{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:YIUESU675GIHG2SAR3QBMZC4ME","short_pith_number":"pith:YIUESU67","schema_version":"1.0","canonical_sha256":"c2284953dfe990736a408ee016645c6125acde793248fb9ceaf2207485e54c67","source":{"kind":"arxiv","id":"1406.5252","version":3},"attestation_state":"computed","paper":{"title":"Robust and efficient solution of the drum problem via Nystrom approximation of the Fredholm determinant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Alex Barnett, Lin Zhao","submitted_at":"2014-06-20T01:37:43Z","abstract_excerpt":"The drum problem-finding the eigenvalues and eigenfunctions of the Laplacian with Dirichlet boundary condition-has many applications, yet remains challenging for general domains when high accuracy or high frequency is needed. Boundary integral equations are appealing for large-scale problems, yet certain difficulties have limited their use. We introduce two ideas to remedy this: 1) We solve the resulting nonlinear eigenvalue problem using Boyd's method for analytic root-finding applied to the Fredholm determinant. We show that this is many times faster than the usual iterative minimization of "},"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":"1406.5252","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-06-20T01:37:43Z","cross_cats_sorted":[],"title_canon_sha256":"c70885c8cc29a386a7130c4cfddd1529af6dc7ccef3ecaddcd2ca77a45feace6","abstract_canon_sha256":"ef88aa187441949974c19fb8da9302aca6c4f683898a604e815e2ec41b973345"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:43:10.728019Z","signature_b64":"WmEzKKbe9j45BZaK1blhUaZptiS+UVI5n1wt3vvhOv02LYV8d2kH6fRS+7ZKShdo7i69Wa4Qv+7yRiCq8u5GBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c2284953dfe990736a408ee016645c6125acde793248fb9ceaf2207485e54c67","last_reissued_at":"2026-05-18T02:43:10.727553Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:43:10.727553Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Robust and efficient solution of the drum problem via Nystrom approximation of the Fredholm determinant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Alex Barnett, Lin Zhao","submitted_at":"2014-06-20T01:37:43Z","abstract_excerpt":"The drum problem-finding the eigenvalues and eigenfunctions of the Laplacian with Dirichlet boundary condition-has many applications, yet remains challenging for general domains when high accuracy or high frequency is needed. Boundary integral equations are appealing for large-scale problems, yet certain difficulties have limited their use. We introduce two ideas to remedy this: 1) We solve the resulting nonlinear eigenvalue problem using Boyd's method for analytic root-finding applied to the Fredholm determinant. We show that this is many times faster than the usual iterative minimization of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.5252","kind":"arxiv","version":3},"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":"1406.5252","created_at":"2026-05-18T02:43:10.727628+00:00"},{"alias_kind":"arxiv_version","alias_value":"1406.5252v3","created_at":"2026-05-18T02:43:10.727628+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.5252","created_at":"2026-05-18T02:43:10.727628+00:00"},{"alias_kind":"pith_short_12","alias_value":"YIUESU675GIH","created_at":"2026-05-18T12:28:57.508820+00:00"},{"alias_kind":"pith_short_16","alias_value":"YIUESU675GIHG2SA","created_at":"2026-05-18T12:28:57.508820+00:00"},{"alias_kind":"pith_short_8","alias_value":"YIUESU67","created_at":"2026-05-18T12:28:57.508820+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/YIUESU675GIHG2SAR3QBMZC4ME","json":"https://pith.science/pith/YIUESU675GIHG2SAR3QBMZC4ME.json","graph_json":"https://pith.science/api/pith-number/YIUESU675GIHG2SAR3QBMZC4ME/graph.json","events_json":"https://pith.science/api/pith-number/YIUESU675GIHG2SAR3QBMZC4ME/events.json","paper":"https://pith.science/paper/YIUESU67"},"agent_actions":{"view_html":"https://pith.science/pith/YIUESU675GIHG2SAR3QBMZC4ME","download_json":"https://pith.science/pith/YIUESU675GIHG2SAR3QBMZC4ME.json","view_paper":"https://pith.science/paper/YIUESU67","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1406.5252&json=true","fetch_graph":"https://pith.science/api/pith-number/YIUESU675GIHG2SAR3QBMZC4ME/graph.json","fetch_events":"https://pith.science/api/pith-number/YIUESU675GIHG2SAR3QBMZC4ME/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YIUESU675GIHG2SAR3QBMZC4ME/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YIUESU675GIHG2SAR3QBMZC4ME/action/storage_attestation","attest_author":"https://pith.science/pith/YIUESU675GIHG2SAR3QBMZC4ME/action/author_attestation","sign_citation":"https://pith.science/pith/YIUESU675GIHG2SAR3QBMZC4ME/action/citation_signature","submit_replication":"https://pith.science/pith/YIUESU675GIHG2SAR3QBMZC4ME/action/replication_record"}},"created_at":"2026-05-18T02:43:10.727628+00:00","updated_at":"2026-05-18T02:43:10.727628+00:00"}