{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:D7HJGBGWCAXNGVDVAEFJMFOJ7Z","short_pith_number":"pith:D7HJGBGW","schema_version":"1.0","canonical_sha256":"1fce9304d6102ed35475010a9615c9fe61c7735eaaccdb12013f4ca244d725eb","source":{"kind":"arxiv","id":"1208.3578","version":2},"attestation_state":"computed","paper":{"title":"Integrable vortex-type equations on the two-sphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Alexander D. Popov","submitted_at":"2012-08-17T11:47:45Z","abstract_excerpt":"We consider the Yang-Mills instanton equations on the four-dimensional manifold S^2xSigma, where Sigma is a compact Riemann surface of genus g>1 or its covering space H^2=SU(1,1)/U(1). Introducing a natural ansatz for the gauge potential, we reduce the instanton equations on S^2xSigma to vortex-type equations on the sphere S^2. It is shown that when the scalar curvature of the manifold S^2xSigma vanishes, the vortex-type equations are integrable, i.e. can be obtained as compatibility conditions of two linear equations (Lax pair) which are written down explicitly. Thus, the standard methods of "},"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":"1208.3578","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-08-17T11:47:45Z","cross_cats_sorted":[],"title_canon_sha256":"484a51ed0926076c92d9586fce3060d45bb0eca2cc3e7377e62e4bfbd0758cb6","abstract_canon_sha256":"6b0c335cc088381aeff0ee00de4fa98f81f4670b8a6293f494f0ca1c3cea8153"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:22:29.275600Z","signature_b64":"RIecjCDS9AnhpMpv36OTWY4Qn5TRvql0jUezSMqb0+dsPDOPVNvOMPnoLj57IH5i5KnkjPYV65jVrWoXqaIjCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1fce9304d6102ed35475010a9615c9fe61c7735eaaccdb12013f4ca244d725eb","last_reissued_at":"2026-05-18T03:22:29.274866Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:22:29.274866Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Integrable vortex-type equations on the two-sphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Alexander D. Popov","submitted_at":"2012-08-17T11:47:45Z","abstract_excerpt":"We consider the Yang-Mills instanton equations on the four-dimensional manifold S^2xSigma, where Sigma is a compact Riemann surface of genus g>1 or its covering space H^2=SU(1,1)/U(1). Introducing a natural ansatz for the gauge potential, we reduce the instanton equations on S^2xSigma to vortex-type equations on the sphere S^2. It is shown that when the scalar curvature of the manifold S^2xSigma vanishes, the vortex-type equations are integrable, i.e. can be obtained as compatibility conditions of two linear equations (Lax pair) which are written down explicitly. Thus, the standard methods of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.3578","kind":"arxiv","version":2},"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":"1208.3578","created_at":"2026-05-18T03:22:29.274977+00:00"},{"alias_kind":"arxiv_version","alias_value":"1208.3578v2","created_at":"2026-05-18T03:22:29.274977+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.3578","created_at":"2026-05-18T03:22:29.274977+00:00"},{"alias_kind":"pith_short_12","alias_value":"D7HJGBGWCAXN","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_16","alias_value":"D7HJGBGWCAXNGVDV","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_8","alias_value":"D7HJGBGW","created_at":"2026-05-18T12:27:01.376967+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/D7HJGBGWCAXNGVDVAEFJMFOJ7Z","json":"https://pith.science/pith/D7HJGBGWCAXNGVDVAEFJMFOJ7Z.json","graph_json":"https://pith.science/api/pith-number/D7HJGBGWCAXNGVDVAEFJMFOJ7Z/graph.json","events_json":"https://pith.science/api/pith-number/D7HJGBGWCAXNGVDVAEFJMFOJ7Z/events.json","paper":"https://pith.science/paper/D7HJGBGW"},"agent_actions":{"view_html":"https://pith.science/pith/D7HJGBGWCAXNGVDVAEFJMFOJ7Z","download_json":"https://pith.science/pith/D7HJGBGWCAXNGVDVAEFJMFOJ7Z.json","view_paper":"https://pith.science/paper/D7HJGBGW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1208.3578&json=true","fetch_graph":"https://pith.science/api/pith-number/D7HJGBGWCAXNGVDVAEFJMFOJ7Z/graph.json","fetch_events":"https://pith.science/api/pith-number/D7HJGBGWCAXNGVDVAEFJMFOJ7Z/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/D7HJGBGWCAXNGVDVAEFJMFOJ7Z/action/timestamp_anchor","attest_storage":"https://pith.science/pith/D7HJGBGWCAXNGVDVAEFJMFOJ7Z/action/storage_attestation","attest_author":"https://pith.science/pith/D7HJGBGWCAXNGVDVAEFJMFOJ7Z/action/author_attestation","sign_citation":"https://pith.science/pith/D7HJGBGWCAXNGVDVAEFJMFOJ7Z/action/citation_signature","submit_replication":"https://pith.science/pith/D7HJGBGWCAXNGVDVAEFJMFOJ7Z/action/replication_record"}},"created_at":"2026-05-18T03:22:29.274977+00:00","updated_at":"2026-05-18T03:22:29.274977+00:00"}