{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:AO3EHTFUTER6ICEUGJEAZ4OEU5","short_pith_number":"pith:AO3EHTFU","canonical_record":{"source":{"id":"1103.4305","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-03-22T16:48:41Z","cross_cats_sorted":["math.SG"],"title_canon_sha256":"61788e0c3992bcfdaee71c1ff0eb6798ce700d8ec69ba5469a34c4cb0a20ba9b","abstract_canon_sha256":"96bf8784f9e5c30baa5ea11f09b14dff48b83ab184851cbb54f0b7f5c54c25d4"},"schema_version":"1.0"},"canonical_sha256":"03b643ccb49923e4089432480cf1c4a75ad7c01509312ea44bc356d7e72adc3d","source":{"kind":"arxiv","id":"1103.4305","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.4305","created_at":"2026-05-18T03:49:32Z"},{"alias_kind":"arxiv_version","alias_value":"1103.4305v2","created_at":"2026-05-18T03:49:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.4305","created_at":"2026-05-18T03:49:32Z"},{"alias_kind":"pith_short_12","alias_value":"AO3EHTFUTER6","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"AO3EHTFUTER6ICEU","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"AO3EHTFU","created_at":"2026-05-18T12:26:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:AO3EHTFUTER6ICEUGJEAZ4OEU5","target":"record","payload":{"canonical_record":{"source":{"id":"1103.4305","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-03-22T16:48:41Z","cross_cats_sorted":["math.SG"],"title_canon_sha256":"61788e0c3992bcfdaee71c1ff0eb6798ce700d8ec69ba5469a34c4cb0a20ba9b","abstract_canon_sha256":"96bf8784f9e5c30baa5ea11f09b14dff48b83ab184851cbb54f0b7f5c54c25d4"},"schema_version":"1.0"},"canonical_sha256":"03b643ccb49923e4089432480cf1c4a75ad7c01509312ea44bc356d7e72adc3d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:49:32.997056Z","signature_b64":"bX+INz5ewpTN/rkVP1lisss06ZZKc5O5EST79V3z+vvD8kpVjOg/iqrmXMpsoOgw8kuZUOUSl3Ba5Mj+YFq3AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"03b643ccb49923e4089432480cf1c4a75ad7c01509312ea44bc356d7e72adc3d","last_reissued_at":"2026-05-18T03:49:32.996353Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:49:32.996353Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1103.4305","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":"2026-05-18T03:49:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ls2xtQs/zj38p4BcXzW9mbCHio/M5bQnKXWXH1s+BJ6OTsgY71TXBEaT+KX2fgUk8e4iez8C3Cu0Beko+xnKDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T10:25:05.664810Z"},"content_sha256":"439dba17158f27ff08b461780a8e1558568b1bef042486d88d7c4b08759b0c26","schema_version":"1.0","event_id":"sha256:439dba17158f27ff08b461780a8e1558568b1bef042486d88d7c4b08759b0c26"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:AO3EHTFUTER6ICEUGJEAZ4OEU5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The modular class of a Poisson map","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.DG","authors_text":"Raquel Caseiro, Rui Loja Fernandes","submitted_at":"2011-03-22T16:48:41Z","abstract_excerpt":"We introduce the modular class of a Poisson map. We look at several examples and we use the modular classes of Poisson maps to study the behavior of the modular class of a Poisson manifold under different kinds of reduction. We also discuss their symplectic groupoid version, which lives in groupoid cohomology."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.4305","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":"2026-05-18T03:49:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y09Gri7Onu5RJQykzXEPQWjHsx60ouW9crCLTHOibQ6cIFrm8v6OZ5H5zndNU4wAYm3XKpDzb+Tqbw+3o0hiDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T10:25:05.665155Z"},"content_sha256":"6d5c3fdbda8a63c93ddf17d85bb4f4cb2622c42f79bb3a900578cda479424d00","schema_version":"1.0","event_id":"sha256:6d5c3fdbda8a63c93ddf17d85bb4f4cb2622c42f79bb3a900578cda479424d00"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AO3EHTFUTER6ICEUGJEAZ4OEU5/bundle.json","state_url":"https://pith.science/pith/AO3EHTFUTER6ICEUGJEAZ4OEU5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AO3EHTFUTER6ICEUGJEAZ4OEU5/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":"2026-07-03T10:25:05Z","links":{"resolver":"https://pith.science/pith/AO3EHTFUTER6ICEUGJEAZ4OEU5","bundle":"https://pith.science/pith/AO3EHTFUTER6ICEUGJEAZ4OEU5/bundle.json","state":"https://pith.science/pith/AO3EHTFUTER6ICEUGJEAZ4OEU5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AO3EHTFUTER6ICEUGJEAZ4OEU5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:AO3EHTFUTER6ICEUGJEAZ4OEU5","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":"96bf8784f9e5c30baa5ea11f09b14dff48b83ab184851cbb54f0b7f5c54c25d4","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-03-22T16:48:41Z","title_canon_sha256":"61788e0c3992bcfdaee71c1ff0eb6798ce700d8ec69ba5469a34c4cb0a20ba9b"},"schema_version":"1.0","source":{"id":"1103.4305","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.4305","created_at":"2026-05-18T03:49:32Z"},{"alias_kind":"arxiv_version","alias_value":"1103.4305v2","created_at":"2026-05-18T03:49:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.4305","created_at":"2026-05-18T03:49:32Z"},{"alias_kind":"pith_short_12","alias_value":"AO3EHTFUTER6","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"AO3EHTFUTER6ICEU","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"AO3EHTFU","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:6d5c3fdbda8a63c93ddf17d85bb4f4cb2622c42f79bb3a900578cda479424d00","target":"graph","created_at":"2026-05-18T03:49:32Z","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 introduce the modular class of a Poisson map. We look at several examples and we use the modular classes of Poisson maps to study the behavior of the modular class of a Poisson manifold under different kinds of reduction. We also discuss their symplectic groupoid version, which lives in groupoid cohomology.","authors_text":"Raquel Caseiro, Rui Loja Fernandes","cross_cats":["math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-03-22T16:48:41Z","title":"The modular class of a Poisson map"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.4305","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":"sha256:439dba17158f27ff08b461780a8e1558568b1bef042486d88d7c4b08759b0c26","target":"record","created_at":"2026-05-18T03:49:32Z","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":"96bf8784f9e5c30baa5ea11f09b14dff48b83ab184851cbb54f0b7f5c54c25d4","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-03-22T16:48:41Z","title_canon_sha256":"61788e0c3992bcfdaee71c1ff0eb6798ce700d8ec69ba5469a34c4cb0a20ba9b"},"schema_version":"1.0","source":{"id":"1103.4305","kind":"arxiv","version":2}},"canonical_sha256":"03b643ccb49923e4089432480cf1c4a75ad7c01509312ea44bc356d7e72adc3d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"03b643ccb49923e4089432480cf1c4a75ad7c01509312ea44bc356d7e72adc3d","first_computed_at":"2026-05-18T03:49:32.996353Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:49:32.996353Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bX+INz5ewpTN/rkVP1lisss06ZZKc5O5EST79V3z+vvD8kpVjOg/iqrmXMpsoOgw8kuZUOUSl3Ba5Mj+YFq3AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:49:32.997056Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.4305","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:439dba17158f27ff08b461780a8e1558568b1bef042486d88d7c4b08759b0c26","sha256:6d5c3fdbda8a63c93ddf17d85bb4f4cb2622c42f79bb3a900578cda479424d00"],"state_sha256":"b5599da606878c67ad5d1b6b6d01d066db9f483552ced96650558b9754dcd0b8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8NnZ1boZm79ZDJ4QbF8Y3YKIJF2UpcvgXvC5OKWdhLFbvTrCAcffAQSn2aeu6BGIhmJD5ix8l76CxgKIA/uBBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T10:25:05.667179Z","bundle_sha256":"e53a08cc6e067068efce06e1a8ffe1836b460443c049c717bc6bc107480a1a62"}}