{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:2APC2SP65I4B42B747U24MR4UU","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":"7376942ac3141554ad2db2073aef7cbfce6fc46314c938e0b29eb15c082f5bb4","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.NA","submitted_at":"2012-11-20T07:45:16Z","title_canon_sha256":"6da96d00e071208c60c90d23da0c5912ecf83d79e1fa03f66a177eb019aca93d"},"schema_version":"1.0","source":{"id":"1211.4677","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.4677","created_at":"2026-05-18T03:17:24Z"},{"alias_kind":"arxiv_version","alias_value":"1211.4677v2","created_at":"2026-05-18T03:17:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.4677","created_at":"2026-05-18T03:17:24Z"},{"alias_kind":"pith_short_12","alias_value":"2APC2SP65I4B","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"2APC2SP65I4B42B7","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"2APC2SP6","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:15883b40211e79ae9e88faa7815d3c4c91947958a2bd33fb4dd801134a398b73","target":"graph","created_at":"2026-05-18T03:17:24Z","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":"This paper is devoted to the $L^2$ norm error estimate of the Adini element for the biharmonic equation. Surprisingly, a lower bound is established which proves that the $ L^2$ norm convergence rate can not be higher than that in the energy norm. This proves the conjecture of [Lascaux and Lesaint, Some nonconforming finite elements for the plate bending problem, RAIRO Anal. Numer. 9 (1975), pp. 9--53.] that the convergence rates in both $L^2$ and $H^1$ norms can not be higher than that in the energy norm for this element.","authors_text":"Jun Hu, Zhongci Shi","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.NA","submitted_at":"2012-11-20T07:45:16Z","title":"The lower bound of the error estimate in the L2 norm for the Adini element of the biharmonic equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.4677","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:ba94ef67773e56966e10a73db8a70561e7c3aa5aebb5ea2ad6fe9c60bdd3140d","target":"record","created_at":"2026-05-18T03:17:24Z","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":"7376942ac3141554ad2db2073aef7cbfce6fc46314c938e0b29eb15c082f5bb4","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.NA","submitted_at":"2012-11-20T07:45:16Z","title_canon_sha256":"6da96d00e071208c60c90d23da0c5912ecf83d79e1fa03f66a177eb019aca93d"},"schema_version":"1.0","source":{"id":"1211.4677","kind":"arxiv","version":2}},"canonical_sha256":"d01e2d49feea381e683fe7e9ae323ca5357121c6266a3e41f6b0a273991939d1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d01e2d49feea381e683fe7e9ae323ca5357121c6266a3e41f6b0a273991939d1","first_computed_at":"2026-05-18T03:17:24.733670Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:17:24.733670Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7DIDTS9fOGm9NR9sMPt2g9MD/H3Hk6vSBCtpRqRnT6G1oqQxsrFbKv/fC85ObQe2/hoKmkICBEiE5PmUAkPVAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:17:24.734133Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.4677","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba94ef67773e56966e10a73db8a70561e7c3aa5aebb5ea2ad6fe9c60bdd3140d","sha256:15883b40211e79ae9e88faa7815d3c4c91947958a2bd33fb4dd801134a398b73"],"state_sha256":"ed3dbb2be4c0ef49a9f828867234ebe58738dc18730d4efded2016f7f0e92ef0"}