{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:XC5EOMD4AVEW7PU3U72HRBG3YX","short_pith_number":"pith:XC5EOMD4","schema_version":"1.0","canonical_sha256":"b8ba47307c05496fbe9ba7f47884dbc5e4df1da19211d36dc6565f6bed81b011","source":{"kind":"arxiv","id":"1305.4028","version":1},"attestation_state":"computed","paper":{"title":"A remark on the radial minimizer of the Ginzburg-Landau functional","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Barbara Brandolini, Francesco Chiacchio","submitted_at":"2013-05-17T09:30:39Z","abstract_excerpt":"Denote by $E_\\epsilon$ the Ginzburg-Landau functional in the plane and let $\\tilde u_\\varepsilon$ be the radial solution to the Euler equation associated to the problem $\\min \\left\\{E_\\varepsilon(u,B_1): \\>\\left. u\\right\\vert _{\\partial B_{1}}=(\\cos \\vartheta,\\sin \\vartheta)\\right\\}$. Let $\\Omega\\subset \\R^2$ be a smooth, bounded domain with the same area as $B_1$. Denoted by $$\\mathcal{K}=\\left\\{v=(v_1,v_2) \\in H^1(\\Omega;\\R^2):\\> \\int_\\Omega v_1\\,dx=\\int_\\Omega v_2\\,dx=0,\\> \\int_\\Omega |v|^2\\,dx\\ge \\int_{B_1} |\\tilde u_\\varepsilon|^2\\,dx\\right\\},$$\n  we prove $$ \\min_{v \\in \\mathcal{K}} E_\\v"},"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":"1305.4028","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-17T09:30:39Z","cross_cats_sorted":[],"title_canon_sha256":"0655d9ad5edde1d5b131e94b3f1d89680b3a298ff8db988abbb193535d11b6a7","abstract_canon_sha256":"610437c4cc4e06479f9da409aa5af47e04b21a0864ddd93d8553ac5eba4a1642"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:25:26.519492Z","signature_b64":"vMjKwvGdMVtLqa68IJ4KcU6/eL2ZNjU3xkGQoR+v03EluH0stH5Y363eOEoPBpcidsKHlEnx3WQYGKkDsNeZCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b8ba47307c05496fbe9ba7f47884dbc5e4df1da19211d36dc6565f6bed81b011","last_reissued_at":"2026-05-18T03:25:26.518997Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:25:26.518997Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A remark on the radial minimizer of the Ginzburg-Landau functional","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Barbara Brandolini, Francesco Chiacchio","submitted_at":"2013-05-17T09:30:39Z","abstract_excerpt":"Denote by $E_\\epsilon$ the Ginzburg-Landau functional in the plane and let $\\tilde u_\\varepsilon$ be the radial solution to the Euler equation associated to the problem $\\min \\left\\{E_\\varepsilon(u,B_1): \\>\\left. u\\right\\vert _{\\partial B_{1}}=(\\cos \\vartheta,\\sin \\vartheta)\\right\\}$. Let $\\Omega\\subset \\R^2$ be a smooth, bounded domain with the same area as $B_1$. Denoted by $$\\mathcal{K}=\\left\\{v=(v_1,v_2) \\in H^1(\\Omega;\\R^2):\\> \\int_\\Omega v_1\\,dx=\\int_\\Omega v_2\\,dx=0,\\> \\int_\\Omega |v|^2\\,dx\\ge \\int_{B_1} |\\tilde u_\\varepsilon|^2\\,dx\\right\\},$$\n  we prove $$ \\min_{v \\in \\mathcal{K}} E_\\v"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.4028","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":"1305.4028","created_at":"2026-05-18T03:25:26.519080+00:00"},{"alias_kind":"arxiv_version","alias_value":"1305.4028v1","created_at":"2026-05-18T03:25:26.519080+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.4028","created_at":"2026-05-18T03:25:26.519080+00:00"},{"alias_kind":"pith_short_12","alias_value":"XC5EOMD4AVEW","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_16","alias_value":"XC5EOMD4AVEW7PU3","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_8","alias_value":"XC5EOMD4","created_at":"2026-05-18T12:28:06.772260+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/XC5EOMD4AVEW7PU3U72HRBG3YX","json":"https://pith.science/pith/XC5EOMD4AVEW7PU3U72HRBG3YX.json","graph_json":"https://pith.science/api/pith-number/XC5EOMD4AVEW7PU3U72HRBG3YX/graph.json","events_json":"https://pith.science/api/pith-number/XC5EOMD4AVEW7PU3U72HRBG3YX/events.json","paper":"https://pith.science/paper/XC5EOMD4"},"agent_actions":{"view_html":"https://pith.science/pith/XC5EOMD4AVEW7PU3U72HRBG3YX","download_json":"https://pith.science/pith/XC5EOMD4AVEW7PU3U72HRBG3YX.json","view_paper":"https://pith.science/paper/XC5EOMD4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1305.4028&json=true","fetch_graph":"https://pith.science/api/pith-number/XC5EOMD4AVEW7PU3U72HRBG3YX/graph.json","fetch_events":"https://pith.science/api/pith-number/XC5EOMD4AVEW7PU3U72HRBG3YX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XC5EOMD4AVEW7PU3U72HRBG3YX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XC5EOMD4AVEW7PU3U72HRBG3YX/action/storage_attestation","attest_author":"https://pith.science/pith/XC5EOMD4AVEW7PU3U72HRBG3YX/action/author_attestation","sign_citation":"https://pith.science/pith/XC5EOMD4AVEW7PU3U72HRBG3YX/action/citation_signature","submit_replication":"https://pith.science/pith/XC5EOMD4AVEW7PU3U72HRBG3YX/action/replication_record"}},"created_at":"2026-05-18T03:25:26.519080+00:00","updated_at":"2026-05-18T03:25:26.519080+00:00"}