{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:S3Y22NPE3WYUNV6PKC2YY6X4BS","short_pith_number":"pith:S3Y22NPE","schema_version":"1.0","canonical_sha256":"96f1ad35e4ddb146d7cf50b58c7afc0cb89d0626a22ddafaefd3148e7688ac12","source":{"kind":"arxiv","id":"1406.6520","version":1},"attestation_state":"computed","paper":{"title":"Guaranteed Lower and upper bounds for eigenvalues of second order elliptic operators in any dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Jun Hu, Rui Ma","submitted_at":"2014-06-25T10:44:18Z","abstract_excerpt":"In this paper, a new method is proposed to produce guaranteed lower bounds for eigenvalues of general second order elliptic operators in any dimension. Unlike most methods in the literature, the proposed method only needs to solve one discrete eigenvalue problem but not involves any base or intermediate eigenvalue problems, and does not need any a priori information concerning exact eigenvalues either. Moreover, it just assumes basic regularity of exact eigenfunctions. This method is defined by a novel generalized Crouzeix-Raviart element which is proved to yield asymptotic lower bounds for ei"},"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":"1406.6520","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-06-25T10:44:18Z","cross_cats_sorted":[],"title_canon_sha256":"58e789404ba0faeb0561f107edc29e1a5639c326c61e9e71c78ff8c6448c6901","abstract_canon_sha256":"c509d0c2e9eae1af2ddaad6048c69ae82a06227750468e652dfad719f9dfa047"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:49:02.679766Z","signature_b64":"+zikIGLpf00+U5l8ZNZjDJcU2r5ZF5WGnSUfy9Dvfi2N/DEky1HP3gNRyUA0g5obaeFG0/aS2Yh9jt4Cq5aeAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"96f1ad35e4ddb146d7cf50b58c7afc0cb89d0626a22ddafaefd3148e7688ac12","last_reissued_at":"2026-05-18T02:49:02.679263Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:49:02.679263Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Guaranteed Lower and upper bounds for eigenvalues of second order elliptic operators in any dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Jun Hu, Rui Ma","submitted_at":"2014-06-25T10:44:18Z","abstract_excerpt":"In this paper, a new method is proposed to produce guaranteed lower bounds for eigenvalues of general second order elliptic operators in any dimension. Unlike most methods in the literature, the proposed method only needs to solve one discrete eigenvalue problem but not involves any base or intermediate eigenvalue problems, and does not need any a priori information concerning exact eigenvalues either. Moreover, it just assumes basic regularity of exact eigenfunctions. This method is defined by a novel generalized Crouzeix-Raviart element which is proved to yield asymptotic lower bounds for ei"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.6520","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":"1406.6520","created_at":"2026-05-18T02:49:02.679357+00:00"},{"alias_kind":"arxiv_version","alias_value":"1406.6520v1","created_at":"2026-05-18T02:49:02.679357+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.6520","created_at":"2026-05-18T02:49:02.679357+00:00"},{"alias_kind":"pith_short_12","alias_value":"S3Y22NPE3WYU","created_at":"2026-05-18T12:28:46.137349+00:00"},{"alias_kind":"pith_short_16","alias_value":"S3Y22NPE3WYUNV6P","created_at":"2026-05-18T12:28:46.137349+00:00"},{"alias_kind":"pith_short_8","alias_value":"S3Y22NPE","created_at":"2026-05-18T12:28:46.137349+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/S3Y22NPE3WYUNV6PKC2YY6X4BS","json":"https://pith.science/pith/S3Y22NPE3WYUNV6PKC2YY6X4BS.json","graph_json":"https://pith.science/api/pith-number/S3Y22NPE3WYUNV6PKC2YY6X4BS/graph.json","events_json":"https://pith.science/api/pith-number/S3Y22NPE3WYUNV6PKC2YY6X4BS/events.json","paper":"https://pith.science/paper/S3Y22NPE"},"agent_actions":{"view_html":"https://pith.science/pith/S3Y22NPE3WYUNV6PKC2YY6X4BS","download_json":"https://pith.science/pith/S3Y22NPE3WYUNV6PKC2YY6X4BS.json","view_paper":"https://pith.science/paper/S3Y22NPE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1406.6520&json=true","fetch_graph":"https://pith.science/api/pith-number/S3Y22NPE3WYUNV6PKC2YY6X4BS/graph.json","fetch_events":"https://pith.science/api/pith-number/S3Y22NPE3WYUNV6PKC2YY6X4BS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/S3Y22NPE3WYUNV6PKC2YY6X4BS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/S3Y22NPE3WYUNV6PKC2YY6X4BS/action/storage_attestation","attest_author":"https://pith.science/pith/S3Y22NPE3WYUNV6PKC2YY6X4BS/action/author_attestation","sign_citation":"https://pith.science/pith/S3Y22NPE3WYUNV6PKC2YY6X4BS/action/citation_signature","submit_replication":"https://pith.science/pith/S3Y22NPE3WYUNV6PKC2YY6X4BS/action/replication_record"}},"created_at":"2026-05-18T02:49:02.679357+00:00","updated_at":"2026-05-18T02:49:02.679357+00:00"}