{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:TOT6RPLN27P7U2MTOPSJ5MFWFZ","short_pith_number":"pith:TOT6RPLN","schema_version":"1.0","canonical_sha256":"9ba7e8bd6dd7dffa699373e49eb0b62e5312ef2829832b36450d9a75fadc17fe","source":{"kind":"arxiv","id":"1904.07351","version":1},"attestation_state":"computed","paper":{"title":"A boundary integral equation approach to computing eigenvalues of the Stokes operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.SP"],"primary_cat":"math.NA","authors_text":"Manas Rachh, Travis Askham","submitted_at":"2019-04-15T22:31:14Z","abstract_excerpt":"The eigenvalues and eigenfunctions of the Stokes operator have been the subject of intense analytical investigation and have applications in the study and simulation of the Navier-Stokes equations. As the Stokes operator is a fourth-order operator, computing these eigenvalues and the corresponding eigenfunctions is a challenging task, particularly in complex geometries and at high frequencies. The boundary integral equation (BIE) framework provides robust and scalable eigenvalue computations due to (a) the reduction in the dimension of the problem to be discretized and (b) the absence of high "},"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":"1904.07351","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-04-15T22:31:14Z","cross_cats_sorted":["math.AP","math.SP"],"title_canon_sha256":"4e6e7672aaa074f8892f5b0341e948306519d250ab4909adbf0961cda3ffeb1f","abstract_canon_sha256":"5928e8de9494645e87ae9da02da5dc67cc0ef3b7ab6ba9fe0bd36dbe847251b9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:28.827919Z","signature_b64":"8oYYOcAaLG0/TyllXhljJFFMeb2c+QxCoc7WGOksrnRZUCV8ZeVFmPM557a+QAPJrUQE4sfgZ+xcjdLisI4rCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9ba7e8bd6dd7dffa699373e49eb0b62e5312ef2829832b36450d9a75fadc17fe","last_reissued_at":"2026-05-17T23:48:28.827291Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:28.827291Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A boundary integral equation approach to computing eigenvalues of the Stokes operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.SP"],"primary_cat":"math.NA","authors_text":"Manas Rachh, Travis Askham","submitted_at":"2019-04-15T22:31:14Z","abstract_excerpt":"The eigenvalues and eigenfunctions of the Stokes operator have been the subject of intense analytical investigation and have applications in the study and simulation of the Navier-Stokes equations. As the Stokes operator is a fourth-order operator, computing these eigenvalues and the corresponding eigenfunctions is a challenging task, particularly in complex geometries and at high frequencies. The boundary integral equation (BIE) framework provides robust and scalable eigenvalue computations due to (a) the reduction in the dimension of the problem to be discretized and (b) the absence of high "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.07351","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":"1904.07351","created_at":"2026-05-17T23:48:28.827395+00:00"},{"alias_kind":"arxiv_version","alias_value":"1904.07351v1","created_at":"2026-05-17T23:48:28.827395+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.07351","created_at":"2026-05-17T23:48:28.827395+00:00"},{"alias_kind":"pith_short_12","alias_value":"TOT6RPLN27P7","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_16","alias_value":"TOT6RPLN27P7U2MT","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_8","alias_value":"TOT6RPLN","created_at":"2026-05-18T12:33:30.264802+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/TOT6RPLN27P7U2MTOPSJ5MFWFZ","json":"https://pith.science/pith/TOT6RPLN27P7U2MTOPSJ5MFWFZ.json","graph_json":"https://pith.science/api/pith-number/TOT6RPLN27P7U2MTOPSJ5MFWFZ/graph.json","events_json":"https://pith.science/api/pith-number/TOT6RPLN27P7U2MTOPSJ5MFWFZ/events.json","paper":"https://pith.science/paper/TOT6RPLN"},"agent_actions":{"view_html":"https://pith.science/pith/TOT6RPLN27P7U2MTOPSJ5MFWFZ","download_json":"https://pith.science/pith/TOT6RPLN27P7U2MTOPSJ5MFWFZ.json","view_paper":"https://pith.science/paper/TOT6RPLN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1904.07351&json=true","fetch_graph":"https://pith.science/api/pith-number/TOT6RPLN27P7U2MTOPSJ5MFWFZ/graph.json","fetch_events":"https://pith.science/api/pith-number/TOT6RPLN27P7U2MTOPSJ5MFWFZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TOT6RPLN27P7U2MTOPSJ5MFWFZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TOT6RPLN27P7U2MTOPSJ5MFWFZ/action/storage_attestation","attest_author":"https://pith.science/pith/TOT6RPLN27P7U2MTOPSJ5MFWFZ/action/author_attestation","sign_citation":"https://pith.science/pith/TOT6RPLN27P7U2MTOPSJ5MFWFZ/action/citation_signature","submit_replication":"https://pith.science/pith/TOT6RPLN27P7U2MTOPSJ5MFWFZ/action/replication_record"}},"created_at":"2026-05-17T23:48:28.827395+00:00","updated_at":"2026-05-17T23:48:28.827395+00:00"}