{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:OTPRGQVM46MSDN4IDGTYZKB7VO","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":"6deeacc0d733001b9842a992724c5dc541e5d94349de99464de9e315190b8b9e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-07-16T22:09:15Z","title_canon_sha256":"14e47a364ff6dc0a5050038726ab5a09bd1f48cf517bb242693172d3b5b4c208"},"schema_version":"1.0","source":{"id":"1307.4437","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.4437","created_at":"2026-05-18T01:48:49Z"},{"alias_kind":"arxiv_version","alias_value":"1307.4437v2","created_at":"2026-05-18T01:48:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.4437","created_at":"2026-05-18T01:48:49Z"},{"alias_kind":"pith_short_12","alias_value":"OTPRGQVM46MS","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"OTPRGQVM46MSDN4I","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"OTPRGQVM","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:37fee52c137e738c6f63f5fa73ee579ea53153f710dfead8f33fd0e35ff06b9d","target":"graph","created_at":"2026-05-18T01:48:49Z","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 study tensor-valued minimizers of the Landau-de Gennes energy functional on a simply-connected planar domain $\\Omega$ with non-contractible boundary data. Here the tensorial field represents the second moment of a local orientational distribution of rod-like molecules of a nematic liquid crystal. Under the assumption that the energy depends on a single parameter---a dimensionless elastic constant $\\eps>0$---we establish that, as $\\eps\\to0$, the minimizers converge to a projection-valued map that minimizes the Dirichlet integral away from a single point in $\\Omega$. We also provide a descrip","authors_text":"Alberto Montero, Dmitry Golovaty","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-07-16T22:09:15Z","title":"On Minimizers of the Landau-de Gennes Energy Functional on Planar Domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.4437","kind":"arxiv","version":2},"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":"sha256:5953363f43b5a387ed10b995ed34e6c9034e69ad54477c9eb78a20f00ad79e85","target":"record","created_at":"2026-05-18T01:48:49Z","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":"6deeacc0d733001b9842a992724c5dc541e5d94349de99464de9e315190b8b9e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-07-16T22:09:15Z","title_canon_sha256":"14e47a364ff6dc0a5050038726ab5a09bd1f48cf517bb242693172d3b5b4c208"},"schema_version":"1.0","source":{"id":"1307.4437","kind":"arxiv","version":2}},"canonical_sha256":"74df1342ace79921b78819a78ca83fabb23bf29117e308dc2105ad75162edc1f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"74df1342ace79921b78819a78ca83fabb23bf29117e308dc2105ad75162edc1f","first_computed_at":"2026-05-18T01:48:49.388460Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:48:49.388460Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Mfr+F2tjNuV6GWtszPpCfmmDp25zUD2TK6NQ53PSNpCX5TiBSqbT0MyMSBtTxAPmkXLjO9b1565ubSrdNF7jCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:48:49.389071Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.4437","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5953363f43b5a387ed10b995ed34e6c9034e69ad54477c9eb78a20f00ad79e85","sha256:37fee52c137e738c6f63f5fa73ee579ea53153f710dfead8f33fd0e35ff06b9d"],"state_sha256":"276a80797be00f51bf396c899d335fe399a53872e1afeb5a39f39ecce522a682"}