{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:UFZX5V6YPCXSR2DRSPIP264FLG","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":"a47a6b99eea56b3a16435735ea02126d1560393f9f10861ff45f8b63e273c310","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-10T18:06:40Z","title_canon_sha256":"2c95143395d0503388b96faec093b595d45728e6a5866a40c1c0f583106866f2"},"schema_version":"1.0","source":{"id":"1601.02242","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.02242","created_at":"2026-05-18T00:26:37Z"},{"alias_kind":"arxiv_version","alias_value":"1601.02242v2","created_at":"2026-05-18T00:26:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.02242","created_at":"2026-05-18T00:26:37Z"},{"alias_kind":"pith_short_12","alias_value":"UFZX5V6YPCXS","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"UFZX5V6YPCXSR2DR","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"UFZX5V6Y","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:44d23cf557e79c79621a5c8080bdbb97a3805e0368c609fb43e62bdfe5f8c00c","target":"graph","created_at":"2026-05-18T00:26:37Z","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":"In this paper, we study the existence of corotating and counter-rotating pairs of simply connected patches for Euler equations and the $(\\hbox{SQG})_\\alpha$ equations with $\\alpha\\in (0,1).$ From the numerical experiments implemented for Euler equations in \\cite{DZ, humbert, S-Z} it is conjectured the existence of a curve of steady vortex pairs passing through the point vortex pairs. There are some analytical proofs based on variational principle \\cite{keady, Tur}, however they do not give enough information about the pairs such as the uniqueness or the topological structure of each single vor","authors_text":"Joan Mateu, Taoufik Hmidi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-10T18:06:40Z","title":"Existence of corotating and counter-rotating vortex pairs for active scalar equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.02242","kind":"arxiv","version":2},"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":"sha256:081a57c062af3869ce76f9cf7f3531bab4fa12d67f36d9434b156088fd6674ed","target":"record","created_at":"2026-05-18T00:26:37Z","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":"a47a6b99eea56b3a16435735ea02126d1560393f9f10861ff45f8b63e273c310","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-10T18:06:40Z","title_canon_sha256":"2c95143395d0503388b96faec093b595d45728e6a5866a40c1c0f583106866f2"},"schema_version":"1.0","source":{"id":"1601.02242","kind":"arxiv","version":2}},"canonical_sha256":"a1737ed7d878af28e87193d0fd7b85599ea79f1f66f1a899c76bdbe68b365edd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a1737ed7d878af28e87193d0fd7b85599ea79f1f66f1a899c76bdbe68b365edd","first_computed_at":"2026-05-18T00:26:37.984728Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:26:37.984728Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ta43fZT2E6gjZZVj2LSpK5vd1h6wJMT5Ey3A7z/ABPhodMD5kMWS7nVUVYgWufZRHuJ/LbCxj/STEFlgo6uOAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:26:37.985284Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.02242","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:081a57c062af3869ce76f9cf7f3531bab4fa12d67f36d9434b156088fd6674ed","sha256:44d23cf557e79c79621a5c8080bdbb97a3805e0368c609fb43e62bdfe5f8c00c"],"state_sha256":"7324b286c92d9848899926cac13e405f44e6d10512c132e7c36a900809f39f32"}