{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:RCYVK3I2JG3SW2T75YW37MTE4F","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":"9265bc227d379ca267e4e9b7e3cc87e5b9cc20af9f6b8228cd1110c917dc24ef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-10-08T01:13:57Z","title_canon_sha256":"f0934965f0251510affef41e96109e2af681c0fd688873d8627ca45cd2e40f95"},"schema_version":"1.0","source":{"id":"1210.2124","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.2124","created_at":"2026-05-18T03:43:51Z"},{"alias_kind":"arxiv_version","alias_value":"1210.2124v1","created_at":"2026-05-18T03:43:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.2124","created_at":"2026-05-18T03:43:51Z"},{"alias_kind":"pith_short_12","alias_value":"RCYVK3I2JG3S","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"RCYVK3I2JG3SW2T7","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"RCYVK3I2","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:b71139270fa673cc48e4563f9418de21c1fd25718ca4b56aeaece52c64de0e63","target":"graph","created_at":"2026-05-18T03:43:51Z","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 consider a 2D system that models the nematic liquid crystal flow through the Navier--Stokes equations suitably coupled with a transport-reaction-diffusion equation for the averaged molecular orientations. This system has been proposed as a reasonable approximation of the well-known Ericksen--Leslie system. Taking advantage of previous well-posedness results and proving suitable dissipative estimates, here we show that the system endowed with periodic boundary conditions is a dissipative dynamical system with a smooth global attractor of finite fractal dimension.","authors_text":"Hao Wu, Maurizio Grasselli","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-10-08T01:13:57Z","title":"Finite--dimensional global attractor for a system modeling the 2D nematic liquid crystal flow"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.2124","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":"sha256:4ea6f4c7b34589b9c9fa49f50ab562f8f6a09b6c327dde67e4e96eba556e74ea","target":"record","created_at":"2026-05-18T03:43:51Z","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":"9265bc227d379ca267e4e9b7e3cc87e5b9cc20af9f6b8228cd1110c917dc24ef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-10-08T01:13:57Z","title_canon_sha256":"f0934965f0251510affef41e96109e2af681c0fd688873d8627ca45cd2e40f95"},"schema_version":"1.0","source":{"id":"1210.2124","kind":"arxiv","version":1}},"canonical_sha256":"88b1556d1a49b72b6a7fee2dbfb264e16d9c5324a11371a8e9f4a83a61adcb28","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"88b1556d1a49b72b6a7fee2dbfb264e16d9c5324a11371a8e9f4a83a61adcb28","first_computed_at":"2026-05-18T03:43:51.054259Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:43:51.054259Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"l7dDp7uU3WvWoM6eP/GXMUOwM8nPPHK/BX7CXu17LTvSxGMh+dpAd61fiiaoy8e2KxFDNNjehj+at3yJBXEgBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:43:51.054835Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.2124","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4ea6f4c7b34589b9c9fa49f50ab562f8f6a09b6c327dde67e4e96eba556e74ea","sha256:b71139270fa673cc48e4563f9418de21c1fd25718ca4b56aeaece52c64de0e63"],"state_sha256":"e7c50c8239ab47b8b3164c1e8c896f74c82b25850720fb1ce5eca14cfed316a2"}