{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2000:A63YTXWQZM434GIX5RQMO4YAFG","short_pith_number":"pith:A63YTXWQ","schema_version":"1.0","canonical_sha256":"07b789ded0cb39be1917ec60c7730029aa3f454a8fecc5ac428485447c8642c2","source":{"kind":"arxiv","id":"nlin/0005057","version":1},"attestation_state":"computed","paper":{"title":"A Finite Element Algorithm for High-Lying Eigenvalues and Eigenfunctions with Homogeneous Neumann and Dirichlet Boundary Conditions","license":"","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"nlin.CD","authors_text":"F. Leyvraz, G. Baez, R.A. Mendez-Sanchez, T.H.Seligman","submitted_at":"2000-05-26T15:42:37Z","abstract_excerpt":"We present a finite element algorithm that computes eigenvalues and eigenfunctions of the Laplace operator for two-dimensional problems with homogeneous Neumann or Dirichlet boundary conditions or combinations of either for different parts of the boundary. In order to solve the generalized eigenvalue problem, we use an inverse power plus Gauss-Seidel algorithm. For Neumann boundary conditions the method is much more efficient than the equivalent finite difference algorithm. We have cheked the algorithm comparing the cumulative level density of the espectrum obtained numerically, with the theor"},"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":"nlin/0005057","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"nlin.CD","submitted_at":"2000-05-26T15:42:37Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"51493517b21dbaee2b278a6e66e8e0c80e013ee2d2652b0eca09b3b363da61dd","abstract_canon_sha256":"734354ebc52626e8e44225162289c89532f172d30154f5183889e732372337b1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-03T22:06:22.423663Z","signature_b64":"xWpe9nnJmqQszxZQWDeT64H8K7pI9Gw+M9m1paCBRQe0EvUJ7EkUdNWT6lztUurAKAhdSvRLb66PPo2gUzLfAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"07b789ded0cb39be1917ec60c7730029aa3f454a8fecc5ac428485447c8642c2","last_reissued_at":"2026-06-03T22:06:22.423227Z","signature_status":"signed_v1","first_computed_at":"2026-06-03T22:06:22.423227Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Finite Element Algorithm for High-Lying Eigenvalues and Eigenfunctions with Homogeneous Neumann and Dirichlet Boundary Conditions","license":"","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"nlin.CD","authors_text":"F. Leyvraz, G. Baez, R.A. Mendez-Sanchez, T.H.Seligman","submitted_at":"2000-05-26T15:42:37Z","abstract_excerpt":"We present a finite element algorithm that computes eigenvalues and eigenfunctions of the Laplace operator for two-dimensional problems with homogeneous Neumann or Dirichlet boundary conditions or combinations of either for different parts of the boundary. In order to solve the generalized eigenvalue problem, we use an inverse power plus Gauss-Seidel algorithm. For Neumann boundary conditions the method is much more efficient than the equivalent finite difference algorithm. We have cheked the algorithm comparing the cumulative level density of the espectrum obtained numerically, with the theor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0005057","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/nlin/0005057/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"nlin/0005057","created_at":"2026-06-03T22:06:22.423295+00:00"},{"alias_kind":"arxiv_version","alias_value":"nlin/0005057v1","created_at":"2026-06-03T22:06:22.423295+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.nlin/0005057","created_at":"2026-06-03T22:06:22.423295+00:00"},{"alias_kind":"pith_short_12","alias_value":"A63YTXWQZM43","created_at":"2026-06-03T22:06:22.423295+00:00"},{"alias_kind":"pith_short_16","alias_value":"A63YTXWQZM434GIX","created_at":"2026-06-03T22:06:22.423295+00:00"},{"alias_kind":"pith_short_8","alias_value":"A63YTXWQ","created_at":"2026-06-03T22:06:22.423295+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/A63YTXWQZM434GIX5RQMO4YAFG","json":"https://pith.science/pith/A63YTXWQZM434GIX5RQMO4YAFG.json","graph_json":"https://pith.science/api/pith-number/A63YTXWQZM434GIX5RQMO4YAFG/graph.json","events_json":"https://pith.science/api/pith-number/A63YTXWQZM434GIX5RQMO4YAFG/events.json","paper":"https://pith.science/paper/A63YTXWQ"},"agent_actions":{"view_html":"https://pith.science/pith/A63YTXWQZM434GIX5RQMO4YAFG","download_json":"https://pith.science/pith/A63YTXWQZM434GIX5RQMO4YAFG.json","view_paper":"https://pith.science/paper/A63YTXWQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=nlin/0005057&json=true","fetch_graph":"https://pith.science/api/pith-number/A63YTXWQZM434GIX5RQMO4YAFG/graph.json","fetch_events":"https://pith.science/api/pith-number/A63YTXWQZM434GIX5RQMO4YAFG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/A63YTXWQZM434GIX5RQMO4YAFG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/A63YTXWQZM434GIX5RQMO4YAFG/action/storage_attestation","attest_author":"https://pith.science/pith/A63YTXWQZM434GIX5RQMO4YAFG/action/author_attestation","sign_citation":"https://pith.science/pith/A63YTXWQZM434GIX5RQMO4YAFG/action/citation_signature","submit_replication":"https://pith.science/pith/A63YTXWQZM434GIX5RQMO4YAFG/action/replication_record"}},"created_at":"2026-06-03T22:06:22.423295+00:00","updated_at":"2026-06-03T22:06:22.423295+00:00"}