{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:WWX6N2Z5QYOSGCBY76CQ3JHE27","short_pith_number":"pith:WWX6N2Z5","schema_version":"1.0","canonical_sha256":"b5afe6eb3d861d230838ff850da4e4d7e9760dc044a4e068059359dae04c0af9","source":{"kind":"arxiv","id":"1201.1632","version":1},"attestation_state":"computed","paper":{"title":"Metric tensors for the interpolation error and its gradient in $L^p$ norm","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Hehu Xie, Xiaobo Yin","submitted_at":"2012-01-08T13:29:17Z","abstract_excerpt":"A uniform strategy to derive metric tensors in two spatial dimension for interpolation errors and their gradients in $L^p$ norm is presented. It generates anisotropic adaptive meshes as quasi-uniform ones in corresponding metric space, with the metric tensor being computed based on a posteriori error estimates in different norms. Numerical results show that the corresponding convergence rates are always optimal."},"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":"1201.1632","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.NA","submitted_at":"2012-01-08T13:29:17Z","cross_cats_sorted":[],"title_canon_sha256":"5ffdf88de37cece3de555f7d611fe60e0c9b1fdebc2b763d34f43bc0323956c0","abstract_canon_sha256":"467ac07a93b9a880c0d01f454d825051d022b9c59ab2a544ecabd220ad5c3caa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:05:02.921478Z","signature_b64":"CukcXX1PF6biAeGYV5A3UcjgGE8YftHtfUQRPMkIFGUyFvdUwCsdLj/syrvOvYxRan9SraFx6g6EiTWLI4IwBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b5afe6eb3d861d230838ff850da4e4d7e9760dc044a4e068059359dae04c0af9","last_reissued_at":"2026-05-18T04:05:02.920935Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:05:02.920935Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Metric tensors for the interpolation error and its gradient in $L^p$ norm","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Hehu Xie, Xiaobo Yin","submitted_at":"2012-01-08T13:29:17Z","abstract_excerpt":"A uniform strategy to derive metric tensors in two spatial dimension for interpolation errors and their gradients in $L^p$ norm is presented. It generates anisotropic adaptive meshes as quasi-uniform ones in corresponding metric space, with the metric tensor being computed based on a posteriori error estimates in different norms. Numerical results show that the corresponding convergence rates are always optimal."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.1632","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":"1201.1632","created_at":"2026-05-18T04:05:02.921020+00:00"},{"alias_kind":"arxiv_version","alias_value":"1201.1632v1","created_at":"2026-05-18T04:05:02.921020+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.1632","created_at":"2026-05-18T04:05:02.921020+00:00"},{"alias_kind":"pith_short_12","alias_value":"WWX6N2Z5QYOS","created_at":"2026-05-18T12:27:27.928770+00:00"},{"alias_kind":"pith_short_16","alias_value":"WWX6N2Z5QYOSGCBY","created_at":"2026-05-18T12:27:27.928770+00:00"},{"alias_kind":"pith_short_8","alias_value":"WWX6N2Z5","created_at":"2026-05-18T12:27:27.928770+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/WWX6N2Z5QYOSGCBY76CQ3JHE27","json":"https://pith.science/pith/WWX6N2Z5QYOSGCBY76CQ3JHE27.json","graph_json":"https://pith.science/api/pith-number/WWX6N2Z5QYOSGCBY76CQ3JHE27/graph.json","events_json":"https://pith.science/api/pith-number/WWX6N2Z5QYOSGCBY76CQ3JHE27/events.json","paper":"https://pith.science/paper/WWX6N2Z5"},"agent_actions":{"view_html":"https://pith.science/pith/WWX6N2Z5QYOSGCBY76CQ3JHE27","download_json":"https://pith.science/pith/WWX6N2Z5QYOSGCBY76CQ3JHE27.json","view_paper":"https://pith.science/paper/WWX6N2Z5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1201.1632&json=true","fetch_graph":"https://pith.science/api/pith-number/WWX6N2Z5QYOSGCBY76CQ3JHE27/graph.json","fetch_events":"https://pith.science/api/pith-number/WWX6N2Z5QYOSGCBY76CQ3JHE27/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WWX6N2Z5QYOSGCBY76CQ3JHE27/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WWX6N2Z5QYOSGCBY76CQ3JHE27/action/storage_attestation","attest_author":"https://pith.science/pith/WWX6N2Z5QYOSGCBY76CQ3JHE27/action/author_attestation","sign_citation":"https://pith.science/pith/WWX6N2Z5QYOSGCBY76CQ3JHE27/action/citation_signature","submit_replication":"https://pith.science/pith/WWX6N2Z5QYOSGCBY76CQ3JHE27/action/replication_record"}},"created_at":"2026-05-18T04:05:02.921020+00:00","updated_at":"2026-05-18T04:05:02.921020+00:00"}