{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:7ZLH2OOGVNJESPTG2GAD7623NZ","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":"d6b3c8e7cec3b7c34525589cf619b57f582565327abadb5fe369b49e22bafc91","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-06-26T16:58:53Z","title_canon_sha256":"29b343945d6baa0ff98db5adc5fd67e232c9518edd185c3d890662f610a19b7b"},"schema_version":"1.0","source":{"id":"1406.6944","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.6944","created_at":"2026-05-18T02:48:55Z"},{"alias_kind":"arxiv_version","alias_value":"1406.6944v1","created_at":"2026-05-18T02:48:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.6944","created_at":"2026-05-18T02:48:55Z"},{"alias_kind":"pith_short_12","alias_value":"7ZLH2OOGVNJE","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"7ZLH2OOGVNJESPTG","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"7ZLH2OOG","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:c8852fc6dc8d9c7cc561a6cf7c810f85886a3d63d9e1b5bc58955f09a3c7bd8d","target":"graph","created_at":"2026-05-18T02:48:55Z","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 prove a Poincar\\'e-Bendixson theorem describing the asymptotic behavior of geodesics for a meromorphic connection on a compact Riemann surface. We shall also briefly discuss the case of non-compact Riemann surfaces, and study in detail the geodesics for a holomorphic connection on a complex torus.","authors_text":"Fabrizio Bianchi, Marco Abate","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-06-26T16:58:53Z","title":"A Poincar\\'e-Bendixson theorem for meromorphic connections on Riemann surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.6944","kind":"arxiv","version":1},"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:eb0c5be2204d569349c691526583a135adfae436e3b541c32c50fb74c847f25f","target":"record","created_at":"2026-05-18T02:48:55Z","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":"d6b3c8e7cec3b7c34525589cf619b57f582565327abadb5fe369b49e22bafc91","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-06-26T16:58:53Z","title_canon_sha256":"29b343945d6baa0ff98db5adc5fd67e232c9518edd185c3d890662f610a19b7b"},"schema_version":"1.0","source":{"id":"1406.6944","kind":"arxiv","version":1}},"canonical_sha256":"fe567d39c6ab52493e66d1803ffb5b6e7a41a17ccbd18567b409aebaf14e3b17","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fe567d39c6ab52493e66d1803ffb5b6e7a41a17ccbd18567b409aebaf14e3b17","first_computed_at":"2026-05-18T02:48:55.439489Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:48:55.439489Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ECfJgQ7UXjn6baewb4jnlLQlDwjFZ+p6JlSFwt54EkDeHNcMfqY57qA0Px06KI1qxg4iyKlLIC4yU7geqZDUAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:48:55.440022Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.6944","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eb0c5be2204d569349c691526583a135adfae436e3b541c32c50fb74c847f25f","sha256:c8852fc6dc8d9c7cc561a6cf7c810f85886a3d63d9e1b5bc58955f09a3c7bd8d"],"state_sha256":"7ee797b3fc410c7f43ea29fbff4097489e818ec220f029a8e78460e2bcf88501"}