{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:SO47TYEOBZ3BSS2OQYFLPKOWYK","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":"ffb13637aeb75ef1fa568da1efff2f35c0329c58bc78efb2895515a59b3efcd9","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-05-27T08:47:13Z","title_canon_sha256":"0e01d69f5a001e127a18ed17d7af0b07042f5bd9c5afebb274f9ca3111980f2d"},"schema_version":"1.0","source":{"id":"1205.5950","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.5950","created_at":"2026-05-18T03:54:48Z"},{"alias_kind":"arxiv_version","alias_value":"1205.5950v1","created_at":"2026-05-18T03:54:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.5950","created_at":"2026-05-18T03:54:48Z"},{"alias_kind":"pith_short_12","alias_value":"SO47TYEOBZ3B","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"SO47TYEOBZ3BSS2O","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"SO47TYEO","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:345abdd97a207f02292ebd6179af926db1560e1527468ed88a2c58e3376c465b","target":"graph","created_at":"2026-05-18T03:54:48Z","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":"This paper presents a unique continuation estimate for 2-D Stokes equations with the Naiver slip boundary condition in a bounded and simply connected domain. Consequently, an observability estimate for this equation from a subset of positive measure in time follows from the aforementioned unique continuation estimate and the new strategy developed in [16]. Several applications of the above-mentioned observability estimate to control problems of the Stokes equations are given.","authors_text":"Can Zhang, Yuning Liu","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-05-27T08:47:13Z","title":"Unique Continuation and Observability Estimates for 2-D Stokes Equations with the Navier Slip Boundary Condition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.5950","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":"sha256:0bb2390dd2ce7a2783f5f59ce1105c8ead082caf0541b6a2cba826da998cf561","target":"record","created_at":"2026-05-18T03:54:48Z","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":"ffb13637aeb75ef1fa568da1efff2f35c0329c58bc78efb2895515a59b3efcd9","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-05-27T08:47:13Z","title_canon_sha256":"0e01d69f5a001e127a18ed17d7af0b07042f5bd9c5afebb274f9ca3111980f2d"},"schema_version":"1.0","source":{"id":"1205.5950","kind":"arxiv","version":1}},"canonical_sha256":"93b9f9e08e0e76194b4e860ab7a9d6c29c654e342fda940ee5251fa2e62e82e0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"93b9f9e08e0e76194b4e860ab7a9d6c29c654e342fda940ee5251fa2e62e82e0","first_computed_at":"2026-05-18T03:54:48.691150Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:54:48.691150Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kYU0dEaQUEKXPMGbRbO30fxI3F6YX7z3eF/p4mprJPxzwEhQLcBSOQZPvtfiPzHyUlh0Na0nC9Ueqr0enHfLDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:54:48.691794Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.5950","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0bb2390dd2ce7a2783f5f59ce1105c8ead082caf0541b6a2cba826da998cf561","sha256:345abdd97a207f02292ebd6179af926db1560e1527468ed88a2c58e3376c465b"],"state_sha256":"1fd180eee380800819c2a58821907717dd40c6f8bfe7c5986dc6e15985d9d43f"}