{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ISWRTQX63SIDVYJN5S3ZXMGLQX","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"8d581aeaae965f7948a10751785991fa867f575b7caf649b7723e79268453be0","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-27T13:07:12Z","title_canon_sha256":"f67dce8c62d855de3747515b007f61e206117e04cc0ea6ded0406d6d6c2c5cf0"},"schema_version":"1.0","source":{"id":"1806.10453","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.10453","created_at":"2026-05-18T00:12:12Z"},{"alias_kind":"arxiv_version","alias_value":"1806.10453v1","created_at":"2026-05-18T00:12:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.10453","created_at":"2026-05-18T00:12:12Z"},{"alias_kind":"pith_short_12","alias_value":"ISWRTQX63SID","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"ISWRTQX63SIDVYJN","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"ISWRTQX6","created_at":"2026-05-18T12:32:31Z"}],"graph_snapshots":[{"event_id":"sha256:8056263162388345766af82a273427f6603000aeaa2b253aa0ea2e8770afd70a","target":"graph","created_at":"2026-05-18T00:12:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"For $\\epsilon>0$, we consider the Ginzburg-Landau functional for $\\mathbb R^N$-valued maps defined in the unit ball $B^N\\subset \\mathbb R^N$ with the vortex boundary data $x$ on $\\partial B^N$. In dimensions $N\\geq 7$, we prove that for every $\\epsilon>0$, there exists a unique global minimizer $u_\\epsilon$ of this problem; moreover, $u_\\epsilon$ is symmetric and of the form $u_\\epsilon(x)=f_\\epsilon(|x|)\\frac{x}{|x|}$ for $x\\in B^N$.","authors_text":"Arghir Zarnescu, Luc Nguyen, Radu Ignat, Valeriy Slastikov","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-27T13:07:12Z","title":"Uniqueness of degree-one Ginzburg-Landau vortex in the unit ball in dimensions $N \\geq 7$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.10453","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:a38d4c8cd0f8ecefe87abc0e7b454422804677281b6d828654bd7ae1c2a1546e","target":"record","created_at":"2026-05-18T00:12:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"8d581aeaae965f7948a10751785991fa867f575b7caf649b7723e79268453be0","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-27T13:07:12Z","title_canon_sha256":"f67dce8c62d855de3747515b007f61e206117e04cc0ea6ded0406d6d6c2c5cf0"},"schema_version":"1.0","source":{"id":"1806.10453","kind":"arxiv","version":1}},"canonical_sha256":"44ad19c2fedc903ae12decb79bb0cb85e1081ff15207507dbc1eab66267825be","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"44ad19c2fedc903ae12decb79bb0cb85e1081ff15207507dbc1eab66267825be","first_computed_at":"2026-05-18T00:12:12.384034Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:12.384034Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sly6ZVDImGup/7LNUrpoPkReyg/LaOk9jMnXPaX02XHPOUy1qUEwopryixzzbnHO9JzW3bWO/w56lFZ05ieyDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:12.384589Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.10453","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a38d4c8cd0f8ecefe87abc0e7b454422804677281b6d828654bd7ae1c2a1546e","sha256:8056263162388345766af82a273427f6603000aeaa2b253aa0ea2e8770afd70a"],"state_sha256":"a6d135fc8e95781f4f26172aa8977e4989b26cf1536b85c7ceaef5d9fd1bda59"}