{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:BBNINEASYYRSS5DQ4G5XGOPZH7","short_pith_number":"pith:BBNINEAS","schema_version":"1.0","canonical_sha256":"085a869012c623297470e1bb7339f93fd48f03c7bf8492ca40392ab71cadf0a3","source":{"kind":"arxiv","id":"1208.4204","version":1},"attestation_state":"computed","paper":{"title":"Relative Equilibria in the Four-Vortex Problem with Two Pairs of Equal Vorticities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.flu-dyn"],"primary_cat":"math.CA","authors_text":"Gareth E. Roberts, Manuele Santoprete, Marshall Hampton","submitted_at":"2012-08-21T07:34:53Z","abstract_excerpt":"We examine in detail the relative equilibria in the four-vortex problem where two pairs of vortices have equal strength, that is, \\Gamma_1 = \\Gamma_2 = 1 and \\Gamma_3 = \\Gamma_4 = m where m is a nonzero real parameter. One main result is that for m > 0, the convex configurations all contain a line of symmetry, forming a rhombus or an isosceles trapezoid. The rhombus solutions exist for all m but the isosceles trapezoid case exists only when m is positive. In fact, there exist asymmetric convex configurations when m < 0. In contrast to the Newtonian four-body problem with two equal pairs of mas"},"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":"1208.4204","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-08-21T07:34:53Z","cross_cats_sorted":["physics.flu-dyn"],"title_canon_sha256":"58a29cb8d222f2cffdec1cc9ef8cbf949d3deb7884f9b2fa3648bec95bfdd650","abstract_canon_sha256":"14989fa86c521c7b067d4acb9020d30a2d799a3741b81a9905a46f2a614b1573"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:30.829426Z","signature_b64":"9sq/IhGuHJWls0izzFU38DpwCo+DYCoojAlPP0TubF+OvML3J845MtaVHVuACU2VbikSlmGeg9L3deOmhHoUBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"085a869012c623297470e1bb7339f93fd48f03c7bf8492ca40392ab71cadf0a3","last_reissued_at":"2026-05-18T00:45:30.829028Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:30.829028Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Relative Equilibria in the Four-Vortex Problem with Two Pairs of Equal Vorticities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.flu-dyn"],"primary_cat":"math.CA","authors_text":"Gareth E. Roberts, Manuele Santoprete, Marshall Hampton","submitted_at":"2012-08-21T07:34:53Z","abstract_excerpt":"We examine in detail the relative equilibria in the four-vortex problem where two pairs of vortices have equal strength, that is, \\Gamma_1 = \\Gamma_2 = 1 and \\Gamma_3 = \\Gamma_4 = m where m is a nonzero real parameter. One main result is that for m > 0, the convex configurations all contain a line of symmetry, forming a rhombus or an isosceles trapezoid. The rhombus solutions exist for all m but the isosceles trapezoid case exists only when m is positive. In fact, there exist asymmetric convex configurations when m < 0. In contrast to the Newtonian four-body problem with two equal pairs of mas"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.4204","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":"1208.4204","created_at":"2026-05-18T00:45:30.829085+00:00"},{"alias_kind":"arxiv_version","alias_value":"1208.4204v1","created_at":"2026-05-18T00:45:30.829085+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.4204","created_at":"2026-05-18T00:45:30.829085+00:00"},{"alias_kind":"pith_short_12","alias_value":"BBNINEASYYRS","created_at":"2026-05-18T12:26:58.693483+00:00"},{"alias_kind":"pith_short_16","alias_value":"BBNINEASYYRSS5DQ","created_at":"2026-05-18T12:26:58.693483+00:00"},{"alias_kind":"pith_short_8","alias_value":"BBNINEAS","created_at":"2026-05-18T12:26:58.693483+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/BBNINEASYYRSS5DQ4G5XGOPZH7","json":"https://pith.science/pith/BBNINEASYYRSS5DQ4G5XGOPZH7.json","graph_json":"https://pith.science/api/pith-number/BBNINEASYYRSS5DQ4G5XGOPZH7/graph.json","events_json":"https://pith.science/api/pith-number/BBNINEASYYRSS5DQ4G5XGOPZH7/events.json","paper":"https://pith.science/paper/BBNINEAS"},"agent_actions":{"view_html":"https://pith.science/pith/BBNINEASYYRSS5DQ4G5XGOPZH7","download_json":"https://pith.science/pith/BBNINEASYYRSS5DQ4G5XGOPZH7.json","view_paper":"https://pith.science/paper/BBNINEAS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1208.4204&json=true","fetch_graph":"https://pith.science/api/pith-number/BBNINEASYYRSS5DQ4G5XGOPZH7/graph.json","fetch_events":"https://pith.science/api/pith-number/BBNINEASYYRSS5DQ4G5XGOPZH7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BBNINEASYYRSS5DQ4G5XGOPZH7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BBNINEASYYRSS5DQ4G5XGOPZH7/action/storage_attestation","attest_author":"https://pith.science/pith/BBNINEASYYRSS5DQ4G5XGOPZH7/action/author_attestation","sign_citation":"https://pith.science/pith/BBNINEASYYRSS5DQ4G5XGOPZH7/action/citation_signature","submit_replication":"https://pith.science/pith/BBNINEASYYRSS5DQ4G5XGOPZH7/action/replication_record"}},"created_at":"2026-05-18T00:45:30.829085+00:00","updated_at":"2026-05-18T00:45:30.829085+00:00"}