{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:46TF7T35EBQEZ4XAUL55ADHEDZ","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":"9838aa2503194c557ff0673d8da813c19133b21a1013692c6181961e102df7b3","cross_cats_sorted":["math-ph","math.MP","math.SG"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.DG","submitted_at":"2014-06-27T08:21:36Z","title_canon_sha256":"fa018ae56caf136cad601695bda40a167f7238cf7bd666f2494dd092cc9c370c"},"schema_version":"1.0","source":{"id":"1406.7105","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.7105","created_at":"2026-05-18T01:04:06Z"},{"alias_kind":"arxiv_version","alias_value":"1406.7105v3","created_at":"2026-05-18T01:04:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.7105","created_at":"2026-05-18T01:04:06Z"},{"alias_kind":"pith_short_12","alias_value":"46TF7T35EBQE","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"46TF7T35EBQEZ4XA","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"46TF7T35","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:77f232428dc3123b3b887a196fb5520232ecb777d0a1782f258dd0d3039ceed5","target":"graph","created_at":"2026-05-18T01:04:06Z","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 show that every closed oriented smooth 4-manifold admits a complete singular Poisson structure in each homotopy class of maps to the 2-sphere. The rank of this structure is 2 outside a small singularity set, which consists of finitely many circles and isolated points. The Poisson bivector has rank 0 on the singularities, where we give its local form explicitly.","authors_text":"Luis C. Garc\\'ia-Naranjo, Pablo Su\\'arez-Serrato, Ram\\'on Vera","cross_cats":["math-ph","math.MP","math.SG"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.DG","submitted_at":"2014-06-27T08:21:36Z","title":"Poisson structures on smooth 4-manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.7105","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":"sha256:8f74f9b342b9fe376f520ccc2eaf761cdd1c4e5ab966122fc68fe60c40782169","target":"record","created_at":"2026-05-18T01:04:06Z","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":"9838aa2503194c557ff0673d8da813c19133b21a1013692c6181961e102df7b3","cross_cats_sorted":["math-ph","math.MP","math.SG"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.DG","submitted_at":"2014-06-27T08:21:36Z","title_canon_sha256":"fa018ae56caf136cad601695bda40a167f7238cf7bd666f2494dd092cc9c370c"},"schema_version":"1.0","source":{"id":"1406.7105","kind":"arxiv","version":3}},"canonical_sha256":"e7a65fcf7d20604cf2e0a2fbd00ce41e6bb8ee8c30603197dff0e2487fc5905a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e7a65fcf7d20604cf2e0a2fbd00ce41e6bb8ee8c30603197dff0e2487fc5905a","first_computed_at":"2026-05-18T01:04:06.005007Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:06.005007Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TO+2j1Tq0lx0s9UofNG1WNia44X26m98aUYElXmbpKdn+JSGECxRonQuv0l4Vt1psRr/12k5O6aiB4K3GJk1BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:06.005504Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.7105","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8f74f9b342b9fe376f520ccc2eaf761cdd1c4e5ab966122fc68fe60c40782169","sha256:77f232428dc3123b3b887a196fb5520232ecb777d0a1782f258dd0d3039ceed5"],"state_sha256":"fa614416a85e3089c9a16224fadce36e0da77e74c3e7cd421a23fa87610d1afb"}