{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:QFLJYRAKE4CLOMMNNAGXGTWDQG","short_pith_number":"pith:QFLJYRAK","schema_version":"1.0","canonical_sha256":"81569c440a2704b7318d680d734ec381ae1512967b7ed0e2a0816f2a333e9ce4","source":{"kind":"arxiv","id":"1302.5546","version":3},"attestation_state":"computed","paper":{"title":"Existence of critical points with semi-stiff boundary conditions for singular perturbation problems in simply connected planar domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Petru Mironescu, Xavier Lamy","submitted_at":"2013-02-22T10:50:35Z","abstract_excerpt":"Let $\\Omega$ be a smooth bounded simply connected domain in $\\mathbb{R}^2$. We investigate the existence of critical points of the energy $E_\\varepsilon (u)=1/2\\int_\\Omega |\\nabla u|^2+1/(4\\varepsilon^2)\\int_\\Omega (1-|u|^2)^2$, where the complex map $u$ has modulus one and prescribed degree $d$ on the boundary. Under suitable nondegeneracy assumptions on $\\Omega$, we prove existence of critical points for small $\\varepsilon$. More can be said when the prescribed degree equals one. First, we obtain existence of critical points in domains close to a disc. Next, we prove that critical points exi"},"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":"1302.5546","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-02-22T10:50:35Z","cross_cats_sorted":[],"title_canon_sha256":"82833192ab1edb5e873f667ee7339e6ab9e95ba03f4382daca80b91f5ece631e","abstract_canon_sha256":"51bee6dc2450cff18098ea122c1f7bd08e004f1a0c29b8f1fc873ba4ff0a2f9f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:08:47.301773Z","signature_b64":"4FJFfyNkv/oMR/dnqaVcfqACw3lvV6sdq6fyaJhVxDnS3/mwPt0D6t4kFXg7AS3YwzQrarI9LQBKuW5cEzjXAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"81569c440a2704b7318d680d734ec381ae1512967b7ed0e2a0816f2a333e9ce4","last_reissued_at":"2026-05-18T03:08:47.301207Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:08:47.301207Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Existence of critical points with semi-stiff boundary conditions for singular perturbation problems in simply connected planar domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Petru Mironescu, Xavier Lamy","submitted_at":"2013-02-22T10:50:35Z","abstract_excerpt":"Let $\\Omega$ be a smooth bounded simply connected domain in $\\mathbb{R}^2$. We investigate the existence of critical points of the energy $E_\\varepsilon (u)=1/2\\int_\\Omega |\\nabla u|^2+1/(4\\varepsilon^2)\\int_\\Omega (1-|u|^2)^2$, where the complex map $u$ has modulus one and prescribed degree $d$ on the boundary. Under suitable nondegeneracy assumptions on $\\Omega$, we prove existence of critical points for small $\\varepsilon$. More can be said when the prescribed degree equals one. First, we obtain existence of critical points in domains close to a disc. Next, we prove that critical points exi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.5546","kind":"arxiv","version":3},"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":"1302.5546","created_at":"2026-05-18T03:08:47.301304+00:00"},{"alias_kind":"arxiv_version","alias_value":"1302.5546v3","created_at":"2026-05-18T03:08:47.301304+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.5546","created_at":"2026-05-18T03:08:47.301304+00:00"},{"alias_kind":"pith_short_12","alias_value":"QFLJYRAKE4CL","created_at":"2026-05-18T12:27:57.521954+00:00"},{"alias_kind":"pith_short_16","alias_value":"QFLJYRAKE4CLOMMN","created_at":"2026-05-18T12:27:57.521954+00:00"},{"alias_kind":"pith_short_8","alias_value":"QFLJYRAK","created_at":"2026-05-18T12:27:57.521954+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/QFLJYRAKE4CLOMMNNAGXGTWDQG","json":"https://pith.science/pith/QFLJYRAKE4CLOMMNNAGXGTWDQG.json","graph_json":"https://pith.science/api/pith-number/QFLJYRAKE4CLOMMNNAGXGTWDQG/graph.json","events_json":"https://pith.science/api/pith-number/QFLJYRAKE4CLOMMNNAGXGTWDQG/events.json","paper":"https://pith.science/paper/QFLJYRAK"},"agent_actions":{"view_html":"https://pith.science/pith/QFLJYRAKE4CLOMMNNAGXGTWDQG","download_json":"https://pith.science/pith/QFLJYRAKE4CLOMMNNAGXGTWDQG.json","view_paper":"https://pith.science/paper/QFLJYRAK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1302.5546&json=true","fetch_graph":"https://pith.science/api/pith-number/QFLJYRAKE4CLOMMNNAGXGTWDQG/graph.json","fetch_events":"https://pith.science/api/pith-number/QFLJYRAKE4CLOMMNNAGXGTWDQG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QFLJYRAKE4CLOMMNNAGXGTWDQG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QFLJYRAKE4CLOMMNNAGXGTWDQG/action/storage_attestation","attest_author":"https://pith.science/pith/QFLJYRAKE4CLOMMNNAGXGTWDQG/action/author_attestation","sign_citation":"https://pith.science/pith/QFLJYRAKE4CLOMMNNAGXGTWDQG/action/citation_signature","submit_replication":"https://pith.science/pith/QFLJYRAKE4CLOMMNNAGXGTWDQG/action/replication_record"}},"created_at":"2026-05-18T03:08:47.301304+00:00","updated_at":"2026-05-18T03:08:47.301304+00:00"}