{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:MZSLWTGCUGRJWFQK4KIA5ZZ2IT","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":"760b70cbd5cd1b5b30fef4837caba20133e17bd49529498f22427285ec4fbba2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-09-08T20:39:59Z","title_canon_sha256":"6b7a7a65304f85423b637354836778ac7a995c5427716665cc3c910bd0580432"},"schema_version":"1.0","source":{"id":"1009.1649","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.1649","created_at":"2026-05-18T02:05:32Z"},{"alias_kind":"arxiv_version","alias_value":"1009.1649v1","created_at":"2026-05-18T02:05:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.1649","created_at":"2026-05-18T02:05:32Z"},{"alias_kind":"pith_short_12","alias_value":"MZSLWTGCUGRJ","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"MZSLWTGCUGRJWFQK","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"MZSLWTGC","created_at":"2026-05-18T12:26:10Z"}],"graph_snapshots":[{"event_id":"sha256:d5d20d8849ae7cff4b601e3364016db218be9532fad16deb42a1cab79b68fe23","target":"graph","created_at":"2026-05-18T02:05:32Z","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 deal with a nonconvex and nonlocal variational problem coming from thin-film micromagnetics. It consists in a free-energy functional depending on two small parameters $\\eps$ and $\\eta$ and defined over $S^2-$vector fields $m$ that are tangent at the boundary of a two-dimensional domain $\\Omega$. We are interested in the behavior of minimizers as $\\eps, \\eta \\to 0$. The minimizers tend to be in-plane away from a region of length scale $\\eps$ (generically, an interior vortex ball or two boundary vortex balls) and of vanishing divergence, so that $S^1-$transition layers of length scale $\\eta$ ","authors_text":"Felix Otto, Radu Ignat","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-09-08T20:39:59Z","title":"A compactness result for Landau state in thin-film micromagnetics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.1649","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":"sha256:8376ba5050ac9b24254a944e31fe600f2ad756d284f9ab0080ac3a5c786394d7","target":"record","created_at":"2026-05-18T02:05:32Z","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":"760b70cbd5cd1b5b30fef4837caba20133e17bd49529498f22427285ec4fbba2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-09-08T20:39:59Z","title_canon_sha256":"6b7a7a65304f85423b637354836778ac7a995c5427716665cc3c910bd0580432"},"schema_version":"1.0","source":{"id":"1009.1649","kind":"arxiv","version":1}},"canonical_sha256":"6664bb4cc2a1a29b160ae2900ee73a44f21ecc5ca55f55989600db5a08b7b270","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6664bb4cc2a1a29b160ae2900ee73a44f21ecc5ca55f55989600db5a08b7b270","first_computed_at":"2026-05-18T02:05:32.964946Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:05:32.964946Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6OWdsLBJmhhMmfYVOIzR2m9oA0UDr/NFMQPB6quILPSTQBzgy2QCqHV4hyuS1PMwxpy0SxZUV4SBOWa+zhAvAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:05:32.965727Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.1649","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8376ba5050ac9b24254a944e31fe600f2ad756d284f9ab0080ac3a5c786394d7","sha256:d5d20d8849ae7cff4b601e3364016db218be9532fad16deb42a1cab79b68fe23"],"state_sha256":"7ce54ac1d0f73885f46474b4cda6742b25c02c4c25ec1cb63933ac66f5db6f10"}