{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:FZUWNDHCS4UPL5PSBHMKEY7ZI5","short_pith_number":"pith:FZUWNDHC","schema_version":"1.0","canonical_sha256":"2e69668ce29728f5f5f209d8a263f9477a409efa9f78c0261c25d09864d35d25","source":{"kind":"arxiv","id":"1807.08154","version":1},"attestation_state":"computed","paper":{"title":"Comparison results for eigenvalues of curlcurl operator and Stokes operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Zhibing Zhang","submitted_at":"2018-07-21T13:50:45Z","abstract_excerpt":"This paper mainly establishes comparison results for eigenvalues of $\\curl\\curl$ operator and Stokes operator. For three-dimensional simply connected bounded domains, the $k$-th eigenvalue of $\\curl\\curl$ operator under tangent boundary condition or normal boundary condition is strictly smaller than the $k$-th eigenvalue of Stokes operator. For any dimension $n\\geq2$, the first eigenvalue of Stokes operator is strictly larger than the first eigenvalue of Dirichlet Laplacian. For three-dimensional strictly convex domains, the first eigenvalue of $\\curl\\curl$ operator under tangent boundary cond"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1807.08154","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-07-21T13:50:45Z","cross_cats_sorted":[],"title_canon_sha256":"b875108930080dc5b28a607fd733dcfae1330ef342db13413d41e6958a1013d0","abstract_canon_sha256":"bbf6f8c69cdc0753915e5c2f8c436f693105f4248cc89b3bd08b7fdcb7f7cf39"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:09.077579Z","signature_b64":"53BdMt+x0dzCrfAKBbSzZLjHUrIieS8w0NvTJjJwJDGc/cqtWeWHAdGDMnrkqWzPjD/A90ZJENd1CkUGx4q3CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2e69668ce29728f5f5f209d8a263f9477a409efa9f78c0261c25d09864d35d25","last_reissued_at":"2026-05-18T00:10:09.077057Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:09.077057Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Comparison results for eigenvalues of curlcurl operator and Stokes operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Zhibing Zhang","submitted_at":"2018-07-21T13:50:45Z","abstract_excerpt":"This paper mainly establishes comparison results for eigenvalues of $\\curl\\curl$ operator and Stokes operator. For three-dimensional simply connected bounded domains, the $k$-th eigenvalue of $\\curl\\curl$ operator under tangent boundary condition or normal boundary condition is strictly smaller than the $k$-th eigenvalue of Stokes operator. For any dimension $n\\geq2$, the first eigenvalue of Stokes operator is strictly larger than the first eigenvalue of Dirichlet Laplacian. For three-dimensional strictly convex domains, the first eigenvalue of $\\curl\\curl$ operator under tangent boundary cond"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.08154","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1807.08154","created_at":"2026-05-18T00:10:09.077140+00:00"},{"alias_kind":"arxiv_version","alias_value":"1807.08154v1","created_at":"2026-05-18T00:10:09.077140+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.08154","created_at":"2026-05-18T00:10:09.077140+00:00"},{"alias_kind":"pith_short_12","alias_value":"FZUWNDHCS4UP","created_at":"2026-05-18T12:32:25.280505+00:00"},{"alias_kind":"pith_short_16","alias_value":"FZUWNDHCS4UPL5PS","created_at":"2026-05-18T12:32:25.280505+00:00"},{"alias_kind":"pith_short_8","alias_value":"FZUWNDHC","created_at":"2026-05-18T12:32:25.280505+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FZUWNDHCS4UPL5PSBHMKEY7ZI5","json":"https://pith.science/pith/FZUWNDHCS4UPL5PSBHMKEY7ZI5.json","graph_json":"https://pith.science/api/pith-number/FZUWNDHCS4UPL5PSBHMKEY7ZI5/graph.json","events_json":"https://pith.science/api/pith-number/FZUWNDHCS4UPL5PSBHMKEY7ZI5/events.json","paper":"https://pith.science/paper/FZUWNDHC"},"agent_actions":{"view_html":"https://pith.science/pith/FZUWNDHCS4UPL5PSBHMKEY7ZI5","download_json":"https://pith.science/pith/FZUWNDHCS4UPL5PSBHMKEY7ZI5.json","view_paper":"https://pith.science/paper/FZUWNDHC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1807.08154&json=true","fetch_graph":"https://pith.science/api/pith-number/FZUWNDHCS4UPL5PSBHMKEY7ZI5/graph.json","fetch_events":"https://pith.science/api/pith-number/FZUWNDHCS4UPL5PSBHMKEY7ZI5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FZUWNDHCS4UPL5PSBHMKEY7ZI5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FZUWNDHCS4UPL5PSBHMKEY7ZI5/action/storage_attestation","attest_author":"https://pith.science/pith/FZUWNDHCS4UPL5PSBHMKEY7ZI5/action/author_attestation","sign_citation":"https://pith.science/pith/FZUWNDHCS4UPL5PSBHMKEY7ZI5/action/citation_signature","submit_replication":"https://pith.science/pith/FZUWNDHCS4UPL5PSBHMKEY7ZI5/action/replication_record"}},"created_at":"2026-05-18T00:10:09.077140+00:00","updated_at":"2026-05-18T00:10:09.077140+00:00"}