{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:5J5SEITEKLIHA7ZVBCWLS7L2KG","short_pith_number":"pith:5J5SEITE","schema_version":"1.0","canonical_sha256":"ea7b22226452d0707f3508acb97d7a518188ca0f8ad5f1578a325079d9695611","source":{"kind":"arxiv","id":"2602.17233","version":2},"attestation_state":"computed","paper":{"title":"Planar Degenerate Anchoring in Landau-de Gennes Energy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ho Man Tai, Yong Yu","submitted_at":"2026-02-19T10:27:40Z","abstract_excerpt":"The aim of this article is twofold. First, in the large-body limit and when the temperature is below the nematic-isotropic transition threshold, we verify that the $\\mathbb{S}^2$-valued energy-minimizing harmonic map on a bounded smooth domain $\\Omega \\subset \\mathbb{R}^3$ with tangential boundary condition is a singular limit of the Landau-de Gennes energy minimizers subject to the Fournier-Galatola planar degenerate anchoring [22]. This harmonic map is referred to as the canonical harmonic map. Our second aim is to address the local structure of the canonical harmonic map near the boundary s"},"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":"2602.17233","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-02-19T10:27:40Z","cross_cats_sorted":[],"title_canon_sha256":"9926c77d609a70d27c2b702539e8c787db961da99bc33f89181490db0575881d","abstract_canon_sha256":"0b2b29ee34b29e8a567e652f73fdb07051348a864606bb98de6c92c1a061c917"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:05:42.398321Z","signature_b64":"93GPDlpAoXJSJ34EQ5RrO6BduHtI5qZ2gB9itCe/w7Ctko1LBJuCgTJ8fqI4Fvo8fap+bxxMTJ6l3K/iGJAIBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ea7b22226452d0707f3508acb97d7a518188ca0f8ad5f1578a325079d9695611","last_reissued_at":"2026-05-20T00:05:42.397881Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:05:42.397881Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Planar Degenerate Anchoring in Landau-de Gennes Energy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ho Man Tai, Yong Yu","submitted_at":"2026-02-19T10:27:40Z","abstract_excerpt":"The aim of this article is twofold. First, in the large-body limit and when the temperature is below the nematic-isotropic transition threshold, we verify that the $\\mathbb{S}^2$-valued energy-minimizing harmonic map on a bounded smooth domain $\\Omega \\subset \\mathbb{R}^3$ with tangential boundary condition is a singular limit of the Landau-de Gennes energy minimizers subject to the Fournier-Galatola planar degenerate anchoring [22]. This harmonic map is referred to as the canonical harmonic map. Our second aim is to address the local structure of the canonical harmonic map near the boundary s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.17233","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2602.17233/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2602.17233","created_at":"2026-05-20T00:05:42.397946+00:00"},{"alias_kind":"arxiv_version","alias_value":"2602.17233v2","created_at":"2026-05-20T00:05:42.397946+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.17233","created_at":"2026-05-20T00:05:42.397946+00:00"},{"alias_kind":"pith_short_12","alias_value":"5J5SEITEKLIH","created_at":"2026-05-20T00:05:42.397946+00:00"},{"alias_kind":"pith_short_16","alias_value":"5J5SEITEKLIHA7ZV","created_at":"2026-05-20T00:05:42.397946+00:00"},{"alias_kind":"pith_short_8","alias_value":"5J5SEITE","created_at":"2026-05-20T00:05:42.397946+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/5J5SEITEKLIHA7ZVBCWLS7L2KG","json":"https://pith.science/pith/5J5SEITEKLIHA7ZVBCWLS7L2KG.json","graph_json":"https://pith.science/api/pith-number/5J5SEITEKLIHA7ZVBCWLS7L2KG/graph.json","events_json":"https://pith.science/api/pith-number/5J5SEITEKLIHA7ZVBCWLS7L2KG/events.json","paper":"https://pith.science/paper/5J5SEITE"},"agent_actions":{"view_html":"https://pith.science/pith/5J5SEITEKLIHA7ZVBCWLS7L2KG","download_json":"https://pith.science/pith/5J5SEITEKLIHA7ZVBCWLS7L2KG.json","view_paper":"https://pith.science/paper/5J5SEITE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2602.17233&json=true","fetch_graph":"https://pith.science/api/pith-number/5J5SEITEKLIHA7ZVBCWLS7L2KG/graph.json","fetch_events":"https://pith.science/api/pith-number/5J5SEITEKLIHA7ZVBCWLS7L2KG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5J5SEITEKLIHA7ZVBCWLS7L2KG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5J5SEITEKLIHA7ZVBCWLS7L2KG/action/storage_attestation","attest_author":"https://pith.science/pith/5J5SEITEKLIHA7ZVBCWLS7L2KG/action/author_attestation","sign_citation":"https://pith.science/pith/5J5SEITEKLIHA7ZVBCWLS7L2KG/action/citation_signature","submit_replication":"https://pith.science/pith/5J5SEITEKLIHA7ZVBCWLS7L2KG/action/replication_record"}},"created_at":"2026-05-20T00:05:42.397946+00:00","updated_at":"2026-05-20T00:05:42.397946+00:00"}