{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:NOMSQIGFOD5PB5ETBDOIQ6DG7O","short_pith_number":"pith:NOMSQIGF","schema_version":"1.0","canonical_sha256":"6b992820c570faf0f49308dc887866fba3847ff212d716d4388fe9413f06dc0f","source":{"kind":"arxiv","id":"1704.04724","version":1},"attestation_state":"computed","paper":{"title":"The homology class of a Poisson transversal","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Ioan Marcut, Pedro Frejlich","submitted_at":"2017-04-16T05:07:27Z","abstract_excerpt":"This note is devoted to the study of the homology class of a compact Poisson transversal in a Poisson manifold. For specific classes of Poisson structures, such as unimodular Poisson structures and Poisson manifolds with closed leaves, we prove that all their compact Poisson transversals represent non-trivial homology classes, generalizing the symplectic case. We discuss several examples in which this property does not hold, as well as a weaker version of this property, which holds for log-symplectic structures. Finally, we extend our results to Dirac geometry."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1704.04724","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2017-04-16T05:07:27Z","cross_cats_sorted":[],"title_canon_sha256":"d6fcbbd72dd33f36b9af91c9aa517e53afa1d5d4966c7aab089c63eadb028877","abstract_canon_sha256":"39ecccd5f09701aef4be157f7ccbbb00078b2bdc4bb208e568c6a356ff608f0b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:17.877620Z","signature_b64":"AL+RtTC24UlINoeHWCNWU/N9qZHSBFxJ9JLNJcRrJCjjklV5Wpk/+ObWYadFwp97hlSZG3TCv0leOqKu+sBVDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6b992820c570faf0f49308dc887866fba3847ff212d716d4388fe9413f06dc0f","last_reissued_at":"2026-05-18T00:46:17.877203Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:17.877203Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The homology class of a Poisson transversal","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Ioan Marcut, Pedro Frejlich","submitted_at":"2017-04-16T05:07:27Z","abstract_excerpt":"This note is devoted to the study of the homology class of a compact Poisson transversal in a Poisson manifold. For specific classes of Poisson structures, such as unimodular Poisson structures and Poisson manifolds with closed leaves, we prove that all their compact Poisson transversals represent non-trivial homology classes, generalizing the symplectic case. We discuss several examples in which this property does not hold, as well as a weaker version of this property, which holds for log-symplectic structures. Finally, we extend our results to Dirac geometry."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.04724","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1704.04724","created_at":"2026-05-18T00:46:17.877268+00:00"},{"alias_kind":"arxiv_version","alias_value":"1704.04724v1","created_at":"2026-05-18T00:46:17.877268+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.04724","created_at":"2026-05-18T00:46:17.877268+00:00"},{"alias_kind":"pith_short_12","alias_value":"NOMSQIGFOD5P","created_at":"2026-05-18T12:31:34.259226+00:00"},{"alias_kind":"pith_short_16","alias_value":"NOMSQIGFOD5PB5ET","created_at":"2026-05-18T12:31:34.259226+00:00"},{"alias_kind":"pith_short_8","alias_value":"NOMSQIGF","created_at":"2026-05-18T12:31:34.259226+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/NOMSQIGFOD5PB5ETBDOIQ6DG7O","json":"https://pith.science/pith/NOMSQIGFOD5PB5ETBDOIQ6DG7O.json","graph_json":"https://pith.science/api/pith-number/NOMSQIGFOD5PB5ETBDOIQ6DG7O/graph.json","events_json":"https://pith.science/api/pith-number/NOMSQIGFOD5PB5ETBDOIQ6DG7O/events.json","paper":"https://pith.science/paper/NOMSQIGF"},"agent_actions":{"view_html":"https://pith.science/pith/NOMSQIGFOD5PB5ETBDOIQ6DG7O","download_json":"https://pith.science/pith/NOMSQIGFOD5PB5ETBDOIQ6DG7O.json","view_paper":"https://pith.science/paper/NOMSQIGF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1704.04724&json=true","fetch_graph":"https://pith.science/api/pith-number/NOMSQIGFOD5PB5ETBDOIQ6DG7O/graph.json","fetch_events":"https://pith.science/api/pith-number/NOMSQIGFOD5PB5ETBDOIQ6DG7O/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NOMSQIGFOD5PB5ETBDOIQ6DG7O/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NOMSQIGFOD5PB5ETBDOIQ6DG7O/action/storage_attestation","attest_author":"https://pith.science/pith/NOMSQIGFOD5PB5ETBDOIQ6DG7O/action/author_attestation","sign_citation":"https://pith.science/pith/NOMSQIGFOD5PB5ETBDOIQ6DG7O/action/citation_signature","submit_replication":"https://pith.science/pith/NOMSQIGFOD5PB5ETBDOIQ6DG7O/action/replication_record"}},"created_at":"2026-05-18T00:46:17.877268+00:00","updated_at":"2026-05-18T00:46:17.877268+00:00"}