{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:ZENALELIEDKFHWTRX3T4CQKZA6","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":"dfbb1b823c26c6c930c004673a415050354ed0a5491032ddd3a848f2855e95f1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-03-20T17:48:31Z","title_canon_sha256":"dc8b0207319dac913e470cfeb6d33b2df3e7b8863d0847b95bceaf486e70f61e"},"schema_version":"1.0","source":{"id":"1103.3867","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.3867","created_at":"2026-05-18T04:26:22Z"},{"alias_kind":"arxiv_version","alias_value":"1103.3867v1","created_at":"2026-05-18T04:26:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.3867","created_at":"2026-05-18T04:26:22Z"},{"alias_kind":"pith_short_12","alias_value":"ZENALELIEDKF","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"ZENALELIEDKFHWTR","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"ZENALELI","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:197dfd684b3578ee462b46616acdaaaec02b919abfd14d274befd77642fbb628","target":"graph","created_at":"2026-05-18T04:26:22Z","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":"We consider a Ginzburg-Landau type energy with a piecewise constant pinning term $a$ in the potential $(a^2 - |u|^2)^2$. The function $a$ is different from 1 only on finitely many disjoint domains, called the {\\it pinning domains}. These pinning domains model small impurities in a homogeneous superconductor and shrink to single points in the limit $\\v\\to0$; here, $\\v$ is the inverse of the Ginzburg-Landau parameter. We study the energy minimization in a smooth simply connected domain $\\Omega \\subset \\mathbb{C}$ with Dirichlet boundary condition $g$ on $\\d \\O$, with topological degree ${\\rm deg","authors_text":"Micka\\\"el Dos Santos (ICJ), Oleksandr Misiats","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-03-20T17:48:31Z","title":"Ginzburg-Landau model with small pinning domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.3867","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":"sha256:90a7bdca616436275d9e1c2bbf05e3e0d68ff451b0c01dd5f21dada624079a33","target":"record","created_at":"2026-05-18T04:26:22Z","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":"dfbb1b823c26c6c930c004673a415050354ed0a5491032ddd3a848f2855e95f1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-03-20T17:48:31Z","title_canon_sha256":"dc8b0207319dac913e470cfeb6d33b2df3e7b8863d0847b95bceaf486e70f61e"},"schema_version":"1.0","source":{"id":"1103.3867","kind":"arxiv","version":1}},"canonical_sha256":"c91a05916820d453da71bee7c1415907b22c9983c772dec5edb42ae7eed7cea1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c91a05916820d453da71bee7c1415907b22c9983c772dec5edb42ae7eed7cea1","first_computed_at":"2026-05-18T04:26:22.184074Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:26:22.184074Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eKA2DDFEs8SWtpGfVkkv0U9o9v8KtGkaxzM9J4J6M824LWgKiRSnyPblVeNfFYD+IjaZbIkE099RvVs84GKQAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:26:22.184482Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.3867","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:90a7bdca616436275d9e1c2bbf05e3e0d68ff451b0c01dd5f21dada624079a33","sha256:197dfd684b3578ee462b46616acdaaaec02b919abfd14d274befd77642fbb628"],"state_sha256":"25da083140e26a3fe9a4684eac9499f3549c60350dc6d5ec7d076f1d1eaf42bf"}