{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:UXONIAK4SC4P6ZWWW5P5U6FU4P","short_pith_number":"pith:UXONIAK4","canonical_record":{"source":{"id":"1210.1846","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-10-06T08:52:01Z","cross_cats_sorted":[],"title_canon_sha256":"626957324ddaa370c044fefbf5d1c68ca555123267cdedf7182b462e2df88a9e","abstract_canon_sha256":"568abadb5bdbf5e79ad90a412392838dc24bd276cc6b1991f68bb80699bbcb07"},"schema_version":"1.0"},"canonical_sha256":"a5dcd4015c90b8ff66d6b75fda78b4e3d874d040a0120bce35434e4130c32a5f","source":{"kind":"arxiv","id":"1210.1846","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.1846","created_at":"2026-05-18T03:13:10Z"},{"alias_kind":"arxiv_version","alias_value":"1210.1846v2","created_at":"2026-05-18T03:13:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.1846","created_at":"2026-05-18T03:13:10Z"},{"alias_kind":"pith_short_12","alias_value":"UXONIAK4SC4P","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"UXONIAK4SC4P6ZWW","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"UXONIAK4","created_at":"2026-05-18T12:27:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:UXONIAK4SC4P6ZWWW5P5U6FU4P","target":"record","payload":{"canonical_record":{"source":{"id":"1210.1846","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-10-06T08:52:01Z","cross_cats_sorted":[],"title_canon_sha256":"626957324ddaa370c044fefbf5d1c68ca555123267cdedf7182b462e2df88a9e","abstract_canon_sha256":"568abadb5bdbf5e79ad90a412392838dc24bd276cc6b1991f68bb80699bbcb07"},"schema_version":"1.0"},"canonical_sha256":"a5dcd4015c90b8ff66d6b75fda78b4e3d874d040a0120bce35434e4130c32a5f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:13:10.754264Z","signature_b64":"xvIrE5YsTvaAAng2O/bpzanZ+10BXzC3iXvtpmSb+Pet/Yk9iWOT1iHDAUDo+2NW/S4ADeulrLnA8PeoJO5XCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a5dcd4015c90b8ff66d6b75fda78b4e3d874d040a0120bce35434e4130c32a5f","last_reissued_at":"2026-05-18T03:13:10.753611Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:13:10.753611Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.1846","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:13:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UHIKxBMgsAWaLL47KrvKP+1IZM2KYF66eOHLR8ZRRpIppijKkxfDEiDs3D17fKiC3MklNoI3T0+hSjHm0y5JAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T19:11:25.463786Z"},"content_sha256":"af607f9adc268cf146d70600d3e338a8c5591a3ebafea17df09806133e971c78","schema_version":"1.0","event_id":"sha256:af607f9adc268cf146d70600d3e338a8c5591a3ebafea17df09806133e971c78"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:UXONIAK4SC4P6ZWWW5P5U6FU4P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Convergence Rate and Quasi-Optimal Complexity of Adaptive Finite Element Computations for Multiple Eigenvalues","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Aihui Zhou, Lianhua He, Xiaoying Dai","submitted_at":"2012-10-06T08:52:01Z","abstract_excerpt":"In this paper, we study an adaptive finite element method for multiple eigenvalue problems of a class of second order elliptic equations. By using some eigenspace approximation technology and its crucial property which is also presented in this paper, we extend the results in \\cite{dai-xu-zhou08} to multiple eigenvalue problems, we obtain both convergence rate and quasi-optimal complexity of the adaptive finite element eigenvalue approximation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.1846","kind":"arxiv","version":2},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:13:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"borYPcSqmXRpdttq3Ob9IpE0YIRKNL+24+MQUvq5EpPtEik8eUfviMJCPxu/8xfBnGfBqIfdog7Gyk8uQbI8DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T19:11:25.464124Z"},"content_sha256":"0d7c0fb4aeaa14562a8f38409e1d6ebfbff591500bc0f7c517cefad059fee9a2","schema_version":"1.0","event_id":"sha256:0d7c0fb4aeaa14562a8f38409e1d6ebfbff591500bc0f7c517cefad059fee9a2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UXONIAK4SC4P6ZWWW5P5U6FU4P/bundle.json","state_url":"https://pith.science/pith/UXONIAK4SC4P6ZWWW5P5U6FU4P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UXONIAK4SC4P6ZWWW5P5U6FU4P/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-24T19:11:25Z","links":{"resolver":"https://pith.science/pith/UXONIAK4SC4P6ZWWW5P5U6FU4P","bundle":"https://pith.science/pith/UXONIAK4SC4P6ZWWW5P5U6FU4P/bundle.json","state":"https://pith.science/pith/UXONIAK4SC4P6ZWWW5P5U6FU4P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UXONIAK4SC4P6ZWWW5P5U6FU4P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:UXONIAK4SC4P6ZWWW5P5U6FU4P","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"568abadb5bdbf5e79ad90a412392838dc24bd276cc6b1991f68bb80699bbcb07","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-10-06T08:52:01Z","title_canon_sha256":"626957324ddaa370c044fefbf5d1c68ca555123267cdedf7182b462e2df88a9e"},"schema_version":"1.0","source":{"id":"1210.1846","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.1846","created_at":"2026-05-18T03:13:10Z"},{"alias_kind":"arxiv_version","alias_value":"1210.1846v2","created_at":"2026-05-18T03:13:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.1846","created_at":"2026-05-18T03:13:10Z"},{"alias_kind":"pith_short_12","alias_value":"UXONIAK4SC4P","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"UXONIAK4SC4P6ZWW","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"UXONIAK4","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:0d7c0fb4aeaa14562a8f38409e1d6ebfbff591500bc0f7c517cefad059fee9a2","target":"graph","created_at":"2026-05-18T03:13:10Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper, we study an adaptive finite element method for multiple eigenvalue problems of a class of second order elliptic equations. By using some eigenspace approximation technology and its crucial property which is also presented in this paper, we extend the results in \\cite{dai-xu-zhou08} to multiple eigenvalue problems, we obtain both convergence rate and quasi-optimal complexity of the adaptive finite element eigenvalue approximation.","authors_text":"Aihui Zhou, Lianhua He, Xiaoying Dai","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-10-06T08:52:01Z","title":"Convergence Rate and Quasi-Optimal Complexity of Adaptive Finite Element Computations for Multiple Eigenvalues"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.1846","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:af607f9adc268cf146d70600d3e338a8c5591a3ebafea17df09806133e971c78","target":"record","created_at":"2026-05-18T03:13:10Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"568abadb5bdbf5e79ad90a412392838dc24bd276cc6b1991f68bb80699bbcb07","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-10-06T08:52:01Z","title_canon_sha256":"626957324ddaa370c044fefbf5d1c68ca555123267cdedf7182b462e2df88a9e"},"schema_version":"1.0","source":{"id":"1210.1846","kind":"arxiv","version":2}},"canonical_sha256":"a5dcd4015c90b8ff66d6b75fda78b4e3d874d040a0120bce35434e4130c32a5f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a5dcd4015c90b8ff66d6b75fda78b4e3d874d040a0120bce35434e4130c32a5f","first_computed_at":"2026-05-18T03:13:10.753611Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:13:10.753611Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xvIrE5YsTvaAAng2O/bpzanZ+10BXzC3iXvtpmSb+Pet/Yk9iWOT1iHDAUDo+2NW/S4ADeulrLnA8PeoJO5XCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:13:10.754264Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.1846","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:af607f9adc268cf146d70600d3e338a8c5591a3ebafea17df09806133e971c78","sha256:0d7c0fb4aeaa14562a8f38409e1d6ebfbff591500bc0f7c517cefad059fee9a2"],"state_sha256":"ec6741e25ed2af28a171859b214ba1cf5aa6f2077bbf3f8d7aa5f87877a3e93e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I5BXrsTSEMsmay3yWC1I34haJBvvS135kLad6bPCYpm+qbEX7O7GI40l6fCRXc8i5iJWsbhlY4cYNm7onO+4Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T19:11:25.466021Z","bundle_sha256":"7b412b2f175d2e9b9f1c55a6bcd7b96ceceb0b653dd59b76257730139e066545"}}