{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:2KWRFJZZR62TQPFVO3VGXU6DVP","short_pith_number":"pith:2KWRFJZZ","canonical_record":{"source":{"id":"math/0605669","kind":"arxiv","version":9},"metadata":{"license":"","primary_cat":"math.RA","submitted_at":"2006-05-25T22:52:12Z","cross_cats_sorted":[],"title_canon_sha256":"0e6c02fd7e8af72f7b6ae83135ecd6a1ebe06feb1bc1e48b0e341f1605651a48","abstract_canon_sha256":"577c7aacaf435765d3788dc962409e8bb00807309ec247ae61c14e606710f485"},"schema_version":"1.0"},"canonical_sha256":"d2ad12a7398fb5383cb576ea6bd3c3abe86278ee3e5453d9dc008d585a862e75","source":{"kind":"arxiv","id":"math/0605669","version":9},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0605669","created_at":"2026-05-18T01:38:24Z"},{"alias_kind":"arxiv_version","alias_value":"math/0605669v9","created_at":"2026-05-18T01:38:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0605669","created_at":"2026-05-18T01:38:24Z"},{"alias_kind":"pith_short_12","alias_value":"2KWRFJZZR62T","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"2KWRFJZZR62TQPFV","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"2KWRFJZZ","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:2KWRFJZZR62TQPFVO3VGXU6DVP","target":"record","payload":{"canonical_record":{"source":{"id":"math/0605669","kind":"arxiv","version":9},"metadata":{"license":"","primary_cat":"math.RA","submitted_at":"2006-05-25T22:52:12Z","cross_cats_sorted":[],"title_canon_sha256":"0e6c02fd7e8af72f7b6ae83135ecd6a1ebe06feb1bc1e48b0e341f1605651a48","abstract_canon_sha256":"577c7aacaf435765d3788dc962409e8bb00807309ec247ae61c14e606710f485"},"schema_version":"1.0"},"canonical_sha256":"d2ad12a7398fb5383cb576ea6bd3c3abe86278ee3e5453d9dc008d585a862e75","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:24.085598Z","signature_b64":"BcBtiKfKMVs3jzsOzcQoo2XYpepr2u97E7qeZ6Z3UWbYiJqs1kRagd1ozpwcGXkUDAJL6maeLTn9n7kbUaYbBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d2ad12a7398fb5383cb576ea6bd3c3abe86278ee3e5453d9dc008d585a862e75","last_reissued_at":"2026-05-18T01:38:24.084856Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:24.084856Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0605669","source_version":9,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:38:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EC57JaWnM8/9zl96nWV3nBE8BvqcuaIPKYvcvQ3fPif8GwB2BPOfm/7LX7K83qpLi0RYnVxkWevXKhM1E6FuCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T16:13:47.889469Z"},"content_sha256":"6c9b7688d090cb12a44cc76ffe4874a0b0f074331ed5ac8f1abf762207ccc256","schema_version":"1.0","event_id":"sha256:6c9b7688d090cb12a44cc76ffe4874a0b0f074331ed5ac8f1abf762207ccc256"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:2KWRFJZZR62TQPFVO3VGXU6DVP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hamiltonian type Lie bialgebras","license":"","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Bin Xin, Guang'ai Song, Yucai Su","submitted_at":"2006-05-25T22:52:12Z","abstract_excerpt":"We first prove that, for any generalized Hamiltonian type Lie algebra $L$, the first cohomology group $H^1(L,L \\otimes L)$ is trivial. We then show that all Lie bialgebra structures on $L$ are triangular."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0605669","kind":"arxiv","version":9},"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":"2026-05-18T01:38:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kInORwptug/JS9tKx/aDYRLb+VLYzyoagiqdFN1wi7DFqwnMTGZS6OiiF5eMgqNHeFp1cdTYjOSgsdHdC6R0CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T16:13:47.890050Z"},"content_sha256":"b80ebc16f7d9d98e914fa303b7a760bccd4f1ec83131b6b2cebed1f6a255846e","schema_version":"1.0","event_id":"sha256:b80ebc16f7d9d98e914fa303b7a760bccd4f1ec83131b6b2cebed1f6a255846e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2KWRFJZZR62TQPFVO3VGXU6DVP/bundle.json","state_url":"https://pith.science/pith/2KWRFJZZR62TQPFVO3VGXU6DVP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2KWRFJZZR62TQPFVO3VGXU6DVP/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":"2026-06-08T16:13:47Z","links":{"resolver":"https://pith.science/pith/2KWRFJZZR62TQPFVO3VGXU6DVP","bundle":"https://pith.science/pith/2KWRFJZZR62TQPFVO3VGXU6DVP/bundle.json","state":"https://pith.science/pith/2KWRFJZZR62TQPFVO3VGXU6DVP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2KWRFJZZR62TQPFVO3VGXU6DVP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:2KWRFJZZR62TQPFVO3VGXU6DVP","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":"577c7aacaf435765d3788dc962409e8bb00807309ec247ae61c14e606710f485","cross_cats_sorted":[],"license":"","primary_cat":"math.RA","submitted_at":"2006-05-25T22:52:12Z","title_canon_sha256":"0e6c02fd7e8af72f7b6ae83135ecd6a1ebe06feb1bc1e48b0e341f1605651a48"},"schema_version":"1.0","source":{"id":"math/0605669","kind":"arxiv","version":9}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0605669","created_at":"2026-05-18T01:38:24Z"},{"alias_kind":"arxiv_version","alias_value":"math/0605669v9","created_at":"2026-05-18T01:38:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0605669","created_at":"2026-05-18T01:38:24Z"},{"alias_kind":"pith_short_12","alias_value":"2KWRFJZZR62T","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"2KWRFJZZR62TQPFV","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"2KWRFJZZ","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:b80ebc16f7d9d98e914fa303b7a760bccd4f1ec83131b6b2cebed1f6a255846e","target":"graph","created_at":"2026-05-18T01:38:24Z","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 first prove that, for any generalized Hamiltonian type Lie algebra $L$, the first cohomology group $H^1(L,L \\otimes L)$ is trivial. We then show that all Lie bialgebra structures on $L$ are triangular.","authors_text":"Bin Xin, Guang'ai Song, Yucai Su","cross_cats":[],"headline":"","license":"","primary_cat":"math.RA","submitted_at":"2006-05-25T22:52:12Z","title":"Hamiltonian type Lie bialgebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0605669","kind":"arxiv","version":9},"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":"sha256:6c9b7688d090cb12a44cc76ffe4874a0b0f074331ed5ac8f1abf762207ccc256","target":"record","created_at":"2026-05-18T01:38:24Z","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":"577c7aacaf435765d3788dc962409e8bb00807309ec247ae61c14e606710f485","cross_cats_sorted":[],"license":"","primary_cat":"math.RA","submitted_at":"2006-05-25T22:52:12Z","title_canon_sha256":"0e6c02fd7e8af72f7b6ae83135ecd6a1ebe06feb1bc1e48b0e341f1605651a48"},"schema_version":"1.0","source":{"id":"math/0605669","kind":"arxiv","version":9}},"canonical_sha256":"d2ad12a7398fb5383cb576ea6bd3c3abe86278ee3e5453d9dc008d585a862e75","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d2ad12a7398fb5383cb576ea6bd3c3abe86278ee3e5453d9dc008d585a862e75","first_computed_at":"2026-05-18T01:38:24.084856Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:24.084856Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BcBtiKfKMVs3jzsOzcQoo2XYpepr2u97E7qeZ6Z3UWbYiJqs1kRagd1ozpwcGXkUDAJL6maeLTn9n7kbUaYbBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:24.085598Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0605669","source_kind":"arxiv","source_version":9}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6c9b7688d090cb12a44cc76ffe4874a0b0f074331ed5ac8f1abf762207ccc256","sha256:b80ebc16f7d9d98e914fa303b7a760bccd4f1ec83131b6b2cebed1f6a255846e"],"state_sha256":"de41d1b5e9cd22f941f36e2a9ca5869228924d7af3f8abee323bbd69044eb470"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B5ETMkH9we613nb0m+RC4ynTV60vRgvr/EINUNBYgX7bxCibiINPEb3+5usNoZZDQ7ihpFSSztFzHded3UrgBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T16:13:47.893804Z","bundle_sha256":"b17923724299fd07391abd91ba57ae4836eb889a1831bbf6a7e174d7de2d2cde"}}