{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:SYWWYOWM73XNDJNVAHA3KR6SEU","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":"96df8e66c33e0e9d3521403d57889bb6f52160d9995eb848188af4974f66dbbf","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-06-05T10:52:22Z","title_canon_sha256":"9340c6d772041032b3dd7612a3e350a8cc0d484578321c9247dfbcbe5d5de23f"},"schema_version":"1.0","source":{"id":"2506.04880","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.04880","created_at":"2026-07-05T11:16:38Z"},{"alias_kind":"arxiv_version","alias_value":"2506.04880v1","created_at":"2026-07-05T11:16:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.04880","created_at":"2026-07-05T11:16:38Z"},{"alias_kind":"pith_short_12","alias_value":"SYWWYOWM73XN","created_at":"2026-07-05T11:16:38Z"},{"alias_kind":"pith_short_16","alias_value":"SYWWYOWM73XNDJNV","created_at":"2026-07-05T11:16:38Z"},{"alias_kind":"pith_short_8","alias_value":"SYWWYOWM","created_at":"2026-07-05T11:16:38Z"}],"graph_snapshots":[{"event_id":"sha256:c0b749accbd52cd1663832e61defdb59abfdda4c0aea31256423e9e43124e35b","target":"graph","created_at":"2026-07-05T11:16:38Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2506.04880/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper introduces a comprehensive finite element approximation framework for three-dimensional Landau-de Gennes $Q$-tensor energies for nematic liquid crystals, with a particular focus on the anisotropy of the elastic energy and the Ball-Majumdar singular potential. This potential imposes essential physical constraints on the eigenvalues of the $Q$-tensor, ensuring realistic modeling. We address the approximation of regular solutions to nonlinear elliptic partial differential equations with non-homogeneous boundary conditions associated with Landau-de Gennes energies. The well-posedness of","authors_text":"Heiko Gimperlein, Ruma R. Maity","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-06-05T10:52:22Z","title":"Numerical analysis for constrained and unconstrained Q-tensor energies for liquid crystals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.04880","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":"sha256:77068d657fc6cc0b3405c1c7c9449fdeae642a2a01a98ca2e7f10eb62c380306","target":"record","created_at":"2026-07-05T11:16:38Z","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":"96df8e66c33e0e9d3521403d57889bb6f52160d9995eb848188af4974f66dbbf","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-06-05T10:52:22Z","title_canon_sha256":"9340c6d772041032b3dd7612a3e350a8cc0d484578321c9247dfbcbe5d5de23f"},"schema_version":"1.0","source":{"id":"2506.04880","kind":"arxiv","version":1}},"canonical_sha256":"962d6c3accfeeed1a5b501c1b547d225011aad6ec46212616d77c23de4a5e415","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"962d6c3accfeeed1a5b501c1b547d225011aad6ec46212616d77c23de4a5e415","first_computed_at":"2026-07-05T11:16:38.470448Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:16:38.470448Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"41KSs84IY8k7ohIprip7422YngibtAJ1SpxqCdXMxX63b8g+bbkfyHBGIaW6MI0ZiJ4vmnNrijDEkrNyYCzBDg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:16:38.470975Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.04880","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:77068d657fc6cc0b3405c1c7c9449fdeae642a2a01a98ca2e7f10eb62c380306","sha256:c0b749accbd52cd1663832e61defdb59abfdda4c0aea31256423e9e43124e35b"],"state_sha256":"710105d8b65558c0f865b06872efb2cd17a85baa11f4cc5ea3cbb2bd2a80fc91"}