{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:3R477PODY36TQOZREYGA4I26NW","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":"b21dbb5ec844384f473809a860aa772ce487ebf6b19163be6aef2c3d084fdb6c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-07-21T13:31:30Z","title_canon_sha256":"e2fe6e14fcd7eca1bab1870bba00c234be9fa4400e3855ebaa6d0a370dcc381c"},"schema_version":"1.0","source":{"id":"1807.08151","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.08151","created_at":"2026-05-18T00:10:09Z"},{"alias_kind":"arxiv_version","alias_value":"1807.08151v1","created_at":"2026-05-18T00:10:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.08151","created_at":"2026-05-18T00:10:09Z"},{"alias_kind":"pith_short_12","alias_value":"3R477PODY36T","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"3R477PODY36TQOZR","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"3R477POD","created_at":"2026-05-18T12:32:02Z"}],"graph_snapshots":[{"event_id":"sha256:58504005b6fc408dcf732b8c48e6d7c10b140e33fc6636c456f58537fe0f3e05","target":"graph","created_at":"2026-05-18T00:10:09Z","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 note, we obtain uniqueness results for Beltrami flow in both bounded and unbounded domain with nonempty boundary by establishing an elementary but useful formula involving operators $\\divg$ and $\\curl$. We also use this formula to deal with Maxwell and Stokes eigenvalue problems.","authors_text":"Yong Zeng, Zhibing Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-07-21T13:31:30Z","title":"Applications of a formula on Beltrami flow"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.08151","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:f5a09658b14c1e835e3d31ae276d0bf29e9563d9c72a5f41fecc7014533a41f9","target":"record","created_at":"2026-05-18T00:10:09Z","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":"b21dbb5ec844384f473809a860aa772ce487ebf6b19163be6aef2c3d084fdb6c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-07-21T13:31:30Z","title_canon_sha256":"e2fe6e14fcd7eca1bab1870bba00c234be9fa4400e3855ebaa6d0a370dcc381c"},"schema_version":"1.0","source":{"id":"1807.08151","kind":"arxiv","version":1}},"canonical_sha256":"dc79ffbdc3c6fd383b31260c0e235e6da0768ed33cbfff32e1fc6edf9082a5af","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dc79ffbdc3c6fd383b31260c0e235e6da0768ed33cbfff32e1fc6edf9082a5af","first_computed_at":"2026-05-18T00:10:09.085098Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:09.085098Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MkWcz7v+ENgo+GuySAMob3jA6oCszvmJbcW6+D8bXCQR5yzRmuGjlURoGFS/AXBfzpGc5tka4K8wvZg3mJASDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:09.085643Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.08151","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f5a09658b14c1e835e3d31ae276d0bf29e9563d9c72a5f41fecc7014533a41f9","sha256:58504005b6fc408dcf732b8c48e6d7c10b140e33fc6636c456f58537fe0f3e05"],"state_sha256":"b7d3b1ab17c4544da62910c4d2364c2c5c0d8bcd162b61074274cdea40000678"}