{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:RSUB64Q5MXUC4ROSE2HCWM3BQS","short_pith_number":"pith:RSUB64Q5","schema_version":"1.0","canonical_sha256":"8ca81f721d65e82e45d2268e2b336184a2533f36c4fadbf00808bee279c9661b","source":{"kind":"arxiv","id":"0910.3262","version":1},"attestation_state":"computed","paper":{"title":"Nonabelian generalized Lax pairs, the classical Yang-Baxter equation and PostLie algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Chengming Bai, Li Guo, Xiang Ni","submitted_at":"2009-10-17T01:45:54Z","abstract_excerpt":"We generalize the classical study of (generalized) Lax pairs and the related $O$-operators and the (modified) classical Yang-Baxter equation by introducing the concepts of nonabelian generalized Lax pairs, extended $\\calo$-operators and the extended classical Yang-Baxter equation. We study in this context the nonabelian generalized $r$-matrix ansatz and the related double Lie algebra structures. Relationship between extended $O$-operators and the extended classical Yang-Baxter equation is established, especially for self-dual Lie algebras. This relationship allows us to obtain explicit descrip"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0910.3262","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-10-17T01:45:54Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"14748693bc40ebcd2ccd8103af1bbf4d946f7b5aaa0c71b5ab8e6fc7480518d2","abstract_canon_sha256":"f68c3cc03b7a02fcce7ce82b2264d3f504c2d86dac07b9c4bb3b4205f9d9ce71"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:11:14.811125Z","signature_b64":"wwEkrrUXwJHSZzthdQ+d9qJDIv9VTa4KbgnF57widUWjUEYVLN1c2rH9aa4EyZ1uS/Tp8r9JDsgZqQpuWCIsAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8ca81f721d65e82e45d2268e2b336184a2533f36c4fadbf00808bee279c9661b","last_reissued_at":"2026-05-18T02:11:14.810229Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:11:14.810229Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nonabelian generalized Lax pairs, the classical Yang-Baxter equation and PostLie algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Chengming Bai, Li Guo, Xiang Ni","submitted_at":"2009-10-17T01:45:54Z","abstract_excerpt":"We generalize the classical study of (generalized) Lax pairs and the related $O$-operators and the (modified) classical Yang-Baxter equation by introducing the concepts of nonabelian generalized Lax pairs, extended $\\calo$-operators and the extended classical Yang-Baxter equation. We study in this context the nonabelian generalized $r$-matrix ansatz and the related double Lie algebra structures. Relationship between extended $O$-operators and the extended classical Yang-Baxter equation is established, especially for self-dual Lie algebras. This relationship allows us to obtain explicit descrip"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.3262","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"0910.3262","created_at":"2026-05-18T02:11:14.810385+00:00"},{"alias_kind":"arxiv_version","alias_value":"0910.3262v1","created_at":"2026-05-18T02:11:14.810385+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.3262","created_at":"2026-05-18T02:11:14.810385+00:00"},{"alias_kind":"pith_short_12","alias_value":"RSUB64Q5MXUC","created_at":"2026-05-18T12:26:01.383474+00:00"},{"alias_kind":"pith_short_16","alias_value":"RSUB64Q5MXUC4ROS","created_at":"2026-05-18T12:26:01.383474+00:00"},{"alias_kind":"pith_short_8","alias_value":"RSUB64Q5","created_at":"2026-05-18T12:26:01.383474+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/RSUB64Q5MXUC4ROSE2HCWM3BQS","json":"https://pith.science/pith/RSUB64Q5MXUC4ROSE2HCWM3BQS.json","graph_json":"https://pith.science/api/pith-number/RSUB64Q5MXUC4ROSE2HCWM3BQS/graph.json","events_json":"https://pith.science/api/pith-number/RSUB64Q5MXUC4ROSE2HCWM3BQS/events.json","paper":"https://pith.science/paper/RSUB64Q5"},"agent_actions":{"view_html":"https://pith.science/pith/RSUB64Q5MXUC4ROSE2HCWM3BQS","download_json":"https://pith.science/pith/RSUB64Q5MXUC4ROSE2HCWM3BQS.json","view_paper":"https://pith.science/paper/RSUB64Q5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0910.3262&json=true","fetch_graph":"https://pith.science/api/pith-number/RSUB64Q5MXUC4ROSE2HCWM3BQS/graph.json","fetch_events":"https://pith.science/api/pith-number/RSUB64Q5MXUC4ROSE2HCWM3BQS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RSUB64Q5MXUC4ROSE2HCWM3BQS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RSUB64Q5MXUC4ROSE2HCWM3BQS/action/storage_attestation","attest_author":"https://pith.science/pith/RSUB64Q5MXUC4ROSE2HCWM3BQS/action/author_attestation","sign_citation":"https://pith.science/pith/RSUB64Q5MXUC4ROSE2HCWM3BQS/action/citation_signature","submit_replication":"https://pith.science/pith/RSUB64Q5MXUC4ROSE2HCWM3BQS/action/replication_record"}},"created_at":"2026-05-18T02:11:14.810385+00:00","updated_at":"2026-05-18T02:11:14.810385+00:00"}