{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:CMJYO6JDWURMQM73322IY4ZCHR","short_pith_number":"pith:CMJYO6JD","canonical_record":{"source":{"id":"0904.4062","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-04-26T21:27:36Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"374f4c4da5523762c40232bf4a2426b4149cb5fdae11e734989e52b6d7a9e431","abstract_canon_sha256":"7a185437c50f4aeae5df1de9f448c6c34e33e1dccb234648b606e878058fd6f0"},"schema_version":"1.0"},"canonical_sha256":"1313877923b522c833fbdeb48c73223c7541f13bdf2ad00050a493fc8870b174","source":{"kind":"arxiv","id":"0904.4062","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0904.4062","created_at":"2026-05-18T00:38:36Z"},{"alias_kind":"arxiv_version","alias_value":"0904.4062v2","created_at":"2026-05-18T00:38:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0904.4062","created_at":"2026-05-18T00:38:36Z"},{"alias_kind":"pith_short_12","alias_value":"CMJYO6JDWURM","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"CMJYO6JDWURMQM73","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"CMJYO6JD","created_at":"2026-05-18T12:25:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:CMJYO6JDWURMQM73322IY4ZCHR","target":"record","payload":{"canonical_record":{"source":{"id":"0904.4062","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-04-26T21:27:36Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"374f4c4da5523762c40232bf4a2426b4149cb5fdae11e734989e52b6d7a9e431","abstract_canon_sha256":"7a185437c50f4aeae5df1de9f448c6c34e33e1dccb234648b606e878058fd6f0"},"schema_version":"1.0"},"canonical_sha256":"1313877923b522c833fbdeb48c73223c7541f13bdf2ad00050a493fc8870b174","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:38:36.954887Z","signature_b64":"RLjm/M2CQ7yN3fmyg7dPrAAzvHc+5l/zl4m3k8vjIl4UKYD3yAQLLjVHaR//CF6A1UOSm3+4fxDP8QwvM0y6Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1313877923b522c833fbdeb48c73223c7541f13bdf2ad00050a493fc8870b174","last_reissued_at":"2026-05-18T00:38:36.954326Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:38:36.954326Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0904.4062","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":"2026-05-18T00:38:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WhacEHz3yPR0VxtbJgDYFwNFk7RScZHeIJJKkqUT8wTOyx7Xq6GuaLNE4EZWHOzDKBdtAgeEDVEVGG5CurwZCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T10:30:55.349095Z"},"content_sha256":"288ab5f55266dd2cfa4f6b781b4b50b48676d0f1dda45dfe97b3725293569f53","schema_version":"1.0","event_id":"sha256:288ab5f55266dd2cfa4f6b781b4b50b48676d0f1dda45dfe97b3725293569f53"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:CMJYO6JDWURMQM73322IY4ZCHR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Geometry of Maurer-Cartan Elements on Complex Manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DG","authors_text":"Mathieu Stienon, Ping Xu, Zhuo Chen","submitted_at":"2009-04-26T21:27:36Z","abstract_excerpt":"The semi-classical data attached to stacks of algebroids in the sense of Kashiwara and Kontsevich are Maurer-Cartan elements on complex manifolds, which we call extended Poisson structures as they generalize holomorphic Poisson structures. A canonical Lie algebroid is associated to each Maurer-Cartan element. We study the geometry underlying these Maurer-Cartan elements in the light of Lie algebroid theory. In particular, we extend Lichnerowicz-Poisson cohomology and Koszul-Brylinski homology to the realm of extended Poisson manifolds; we establish a sufficient criterion for these to be finite"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.4062","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":""},"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":"2026-05-18T00:38:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"md7PeToXmdTXMHLGdmomPc/JEWwLXKP56tlalS0Y0yAWUBUdr3wDwJbO+ac9dMdSwfntm7U5ilE8PiPwW5s4Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T10:30:55.349589Z"},"content_sha256":"93a766499594d2dde82520707858b029ce7e67a40bc3cb8e9f36de582776b604","schema_version":"1.0","event_id":"sha256:93a766499594d2dde82520707858b029ce7e67a40bc3cb8e9f36de582776b604"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CMJYO6JDWURMQM73322IY4ZCHR/bundle.json","state_url":"https://pith.science/pith/CMJYO6JDWURMQM73322IY4ZCHR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CMJYO6JDWURMQM73322IY4ZCHR/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":"2026-05-27T10:30:55Z","links":{"resolver":"https://pith.science/pith/CMJYO6JDWURMQM73322IY4ZCHR","bundle":"https://pith.science/pith/CMJYO6JDWURMQM73322IY4ZCHR/bundle.json","state":"https://pith.science/pith/CMJYO6JDWURMQM73322IY4ZCHR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CMJYO6JDWURMQM73322IY4ZCHR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:CMJYO6JDWURMQM73322IY4ZCHR","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":"7a185437c50f4aeae5df1de9f448c6c34e33e1dccb234648b606e878058fd6f0","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-04-26T21:27:36Z","title_canon_sha256":"374f4c4da5523762c40232bf4a2426b4149cb5fdae11e734989e52b6d7a9e431"},"schema_version":"1.0","source":{"id":"0904.4062","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0904.4062","created_at":"2026-05-18T00:38:36Z"},{"alias_kind":"arxiv_version","alias_value":"0904.4062v2","created_at":"2026-05-18T00:38:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0904.4062","created_at":"2026-05-18T00:38:36Z"},{"alias_kind":"pith_short_12","alias_value":"CMJYO6JDWURM","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"CMJYO6JDWURMQM73","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"CMJYO6JD","created_at":"2026-05-18T12:25:59Z"}],"graph_snapshots":[{"event_id":"sha256:93a766499594d2dde82520707858b029ce7e67a40bc3cb8e9f36de582776b604","target":"graph","created_at":"2026-05-18T00:38:36Z","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":"The semi-classical data attached to stacks of algebroids in the sense of Kashiwara and Kontsevich are Maurer-Cartan elements on complex manifolds, which we call extended Poisson structures as they generalize holomorphic Poisson structures. A canonical Lie algebroid is associated to each Maurer-Cartan element. We study the geometry underlying these Maurer-Cartan elements in the light of Lie algebroid theory. In particular, we extend Lichnerowicz-Poisson cohomology and Koszul-Brylinski homology to the realm of extended Poisson manifolds; we establish a sufficient criterion for these to be finite","authors_text":"Mathieu Stienon, Ping Xu, Zhuo Chen","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-04-26T21:27:36Z","title":"Geometry of Maurer-Cartan Elements on Complex Manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.4062","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":"sha256:288ab5f55266dd2cfa4f6b781b4b50b48676d0f1dda45dfe97b3725293569f53","target":"record","created_at":"2026-05-18T00:38:36Z","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":"7a185437c50f4aeae5df1de9f448c6c34e33e1dccb234648b606e878058fd6f0","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-04-26T21:27:36Z","title_canon_sha256":"374f4c4da5523762c40232bf4a2426b4149cb5fdae11e734989e52b6d7a9e431"},"schema_version":"1.0","source":{"id":"0904.4062","kind":"arxiv","version":2}},"canonical_sha256":"1313877923b522c833fbdeb48c73223c7541f13bdf2ad00050a493fc8870b174","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1313877923b522c833fbdeb48c73223c7541f13bdf2ad00050a493fc8870b174","first_computed_at":"2026-05-18T00:38:36.954326Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:38:36.954326Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RLjm/M2CQ7yN3fmyg7dPrAAzvHc+5l/zl4m3k8vjIl4UKYD3yAQLLjVHaR//CF6A1UOSm3+4fxDP8QwvM0y6Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:38:36.954887Z","signed_message":"canonical_sha256_bytes"},"source_id":"0904.4062","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:288ab5f55266dd2cfa4f6b781b4b50b48676d0f1dda45dfe97b3725293569f53","sha256:93a766499594d2dde82520707858b029ce7e67a40bc3cb8e9f36de582776b604"],"state_sha256":"b41dce37c90e371211ed48e0f76273b9760c6270dead5a41d75219b2dc834e20"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jcYihP++cxYJSIHVP36HJPiWP99HEjMb/e1z7vyE6QipM5Hf4rqPR55Gj/vjwUJQ/Dj8CUxiuzSGHxXmR/PADw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T10:30:55.352159Z","bundle_sha256":"26fc704bb5144625702c5b87b3c25106ed19e8fadb27d1697fb2bc8ca630b1b7"}}