{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:QLOS32X5MZ65A6US3NRGIMVUQJ","short_pith_number":"pith:QLOS32X5","schema_version":"1.0","canonical_sha256":"82dd2deafd667dd07a92db626432b482744b846589486c5e93209b10e1ec73f2","source":{"kind":"arxiv","id":"1009.1175","version":2},"attestation_state":"computed","paper":{"title":"Codimension one symplectic foliations and regular Poisson structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DG","math.MP"],"primary_cat":"math.SG","authors_text":"Ana Rita Pires, Eva Miranda, Victor Guillemin","submitted_at":"2010-09-06T23:10:46Z","abstract_excerpt":"In this short note we give a complete characterization of a certain class of compact corank one Poisson manifolds, those equipped with a closed one-form defining the symplectic foliation and a closed two-form extending the symplectic form on each leaf. If such a manifold has a compact leaf, then all the leaves are compact, and furthermore the manifold is a mapping torus of a compact leaf. These manifolds and their regular Poisson structures admit an extension as the critical hypersurface of a Poisson b-manifold as we consider in a later paper."},"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":"1009.1175","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2010-09-06T23:10:46Z","cross_cats_sorted":["math-ph","math.DG","math.MP"],"title_canon_sha256":"48de287610c22951bcd2f2a97f1e30187667071665b2b1506853112ed064012b","abstract_canon_sha256":"c5a03a699cccd1d3ce6407f8c9728cb66999de9368e21da20acba28db0bf103a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:33:49.506966Z","signature_b64":"snWT/28Pvs4kG7BMpFPEhwnyNi0tstvJPPztIoHfFw2sjosSK/QStL2pi1FqZXa7CaUv07HDEL8fgP4A8RZiDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"82dd2deafd667dd07a92db626432b482744b846589486c5e93209b10e1ec73f2","last_reissued_at":"2026-05-18T01:33:49.506302Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:33:49.506302Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Codimension one symplectic foliations and regular Poisson structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DG","math.MP"],"primary_cat":"math.SG","authors_text":"Ana Rita Pires, Eva Miranda, Victor Guillemin","submitted_at":"2010-09-06T23:10:46Z","abstract_excerpt":"In this short note we give a complete characterization of a certain class of compact corank one Poisson manifolds, those equipped with a closed one-form defining the symplectic foliation and a closed two-form extending the symplectic form on each leaf. If such a manifold has a compact leaf, then all the leaves are compact, and furthermore the manifold is a mapping torus of a compact leaf. These manifolds and their regular Poisson structures admit an extension as the critical hypersurface of a Poisson b-manifold as we consider in a later paper."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.1175","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1009.1175","created_at":"2026-05-18T01:33:49.506422+00:00"},{"alias_kind":"arxiv_version","alias_value":"1009.1175v2","created_at":"2026-05-18T01:33:49.506422+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.1175","created_at":"2026-05-18T01:33:49.506422+00:00"},{"alias_kind":"pith_short_12","alias_value":"QLOS32X5MZ65","created_at":"2026-05-18T12:26:12.377268+00:00"},{"alias_kind":"pith_short_16","alias_value":"QLOS32X5MZ65A6US","created_at":"2026-05-18T12:26:12.377268+00:00"},{"alias_kind":"pith_short_8","alias_value":"QLOS32X5","created_at":"2026-05-18T12:26:12.377268+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/QLOS32X5MZ65A6US3NRGIMVUQJ","json":"https://pith.science/pith/QLOS32X5MZ65A6US3NRGIMVUQJ.json","graph_json":"https://pith.science/api/pith-number/QLOS32X5MZ65A6US3NRGIMVUQJ/graph.json","events_json":"https://pith.science/api/pith-number/QLOS32X5MZ65A6US3NRGIMVUQJ/events.json","paper":"https://pith.science/paper/QLOS32X5"},"agent_actions":{"view_html":"https://pith.science/pith/QLOS32X5MZ65A6US3NRGIMVUQJ","download_json":"https://pith.science/pith/QLOS32X5MZ65A6US3NRGIMVUQJ.json","view_paper":"https://pith.science/paper/QLOS32X5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1009.1175&json=true","fetch_graph":"https://pith.science/api/pith-number/QLOS32X5MZ65A6US3NRGIMVUQJ/graph.json","fetch_events":"https://pith.science/api/pith-number/QLOS32X5MZ65A6US3NRGIMVUQJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QLOS32X5MZ65A6US3NRGIMVUQJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QLOS32X5MZ65A6US3NRGIMVUQJ/action/storage_attestation","attest_author":"https://pith.science/pith/QLOS32X5MZ65A6US3NRGIMVUQJ/action/author_attestation","sign_citation":"https://pith.science/pith/QLOS32X5MZ65A6US3NRGIMVUQJ/action/citation_signature","submit_replication":"https://pith.science/pith/QLOS32X5MZ65A6US3NRGIMVUQJ/action/replication_record"}},"created_at":"2026-05-18T01:33:49.506422+00:00","updated_at":"2026-05-18T01:33:49.506422+00:00"}