{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:RSUB64Q5MXUC4ROSE2HCWM3BQS","short_pith_number":"pith:RSUB64Q5","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"},"canonical_sha256":"8ca81f721d65e82e45d2268e2b336184a2533f36c4fadbf00808bee279c9661b","source":{"kind":"arxiv","id":"0910.3262","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0910.3262","created_at":"2026-05-18T02:11:14Z"},{"alias_kind":"arxiv_version","alias_value":"0910.3262v1","created_at":"2026-05-18T02:11:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.3262","created_at":"2026-05-18T02:11:14Z"},{"alias_kind":"pith_short_12","alias_value":"RSUB64Q5MXUC","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"RSUB64Q5MXUC4ROS","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"RSUB64Q5","created_at":"2026-05-18T12:26:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:RSUB64Q5MXUC4ROSE2HCWM3BQS","target":"record","payload":{"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"},"canonical_sha256":"8ca81f721d65e82e45d2268e2b336184a2533f36c4fadbf00808bee279c9661b","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"},"source_kind":"arxiv","source_id":"0910.3262","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:11:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d7eqZzfGpiIotg4kwhHMBAljiSjflks6OdRvQdS1lawOIS04LAnvZtBIkLXUaKk2acMlkj60kqhCDEnry3E4CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T17:05:13.079385Z"},"content_sha256":"7edc0012c9593b288f49d174c9f0af95e265fa169e594202657c6412f5665b98","schema_version":"1.0","event_id":"sha256:7edc0012c9593b288f49d174c9f0af95e265fa169e594202657c6412f5665b98"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:RSUB64Q5MXUC4ROSE2HCWM3BQS","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:11:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iXa/FCGOLb31IE8hKf8UdGxeeqckPxMie9dR+Qd589LGoURHAuA1Y2Q3+aSqQ8w+fAS0GikjxvrzbHEuUmy8AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T17:05:13.079869Z"},"content_sha256":"96a0de7e61477a7c985e220150d20d53cf3062a1d0e4fd834113732fbf81bb95","schema_version":"1.0","event_id":"sha256:96a0de7e61477a7c985e220150d20d53cf3062a1d0e4fd834113732fbf81bb95"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RSUB64Q5MXUC4ROSE2HCWM3BQS/bundle.json","state_url":"https://pith.science/pith/RSUB64Q5MXUC4ROSE2HCWM3BQS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RSUB64Q5MXUC4ROSE2HCWM3BQS/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":"2026-05-26T17:05:13Z","links":{"resolver":"https://pith.science/pith/RSUB64Q5MXUC4ROSE2HCWM3BQS","bundle":"https://pith.science/pith/RSUB64Q5MXUC4ROSE2HCWM3BQS/bundle.json","state":"https://pith.science/pith/RSUB64Q5MXUC4ROSE2HCWM3BQS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RSUB64Q5MXUC4ROSE2HCWM3BQS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:RSUB64Q5MXUC4ROSE2HCWM3BQS","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":"f68c3cc03b7a02fcce7ce82b2264d3f504c2d86dac07b9c4bb3b4205f9d9ce71","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-10-17T01:45:54Z","title_canon_sha256":"14748693bc40ebcd2ccd8103af1bbf4d946f7b5aaa0c71b5ab8e6fc7480518d2"},"schema_version":"1.0","source":{"id":"0910.3262","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0910.3262","created_at":"2026-05-18T02:11:14Z"},{"alias_kind":"arxiv_version","alias_value":"0910.3262v1","created_at":"2026-05-18T02:11:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.3262","created_at":"2026-05-18T02:11:14Z"},{"alias_kind":"pith_short_12","alias_value":"RSUB64Q5MXUC","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"RSUB64Q5MXUC4ROS","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"RSUB64Q5","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:96a0de7e61477a7c985e220150d20d53cf3062a1d0e4fd834113732fbf81bb95","target":"graph","created_at":"2026-05-18T02:11:14Z","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":"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","authors_text":"Chengming Bai, Li Guo, Xiang Ni","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-10-17T01:45:54Z","title":"Nonabelian generalized Lax pairs, the classical Yang-Baxter equation and PostLie algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.3262","kind":"arxiv","version":1},"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":"sha256:7edc0012c9593b288f49d174c9f0af95e265fa169e594202657c6412f5665b98","target":"record","created_at":"2026-05-18T02:11:14Z","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":"f68c3cc03b7a02fcce7ce82b2264d3f504c2d86dac07b9c4bb3b4205f9d9ce71","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-10-17T01:45:54Z","title_canon_sha256":"14748693bc40ebcd2ccd8103af1bbf4d946f7b5aaa0c71b5ab8e6fc7480518d2"},"schema_version":"1.0","source":{"id":"0910.3262","kind":"arxiv","version":1}},"canonical_sha256":"8ca81f721d65e82e45d2268e2b336184a2533f36c4fadbf00808bee279c9661b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8ca81f721d65e82e45d2268e2b336184a2533f36c4fadbf00808bee279c9661b","first_computed_at":"2026-05-18T02:11:14.810229Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:11:14.810229Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wwEkrrUXwJHSZzthdQ+d9qJDIv9VTa4KbgnF57widUWjUEYVLN1c2rH9aa4EyZ1uS/Tp8r9JDsgZqQpuWCIsAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:11:14.811125Z","signed_message":"canonical_sha256_bytes"},"source_id":"0910.3262","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7edc0012c9593b288f49d174c9f0af95e265fa169e594202657c6412f5665b98","sha256:96a0de7e61477a7c985e220150d20d53cf3062a1d0e4fd834113732fbf81bb95"],"state_sha256":"d1051e7b310486a3f34a60fe39efbe70d9f70ad2b2d3723f2e4d0b92fb999737"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OhyWVVA5QCqI8PgYZn7Cu1Y8clm2uFRr8jgnOEf4EnPSv2d1hhCAEKq7c2jWGBzCAK49t5+743AKIJ53vhM9Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T17:05:13.083239Z","bundle_sha256":"bc5cb75e1e5512dce0cdea0ee9daeab584cdecf081fce30d6d9e2cf4e526a0f4"}}