{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:U4VAQVVSQHRYHA7UQGGMYCDX3Q","short_pith_number":"pith:U4VAQVVS","schema_version":"1.0","canonical_sha256":"a72a0856b281e38383f4818ccc0877dc32089dbdc4cb8d589ed1536c43d72b8e","source":{"kind":"arxiv","id":"1805.05310","version":1},"attestation_state":"computed","paper":{"title":"Real Analytic Vector Fields with First Integral and Separatrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Fernando Sanz S\\'anchez, Rog\\'erio Mol","submitted_at":"2018-05-14T17:47:07Z","abstract_excerpt":"We prove that a germ of analytic vector field at $(\\mathbb{R}^3,0)$ that possesses a non-constant analytic first integral has a real formal separatrix. We provide an example which shows that such a vector field does not necessarily have a real analytic separatrix."},"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":"1805.05310","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-05-14T17:47:07Z","cross_cats_sorted":[],"title_canon_sha256":"fa6527092e3210cbd802a4e5ed6a2b00aed9c242ba7be6f01820125291f08c4e","abstract_canon_sha256":"59aaf7a52e82236056f5357e8b9184ae762390dba18712341e8efc183649f0c6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:03.484613Z","signature_b64":"zpBTtburzMzz0E4XHbjeVkFrpXaloQnDhxeFqAe9h1ecs2reN4GYLhvcy+dJRsx5nyBdsqJfe6F8xt0qZePbCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a72a0856b281e38383f4818ccc0877dc32089dbdc4cb8d589ed1536c43d72b8e","last_reissued_at":"2026-05-18T00:16:03.484238Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:03.484238Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Real Analytic Vector Fields with First Integral and Separatrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Fernando Sanz S\\'anchez, Rog\\'erio Mol","submitted_at":"2018-05-14T17:47:07Z","abstract_excerpt":"We prove that a germ of analytic vector field at $(\\mathbb{R}^3,0)$ that possesses a non-constant analytic first integral has a real formal separatrix. We provide an example which shows that such a vector field does not necessarily have a real analytic separatrix."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.05310","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":"1805.05310","created_at":"2026-05-18T00:16:03.484297+00:00"},{"alias_kind":"arxiv_version","alias_value":"1805.05310v1","created_at":"2026-05-18T00:16:03.484297+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.05310","created_at":"2026-05-18T00:16:03.484297+00:00"},{"alias_kind":"pith_short_12","alias_value":"U4VAQVVSQHRY","created_at":"2026-05-18T12:32:56.356000+00:00"},{"alias_kind":"pith_short_16","alias_value":"U4VAQVVSQHRYHA7U","created_at":"2026-05-18T12:32:56.356000+00:00"},{"alias_kind":"pith_short_8","alias_value":"U4VAQVVS","created_at":"2026-05-18T12:32:56.356000+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/U4VAQVVSQHRYHA7UQGGMYCDX3Q","json":"https://pith.science/pith/U4VAQVVSQHRYHA7UQGGMYCDX3Q.json","graph_json":"https://pith.science/api/pith-number/U4VAQVVSQHRYHA7UQGGMYCDX3Q/graph.json","events_json":"https://pith.science/api/pith-number/U4VAQVVSQHRYHA7UQGGMYCDX3Q/events.json","paper":"https://pith.science/paper/U4VAQVVS"},"agent_actions":{"view_html":"https://pith.science/pith/U4VAQVVSQHRYHA7UQGGMYCDX3Q","download_json":"https://pith.science/pith/U4VAQVVSQHRYHA7UQGGMYCDX3Q.json","view_paper":"https://pith.science/paper/U4VAQVVS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1805.05310&json=true","fetch_graph":"https://pith.science/api/pith-number/U4VAQVVSQHRYHA7UQGGMYCDX3Q/graph.json","fetch_events":"https://pith.science/api/pith-number/U4VAQVVSQHRYHA7UQGGMYCDX3Q/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/U4VAQVVSQHRYHA7UQGGMYCDX3Q/action/timestamp_anchor","attest_storage":"https://pith.science/pith/U4VAQVVSQHRYHA7UQGGMYCDX3Q/action/storage_attestation","attest_author":"https://pith.science/pith/U4VAQVVSQHRYHA7UQGGMYCDX3Q/action/author_attestation","sign_citation":"https://pith.science/pith/U4VAQVVSQHRYHA7UQGGMYCDX3Q/action/citation_signature","submit_replication":"https://pith.science/pith/U4VAQVVSQHRYHA7UQGGMYCDX3Q/action/replication_record"}},"created_at":"2026-05-18T00:16:03.484297+00:00","updated_at":"2026-05-18T00:16:03.484297+00:00"}