{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:77TSFPQBNEUXWGP2OVGWHUQVJC","short_pith_number":"pith:77TSFPQB","schema_version":"1.0","canonical_sha256":"ffe722be0169297b19fa754d63d21548817ccfe5f8d8da1b76f631a12420f905","source":{"kind":"arxiv","id":"1211.0217","version":1},"attestation_state":"computed","paper":{"title":"U(1)-vortices and quantum Kirwan map","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SG","authors_text":"Guangbo Xu","submitted_at":"2012-11-01T16:25:49Z","abstract_excerpt":"We study the symplectic vortex equation over the complex plane, for the target space ${\\mathbb C}^N$ ($N\\geq 2$) with diagonal U(1)-action. We classify all solutions with finite energy and identify their moduli spaces, which generalizes Taubes' result for N=1. We also studied their compactifications and use them to compute the associated quantum Kirwan maps $\\kappa_Q: H^*_{U(1)}({\\mathbb C}^N) \\to QH^*({\\mathbb P}^{N-1})$."},"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":"1211.0217","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2012-11-01T16:25:49Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"cd5f31c1388b059780a568296be5a69b0638493ed82d397c683046fceb07f845","abstract_canon_sha256":"f1fb108bb740732e4207ed05ba60aacb3834bea0d98f9d939a3eec7f2d53b215"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:16.959732Z","signature_b64":"qMPAm8zX/ZmQwL6pI13me6b7fgH7yzYuJGNvpov4SJFAcvgABmI2WSUbneAOafR/MyHD3U1b3RTYwnFO7MsZDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ffe722be0169297b19fa754d63d21548817ccfe5f8d8da1b76f631a12420f905","last_reissued_at":"2026-05-18T00:26:16.959248Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:16.959248Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"U(1)-vortices and quantum Kirwan map","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SG","authors_text":"Guangbo Xu","submitted_at":"2012-11-01T16:25:49Z","abstract_excerpt":"We study the symplectic vortex equation over the complex plane, for the target space ${\\mathbb C}^N$ ($N\\geq 2$) with diagonal U(1)-action. We classify all solutions with finite energy and identify their moduli spaces, which generalizes Taubes' result for N=1. We also studied their compactifications and use them to compute the associated quantum Kirwan maps $\\kappa_Q: H^*_{U(1)}({\\mathbb C}^N) \\to QH^*({\\mathbb P}^{N-1})$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.0217","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":"1211.0217","created_at":"2026-05-18T00:26:16.959331+00:00"},{"alias_kind":"arxiv_version","alias_value":"1211.0217v1","created_at":"2026-05-18T00:26:16.959331+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.0217","created_at":"2026-05-18T00:26:16.959331+00:00"},{"alias_kind":"pith_short_12","alias_value":"77TSFPQBNEUX","created_at":"2026-05-18T12:26:56.085431+00:00"},{"alias_kind":"pith_short_16","alias_value":"77TSFPQBNEUXWGP2","created_at":"2026-05-18T12:26:56.085431+00:00"},{"alias_kind":"pith_short_8","alias_value":"77TSFPQB","created_at":"2026-05-18T12:26:56.085431+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/77TSFPQBNEUXWGP2OVGWHUQVJC","json":"https://pith.science/pith/77TSFPQBNEUXWGP2OVGWHUQVJC.json","graph_json":"https://pith.science/api/pith-number/77TSFPQBNEUXWGP2OVGWHUQVJC/graph.json","events_json":"https://pith.science/api/pith-number/77TSFPQBNEUXWGP2OVGWHUQVJC/events.json","paper":"https://pith.science/paper/77TSFPQB"},"agent_actions":{"view_html":"https://pith.science/pith/77TSFPQBNEUXWGP2OVGWHUQVJC","download_json":"https://pith.science/pith/77TSFPQBNEUXWGP2OVGWHUQVJC.json","view_paper":"https://pith.science/paper/77TSFPQB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1211.0217&json=true","fetch_graph":"https://pith.science/api/pith-number/77TSFPQBNEUXWGP2OVGWHUQVJC/graph.json","fetch_events":"https://pith.science/api/pith-number/77TSFPQBNEUXWGP2OVGWHUQVJC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/77TSFPQBNEUXWGP2OVGWHUQVJC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/77TSFPQBNEUXWGP2OVGWHUQVJC/action/storage_attestation","attest_author":"https://pith.science/pith/77TSFPQBNEUXWGP2OVGWHUQVJC/action/author_attestation","sign_citation":"https://pith.science/pith/77TSFPQBNEUXWGP2OVGWHUQVJC/action/citation_signature","submit_replication":"https://pith.science/pith/77TSFPQBNEUXWGP2OVGWHUQVJC/action/replication_record"}},"created_at":"2026-05-18T00:26:16.959331+00:00","updated_at":"2026-05-18T00:26:16.959331+00:00"}