{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:EUUOHED7SBOQU76OD2KT4GW7FL","short_pith_number":"pith:EUUOHED7","canonical_record":{"source":{"id":"0710.3098","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.SG","submitted_at":"2007-10-16T15:58:40Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"94a0683e7980554b71efbbc1003019d0974ff268179dd91118e229ad223b4d80","abstract_canon_sha256":"47f6e108201e72e486d52212f2e79d4fc97cdd0dca068411fb57fd0b1dc9cb38"},"schema_version":"1.0"},"canonical_sha256":"2528e3907f905d0a7fce1e953e1adf2ada23c5b8d3a008f4f74f25fe802fb40f","source":{"kind":"arxiv","id":"0710.3098","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0710.3098","created_at":"2026-05-18T03:39:17Z"},{"alias_kind":"arxiv_version","alias_value":"0710.3098v3","created_at":"2026-05-18T03:39:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0710.3098","created_at":"2026-05-18T03:39:17Z"},{"alias_kind":"pith_short_12","alias_value":"EUUOHED7SBOQ","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"EUUOHED7SBOQU76O","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"EUUOHED7","created_at":"2026-05-18T12:25:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:EUUOHED7SBOQU76OD2KT4GW7FL","target":"record","payload":{"canonical_record":{"source":{"id":"0710.3098","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.SG","submitted_at":"2007-10-16T15:58:40Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"94a0683e7980554b71efbbc1003019d0974ff268179dd91118e229ad223b4d80","abstract_canon_sha256":"47f6e108201e72e486d52212f2e79d4fc97cdd0dca068411fb57fd0b1dc9cb38"},"schema_version":"1.0"},"canonical_sha256":"2528e3907f905d0a7fce1e953e1adf2ada23c5b8d3a008f4f74f25fe802fb40f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:39:17.108749Z","signature_b64":"1clhrM8v1g5T2xSE2byhFR4R9HghEXVNNopoz/N619g9apEoIDgmLm9EaE5Lq1K/u5PQDI0xOS7XlS3ty+7JCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2528e3907f905d0a7fce1e953e1adf2ada23c5b8d3a008f4f74f25fe802fb40f","last_reissued_at":"2026-05-18T03:39:17.108206Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:39:17.108206Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0710.3098","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:39:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gywHTuh/9VjIL01KFltbUA9wgBCY1tudX4t721FE2g67vv7Loi+7gseiqycr8T9gaq2t89Gma0B7M1rtisjEBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T13:33:12.855456Z"},"content_sha256":"751ae5dda881e355d03854e3fb131362550839e4831312885484ceb8ba8aa543","schema_version":"1.0","event_id":"sha256:751ae5dda881e355d03854e3fb131362550839e4831312885484ceb8ba8aa543"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:EUUOHED7SBOQU76OD2KT4GW7FL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Poisson Manifolds, Lie Algebroids, Modular Classes: a Survey","license":"","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SG","authors_text":"Yvette Kosmann-Schwarzbach","submitted_at":"2007-10-16T15:58:40Z","abstract_excerpt":"After a brief summary of the main properties of Poisson manifolds and Lie algebroids in general, we survey recent work on the modular classes of Poisson and twisted Poisson manifolds, of Lie algebroids with a Poisson or twisted Poisson structure, and of Poisson-Nijenhuis manifolds. A review of the spinor approach to the modular class concludes the paper."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0710.3098","kind":"arxiv","version":3},"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":"2026-05-18T03:39:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tP8QpYLZCT3/EbKbmJEHn6dysJat02DZOjIdf0JE0sqUaKTwQPciqtzP/WJ2DBcb0nCKbvOyMsbroOGvOL1YAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T13:33:12.856136Z"},"content_sha256":"583b39d4e4827b35e6d15b3decc8bc6c1d764a1bfbcf3528dc3ab7ec9480f56b","schema_version":"1.0","event_id":"sha256:583b39d4e4827b35e6d15b3decc8bc6c1d764a1bfbcf3528dc3ab7ec9480f56b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EUUOHED7SBOQU76OD2KT4GW7FL/bundle.json","state_url":"https://pith.science/pith/EUUOHED7SBOQU76OD2KT4GW7FL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EUUOHED7SBOQU76OD2KT4GW7FL/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":"2026-06-07T13:33:12Z","links":{"resolver":"https://pith.science/pith/EUUOHED7SBOQU76OD2KT4GW7FL","bundle":"https://pith.science/pith/EUUOHED7SBOQU76OD2KT4GW7FL/bundle.json","state":"https://pith.science/pith/EUUOHED7SBOQU76OD2KT4GW7FL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EUUOHED7SBOQU76OD2KT4GW7FL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:EUUOHED7SBOQU76OD2KT4GW7FL","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":"47f6e108201e72e486d52212f2e79d4fc97cdd0dca068411fb57fd0b1dc9cb38","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"math.SG","submitted_at":"2007-10-16T15:58:40Z","title_canon_sha256":"94a0683e7980554b71efbbc1003019d0974ff268179dd91118e229ad223b4d80"},"schema_version":"1.0","source":{"id":"0710.3098","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0710.3098","created_at":"2026-05-18T03:39:17Z"},{"alias_kind":"arxiv_version","alias_value":"0710.3098v3","created_at":"2026-05-18T03:39:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0710.3098","created_at":"2026-05-18T03:39:17Z"},{"alias_kind":"pith_short_12","alias_value":"EUUOHED7SBOQ","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"EUUOHED7SBOQU76O","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"EUUOHED7","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:583b39d4e4827b35e6d15b3decc8bc6c1d764a1bfbcf3528dc3ab7ec9480f56b","target":"graph","created_at":"2026-05-18T03:39:17Z","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":"After a brief summary of the main properties of Poisson manifolds and Lie algebroids in general, we survey recent work on the modular classes of Poisson and twisted Poisson manifolds, of Lie algebroids with a Poisson or twisted Poisson structure, and of Poisson-Nijenhuis manifolds. A review of the spinor approach to the modular class concludes the paper.","authors_text":"Yvette Kosmann-Schwarzbach","cross_cats":["math-ph","math.MP"],"headline":"","license":"","primary_cat":"math.SG","submitted_at":"2007-10-16T15:58:40Z","title":"Poisson Manifolds, Lie Algebroids, Modular Classes: a Survey"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0710.3098","kind":"arxiv","version":3},"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":"sha256:751ae5dda881e355d03854e3fb131362550839e4831312885484ceb8ba8aa543","target":"record","created_at":"2026-05-18T03:39:17Z","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":"47f6e108201e72e486d52212f2e79d4fc97cdd0dca068411fb57fd0b1dc9cb38","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"math.SG","submitted_at":"2007-10-16T15:58:40Z","title_canon_sha256":"94a0683e7980554b71efbbc1003019d0974ff268179dd91118e229ad223b4d80"},"schema_version":"1.0","source":{"id":"0710.3098","kind":"arxiv","version":3}},"canonical_sha256":"2528e3907f905d0a7fce1e953e1adf2ada23c5b8d3a008f4f74f25fe802fb40f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2528e3907f905d0a7fce1e953e1adf2ada23c5b8d3a008f4f74f25fe802fb40f","first_computed_at":"2026-05-18T03:39:17.108206Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:39:17.108206Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1clhrM8v1g5T2xSE2byhFR4R9HghEXVNNopoz/N619g9apEoIDgmLm9EaE5Lq1K/u5PQDI0xOS7XlS3ty+7JCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:39:17.108749Z","signed_message":"canonical_sha256_bytes"},"source_id":"0710.3098","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:751ae5dda881e355d03854e3fb131362550839e4831312885484ceb8ba8aa543","sha256:583b39d4e4827b35e6d15b3decc8bc6c1d764a1bfbcf3528dc3ab7ec9480f56b"],"state_sha256":"17099d27cc64223f84149e6d56682a0600b842c7f8de3ca83b6fd6316fc93839"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n+GIqhz59F50bBsKnzcH/Plo0VVi/1Xeib5s5hrmEqzbpU2V5jmsc7njUQpEBUdbXceQ+la/kLJb+rXzDc79CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T13:33:12.859777Z","bundle_sha256":"5ea742be82c28a0f8209f25d47f6f8f4df7d6cb7c5be444e09a6f1a9bb5f7ce9"}}