{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:KAFHGDZMG3HUVVGS26HKX4W2KI","short_pith_number":"pith:KAFHGDZM","schema_version":"1.0","canonical_sha256":"500a730f2c36cf4ad4d2d78eabf2da521a7f26c233cc6f0e918aef7e9ec22183","source":{"kind":"arxiv","id":"1402.4911","version":1},"attestation_state":"computed","paper":{"title":"Finite element eigenvalue enclosures for the Maxwell operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"math.AP","authors_text":"Gabriel Ra\\'ul Barrenechea, Lyonell Boulton, Nabile Boussaid (LM-Besan\\c{c}on)","submitted_at":"2014-02-20T07:13:49Z","abstract_excerpt":"We propose employing the extension of the Lehmann-Maehly-Goerisch method developed by Zimmermann and Mertins, as a highly effective tool for the pollution-free finite element computation of the eigenfrequencies of the resonant cavity problem on a bounded region. This method gives complementary bounds for the eigenfrequencies which are adjacent to a given real parameter. We present a concrete numerical scheme which provides certified enclosures in a suitable asymptotic regime. We illustrate the applicability of this scheme by means of some numerical experiments on benchmark data using Lagrange "},"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":"1402.4911","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-02-20T07:13:49Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"7189ead539984bd3addeec13daa0e04d0392985a73885e4d964a7778b0b0dede","abstract_canon_sha256":"aca2f8811ad987e57deb1be4a6dfa8453094859925429d2a04d9ce6623fd3e02"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:57:25.987536Z","signature_b64":"qUW43/Mh+oLDmwcz/GuOebsgCXCkxs69F4uY8Gxg1pHB+D7j7RdjtQJxTP+Kiqzj6cN/5aeUzk9OGyPgaQPXDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"500a730f2c36cf4ad4d2d78eabf2da521a7f26c233cc6f0e918aef7e9ec22183","last_reissued_at":"2026-05-18T02:57:25.987033Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:57:25.987033Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Finite element eigenvalue enclosures for the Maxwell operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"math.AP","authors_text":"Gabriel Ra\\'ul Barrenechea, Lyonell Boulton, Nabile Boussaid (LM-Besan\\c{c}on)","submitted_at":"2014-02-20T07:13:49Z","abstract_excerpt":"We propose employing the extension of the Lehmann-Maehly-Goerisch method developed by Zimmermann and Mertins, as a highly effective tool for the pollution-free finite element computation of the eigenfrequencies of the resonant cavity problem on a bounded region. This method gives complementary bounds for the eigenfrequencies which are adjacent to a given real parameter. We present a concrete numerical scheme which provides certified enclosures in a suitable asymptotic regime. We illustrate the applicability of this scheme by means of some numerical experiments on benchmark data using Lagrange "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.4911","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":"1402.4911","created_at":"2026-05-18T02:57:25.987108+00:00"},{"alias_kind":"arxiv_version","alias_value":"1402.4911v1","created_at":"2026-05-18T02:57:25.987108+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.4911","created_at":"2026-05-18T02:57:25.987108+00:00"},{"alias_kind":"pith_short_12","alias_value":"KAFHGDZMG3HU","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_16","alias_value":"KAFHGDZMG3HUVVGS","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_8","alias_value":"KAFHGDZM","created_at":"2026-05-18T12:28:35.611951+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/KAFHGDZMG3HUVVGS26HKX4W2KI","json":"https://pith.science/pith/KAFHGDZMG3HUVVGS26HKX4W2KI.json","graph_json":"https://pith.science/api/pith-number/KAFHGDZMG3HUVVGS26HKX4W2KI/graph.json","events_json":"https://pith.science/api/pith-number/KAFHGDZMG3HUVVGS26HKX4W2KI/events.json","paper":"https://pith.science/paper/KAFHGDZM"},"agent_actions":{"view_html":"https://pith.science/pith/KAFHGDZMG3HUVVGS26HKX4W2KI","download_json":"https://pith.science/pith/KAFHGDZMG3HUVVGS26HKX4W2KI.json","view_paper":"https://pith.science/paper/KAFHGDZM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1402.4911&json=true","fetch_graph":"https://pith.science/api/pith-number/KAFHGDZMG3HUVVGS26HKX4W2KI/graph.json","fetch_events":"https://pith.science/api/pith-number/KAFHGDZMG3HUVVGS26HKX4W2KI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KAFHGDZMG3HUVVGS26HKX4W2KI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KAFHGDZMG3HUVVGS26HKX4W2KI/action/storage_attestation","attest_author":"https://pith.science/pith/KAFHGDZMG3HUVVGS26HKX4W2KI/action/author_attestation","sign_citation":"https://pith.science/pith/KAFHGDZMG3HUVVGS26HKX4W2KI/action/citation_signature","submit_replication":"https://pith.science/pith/KAFHGDZMG3HUVVGS26HKX4W2KI/action/replication_record"}},"created_at":"2026-05-18T02:57:25.987108+00:00","updated_at":"2026-05-18T02:57:25.987108+00:00"}