{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:AGSS3JBBSWGXDMECW7JCWETI4X","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":"594371adde49f84c778a8aae841fd62e6c54b73a4410566be47822bdfb0c823f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-08T15:59:49Z","title_canon_sha256":"6444e0124910f29bf32c82004deee2a216175287c083b2483fa7a358f11dd8e1"},"schema_version":"1.0","source":{"id":"1811.03512","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.03512","created_at":"2026-05-18T00:01:15Z"},{"alias_kind":"arxiv_version","alias_value":"1811.03512v1","created_at":"2026-05-18T00:01:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.03512","created_at":"2026-05-18T00:01:15Z"},{"alias_kind":"pith_short_12","alias_value":"AGSS3JBBSWGX","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"AGSS3JBBSWGXDMEC","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"AGSS3JBB","created_at":"2026-05-18T12:32:13Z"}],"graph_snapshots":[{"event_id":"sha256:44c6c1f3cf84725c6c02464c23063de7c51b49e89612f207bf5948d882102666","target":"graph","created_at":"2026-05-18T00:01:15Z","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":"In this paper, we consider the boundary value problem of a simplified Ericksen-Leslie system in dimension two with non-slip boundary condition for the velocity field $u$ and time-dependent boundary condition for the director field $d$ of unit length. For such a system, we first establish the existence of a global weak solution that is smooth away from finitely many singular times, then establish the existence of a unique global strong solution that is smooth for $t>0$ under the assumption that the image of boundary data is contained in the hemisphere $\\mathbb S^2_+$. Finally, we apply these th","authors_text":"Changyou Wang, Jianfeng Zhou, Qiao Liu, Xiaotao Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-08T15:59:49Z","title":"On optimal boundary control of Ericksen-Leslie system in dimension two"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.03512","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":"sha256:21b914b2d66a4ef43695e74a5721efeeb274132f38cd538df2941db72c0ce54a","target":"record","created_at":"2026-05-18T00:01:15Z","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":"594371adde49f84c778a8aae841fd62e6c54b73a4410566be47822bdfb0c823f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-08T15:59:49Z","title_canon_sha256":"6444e0124910f29bf32c82004deee2a216175287c083b2483fa7a358f11dd8e1"},"schema_version":"1.0","source":{"id":"1811.03512","kind":"arxiv","version":1}},"canonical_sha256":"01a52da421958d71b082b7d22b1268e5fea185a9091e0865d51fac8ad0c4a65f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"01a52da421958d71b082b7d22b1268e5fea185a9091e0865d51fac8ad0c4a65f","first_computed_at":"2026-05-18T00:01:15.910694Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:15.910694Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZIHFJpY8DPDivuwpJGVU1pgYRsSbRWLfydXxZr98SkRgpef1es1t0N9vvp1NCX1p9/tM9ttKjdHW9JUsiun/BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:15.911285Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.03512","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:21b914b2d66a4ef43695e74a5721efeeb274132f38cd538df2941db72c0ce54a","sha256:44c6c1f3cf84725c6c02464c23063de7c51b49e89612f207bf5948d882102666"],"state_sha256":"68f58abea6f37c4917ae644f1c368d535a472729912acddd24f2388d1cc7bfe4"}