{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:OTPRGQVM46MSDN4IDGTYZKB7VO","short_pith_number":"pith:OTPRGQVM","schema_version":"1.0","canonical_sha256":"74df1342ace79921b78819a78ca83fabb23bf29117e308dc2105ad75162edc1f","source":{"kind":"arxiv","id":"1307.4437","version":2},"attestation_state":"computed","paper":{"title":"On Minimizers of the Landau-de Gennes Energy Functional on Planar Domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alberto Montero, Dmitry Golovaty","submitted_at":"2013-07-16T22:09:15Z","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"},"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":"1307.4437","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-07-16T22:09:15Z","cross_cats_sorted":[],"title_canon_sha256":"14e47a364ff6dc0a5050038726ab5a09bd1f48cf517bb242693172d3b5b4c208","abstract_canon_sha256":"6deeacc0d733001b9842a992724c5dc541e5d94349de99464de9e315190b8b9e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:48:49.389071Z","signature_b64":"Mfr+F2tjNuV6GWtszPpCfmmDp25zUD2TK6NQ53PSNpCX5TiBSqbT0MyMSBtTxAPmkXLjO9b1565ubSrdNF7jCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"74df1342ace79921b78819a78ca83fabb23bf29117e308dc2105ad75162edc1f","last_reissued_at":"2026-05-18T01:48:49.388460Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:48:49.388460Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Minimizers of the Landau-de Gennes Energy Functional on Planar Domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alberto Montero, Dmitry Golovaty","submitted_at":"2013-07-16T22:09:15Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.4437","kind":"arxiv","version":2},"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":"1307.4437","created_at":"2026-05-18T01:48:49.388548+00:00"},{"alias_kind":"arxiv_version","alias_value":"1307.4437v2","created_at":"2026-05-18T01:48:49.388548+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.4437","created_at":"2026-05-18T01:48:49.388548+00:00"},{"alias_kind":"pith_short_12","alias_value":"OTPRGQVM46MS","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_16","alias_value":"OTPRGQVM46MSDN4I","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_8","alias_value":"OTPRGQVM","created_at":"2026-05-18T12:27:54.935989+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/OTPRGQVM46MSDN4IDGTYZKB7VO","json":"https://pith.science/pith/OTPRGQVM46MSDN4IDGTYZKB7VO.json","graph_json":"https://pith.science/api/pith-number/OTPRGQVM46MSDN4IDGTYZKB7VO/graph.json","events_json":"https://pith.science/api/pith-number/OTPRGQVM46MSDN4IDGTYZKB7VO/events.json","paper":"https://pith.science/paper/OTPRGQVM"},"agent_actions":{"view_html":"https://pith.science/pith/OTPRGQVM46MSDN4IDGTYZKB7VO","download_json":"https://pith.science/pith/OTPRGQVM46MSDN4IDGTYZKB7VO.json","view_paper":"https://pith.science/paper/OTPRGQVM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1307.4437&json=true","fetch_graph":"https://pith.science/api/pith-number/OTPRGQVM46MSDN4IDGTYZKB7VO/graph.json","fetch_events":"https://pith.science/api/pith-number/OTPRGQVM46MSDN4IDGTYZKB7VO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OTPRGQVM46MSDN4IDGTYZKB7VO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OTPRGQVM46MSDN4IDGTYZKB7VO/action/storage_attestation","attest_author":"https://pith.science/pith/OTPRGQVM46MSDN4IDGTYZKB7VO/action/author_attestation","sign_citation":"https://pith.science/pith/OTPRGQVM46MSDN4IDGTYZKB7VO/action/citation_signature","submit_replication":"https://pith.science/pith/OTPRGQVM46MSDN4IDGTYZKB7VO/action/replication_record"}},"created_at":"2026-05-18T01:48:49.388548+00:00","updated_at":"2026-05-18T01:48:49.388548+00:00"}