-07-05T06:03:25Z"},{"alias_kind":"pith_short_12","alias_value":"5TIUKYUATQMN","created_at":"2026-07-05T06:03:25Z"},{"alias_kind":"pith_short_16","alias_value":"5TIUKYUATQMNNQ7W","created_at":"2026-07-05T06:03:25Z"},{"alias_kind":"pith_short_8","alias_value":"5TIUKYUA","created_at":"2026-07-05T06:03:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:5TIUKYUATQMNNQ7WGGD5H5KLE3","target":"record","payload":{"canonical_record":{"source":{"id":"2208.05519","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-08-10T18:29:09Z","cross_cats_sorted":[],"title_canon_sha256":"4b2f759b615925a3f30031ee39c20d29eecd6c865db796a29b58cad5d6e57541","abstract_canon_sha256":"f8a23ee899419908d3eeb6a2fa51d5026b858ce2eb4def40d7927edfa7de3e3e"},"schema_version":"1.0"},"canonical_sha256":"ecd14562809c18d6c3f63187d3f54b26f47ffda52572419bfbeb5d286d76eeef","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:03:25.019041Z","signature_b64":"k499GO66PeZapvocZ1aNVWL5rFBFIN0P8jDaL59hyO2n4viSCHvGv9roEcPjug1tbhR2uxtv+15QrGgj1F5XAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ecd14562809c18d6c3f63187d3f54b26f47ffda52572419bfbeb5d286d76eeef","last_reissued_at":"2026-07-05T06:03:25.018613Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:03:25.018613Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2208.05519","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":"2026-07-05T06:03:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z5YOe4Adry1zMNTbnlxvVB0PlXxv8xmrbQlvQlo89WU3sHYGIEy6n74cFDI2iWc0Mkb3orXHecZTnXKQ15rmCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T08:45:06.440780Z"},"content_sha256":"1d4846722fc43168346d480bdbf5aa6ab3410160c11a11b1c1bdd233ac2b2e2a","schema_version":"1.0","event_id":"sha256:1d4846722fc43168346d480bdbf5aa6ab3410160c11a11b1c1bdd233ac2b2e2a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:5TIUKYUATQMNNQ7WGGD5H5KLE3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Kinematic Hopf algebra for amplitudes and form factors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Congkao Wen, Gang Chen, Guanda Lin","submitted_at":"2022-08-10T18:29:09Z","abstract_excerpt":"We propose a kinematic algebra for the Bern-Carrasco-Johansson (BCJ) numerators of tree-level amplitudes and form factors in Yang-Mills theory coupled with bi-adjoint scalars. The algebraic generators of the algebra contain two parts: the first part is simply the flavour factor of the bi-adjoint scalars, and the second part that maps to non-trivial kinematic structures of the BCJ numerators obeys extended quasi-shuffle fusion products. The underlying kinematic algebra allows us to present closed forms for the BCJ numerators with any number of gluons and two or more scalars for both on-shell am"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.05519","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/2208.05519/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":"2026-07-05T06:03:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QtIf7G++xAaNLx9qWuet6WYrwJ000SovktNpd8GojhNnzcjZdJxDy8z544obzf8FYZr6c6U8s/yIXRxnpi2IBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T08:45:06.441343Z"},"content_sha256":"a436b15afb21fd642c72013101ebf17026ba7f1a7e23c4cb9d1d87fee66857d5","schema_version":"1.0","event_id":"sha256:a436b15afb21fd642c72013101ebf17026ba7f1a7e23c4cb9d1d87fee66857d5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5TIUKYUATQMNNQ7WGGD5H5KLE3/bundle.json","state_url":"https://pith.science/pith/5TIUKYUATQMNNQ7WGGD5H5KLE3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5TIUKYUATQMNNQ7WGGD5H5KLE3/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":"2026-08-11T08:45:06Z","links":{"resolver":"https://pith.science/pith/5TIUKYUATQMNNQ7WGGD5H5KLE3","bundle":"https://pith.science/pith/5TIUKYUATQMNNQ7WGGD5H5KLE3/bundle.json","state":"https://pith.science/pith/5TIUKYUATQMNNQ7WGGD5H5KLE3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5TIUKYUATQMNNQ7WGGD5H5KLE3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:5TIUKYUATQMNNQ7WGGD5H5KLE3","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":"f8a23ee899419908d3eeb6a2fa51d5026b858ce2eb4def40d7927edfa7de3e3e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-08-10T18:29:09Z","title_canon_sha256":"4b2f759b615925a3f30031ee39c20d29eecd6c865db796a29b58cad5d6e57541"},"schema_version":"1.0","source":{"id":"2208.05519","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2208.05519","created_at":"2026-07-05T06:03:25Z"},{"alias_kind":"arxiv_version","alias_value":"2208.05519v2","created_at":"2026-07-05T06:03:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2208.05519","created_at":"2026-07-05T06:03:25Z"},{"alias_kind":"pith_short_12","alias_value":"5TIUKYUATQMN","created_at":"2026-07-05T06:03:25Z"},{"alias_kind":"pith_short_16","alias_value":"5TIUKYUATQMNNQ7W","created_at":"2026-07-05T06:03:25Z"},{"alias_kind":"pith_short_8","alias_value":"5TIUKYUA","created_at":"2026-07-05T06:03:25Z"}],"graph_snapshots":[{"event_id":"sha256:a436b15afb21fd642c72013101ebf17026ba7f1a7e23c4cb9d1d87fee66857d5","target":"graph","created_at":"2026-07-05T06:03:25Z","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/2208.05519/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We propose a kinematic algebra for the Bern-Carrasco-Johansson (BCJ) numerators of tree-level amplitudes and form factors in Yang-Mills theory coupled with bi-adjoint scalars. The algebraic generators of the algebra contain two parts: the first part is simply the flavour factor of the bi-adjoint scalars, and the second part that maps to non-trivial kinematic structures of the BCJ numerators obeys extended quasi-shuffle fusion products. The underlying kinematic algebra allows us to present closed forms for the BCJ numerators with any number of gluons and two or more scalars for both on-shell am","authors_text":"Congkao Wen, Gang Chen, Guanda Lin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-08-10T18:29:09Z","title":"Kinematic Hopf algebra for amplitudes and form factors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.05519","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":"sha256:1d4846722fc43168346d480bdbf5aa6ab3410160c11a11b1c1bdd233ac2b2e2a","target":"record","created_at":"2026-07-05T06:03:25Z","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":"f8a23ee899419908d3eeb6a2fa51d5026b858ce2eb4def40d7927edfa7de3e3e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-08-10T18:29:09Z","title_canon_sha256":"4b2f759b615925a3f30031ee39c20d29eecd6c865db796a29b58cad5d6e57541"},"schema_version":"1.0","source":{"id":"2208.05519","kind":"arxiv","version":2}},"canonical_sha256":"ecd14562809c18d6c3f63187d3f54b26f47ffda52572419bfbeb5d286d76eeef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ecd14562809c18d6c3f63187d3f54b26f47ffda52572419bfbeb5d286d76eeef","first_computed_at":"2026-07-05T06:03:25.018613Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:03:25.018613Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"k499GO66PeZapvocZ1aNVWL5rFBFIN0P8jDaL59hyO2n4viSCHvGv9roEcPjug1tbhR2uxtv+15QrGgj1F5XAw==","signature_status":"signed_v1","signed_at":"2026-07-05T06:03:25.019041Z","signed_message":"canonical_sha256_bytes"},"source_id":"2208.05519","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1d4846722fc43168346d480bdbf5aa6ab3410160c11a11b1c1bdd233ac2b2e2a","sha256:a436b15afb21fd642c72013101ebf17026ba7f1a7e23c4cb9d1d87fee66857d5"],"state_sha256":"8df9d9de5ffc19eed33cfe458c2611f74fb31de53adbb2487d1590e8e065ec82"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MkRLwd8Z0Ky0YixTuzN/SAngnynB9s0TaSHJjcMcS7FJIxW9/rk/0Vvi3XPIjO7Ogp6MA5AoDP/4KUyQj0piBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T08:45:06.447064Z","bundle_sha256":"7a6c5a698db0a8bb8e5ac511c419755b390ef29c088b24e305a27e16ed1ad415"}}