{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:P5QDXAWJVXWSIDKTD3XDUECWO6","short_pith_number":"pith:P5QDXAWJ","schema_version":"1.0","canonical_sha256":"7f603b82c9aded240d531eee3a1056778732b75d8dc5b9658cfdf5c1d65faf98","source":{"kind":"arxiv","id":"1904.02084","version":1},"attestation_state":"computed","paper":{"title":"Optimal order finite difference approximation of generalized solutions to the biharmonic equation in a cube","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Endre S\\\"uli, Florian Schweiger, Stefan M\\\"uller","submitted_at":"2019-04-03T16:25:24Z","abstract_excerpt":"We prove an optimal order error bound in the discrete $H^2(\\Omega)$ norm for finite difference approximations of the first boundary-value problem for the biharmonic equation in $n$ space dimensions, with $n \\in \\{2,\\dots,7\\}$, whose generalized solution belongs to the Sobolev space $H^s(\\Omega) \\cap H^2_0(\\Omega)$, for $\\frac{1}{2} \\max(5,n) < s \\leq 4$, where $\\Omega = (0,1)^n$. The result extends the range of the Sobolev index $s$ in the best convergence results currently available in the literature to the maximal range admitted by the Sobolev embedding of $H^s(\\Omega)$ into $C(\\overline\\Ome"},"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":"1904.02084","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-04-03T16:25:24Z","cross_cats_sorted":[],"title_canon_sha256":"6904073c1d0edff3f6fedc6725b3e6a9cdf3ee71dc4403618826379cc3aa075e","abstract_canon_sha256":"71d861ba39f4fe5adde381543c224a271b87907730d451f83dea268cb68c41ad"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:28.503280Z","signature_b64":"TKfmuEUSQCjuigBShG8LZ6GzeFMPz2tDqkIrifciYAjB/9VGKwwXKVie5av/2JXkwkN5uDG82isu3lxVzQ/JDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7f603b82c9aded240d531eee3a1056778732b75d8dc5b9658cfdf5c1d65faf98","last_reissued_at":"2026-05-17T23:49:28.502805Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:28.502805Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Optimal order finite difference approximation of generalized solutions to the biharmonic equation in a cube","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Endre S\\\"uli, Florian Schweiger, Stefan M\\\"uller","submitted_at":"2019-04-03T16:25:24Z","abstract_excerpt":"We prove an optimal order error bound in the discrete $H^2(\\Omega)$ norm for finite difference approximations of the first boundary-value problem for the biharmonic equation in $n$ space dimensions, with $n \\in \\{2,\\dots,7\\}$, whose generalized solution belongs to the Sobolev space $H^s(\\Omega) \\cap H^2_0(\\Omega)$, for $\\frac{1}{2} \\max(5,n) < s \\leq 4$, where $\\Omega = (0,1)^n$. The result extends the range of the Sobolev index $s$ in the best convergence results currently available in the literature to the maximal range admitted by the Sobolev embedding of $H^s(\\Omega)$ into $C(\\overline\\Ome"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.02084","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":"1904.02084","created_at":"2026-05-17T23:49:28.502875+00:00"},{"alias_kind":"arxiv_version","alias_value":"1904.02084v1","created_at":"2026-05-17T23:49:28.502875+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.02084","created_at":"2026-05-17T23:49:28.502875+00:00"},{"alias_kind":"pith_short_12","alias_value":"P5QDXAWJVXWS","created_at":"2026-05-18T12:33:24.271573+00:00"},{"alias_kind":"pith_short_16","alias_value":"P5QDXAWJVXWSIDKT","created_at":"2026-05-18T12:33:24.271573+00:00"},{"alias_kind":"pith_short_8","alias_value":"P5QDXAWJ","created_at":"2026-05-18T12:33:24.271573+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/P5QDXAWJVXWSIDKTD3XDUECWO6","json":"https://pith.science/pith/P5QDXAWJVXWSIDKTD3XDUECWO6.json","graph_json":"https://pith.science/api/pith-number/P5QDXAWJVXWSIDKTD3XDUECWO6/graph.json","events_json":"https://pith.science/api/pith-number/P5QDXAWJVXWSIDKTD3XDUECWO6/events.json","paper":"https://pith.science/paper/P5QDXAWJ"},"agent_actions":{"view_html":"https://pith.science/pith/P5QDXAWJVXWSIDKTD3XDUECWO6","download_json":"https://pith.science/pith/P5QDXAWJVXWSIDKTD3XDUECWO6.json","view_paper":"https://pith.science/paper/P5QDXAWJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1904.02084&json=true","fetch_graph":"https://pith.science/api/pith-number/P5QDXAWJVXWSIDKTD3XDUECWO6/graph.json","fetch_events":"https://pith.science/api/pith-number/P5QDXAWJVXWSIDKTD3XDUECWO6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/P5QDXAWJVXWSIDKTD3XDUECWO6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/P5QDXAWJVXWSIDKTD3XDUECWO6/action/storage_attestation","attest_author":"https://pith.science/pith/P5QDXAWJVXWSIDKTD3XDUECWO6/action/author_attestation","sign_citation":"https://pith.science/pith/P5QDXAWJVXWSIDKTD3XDUECWO6/action/citation_signature","submit_replication":"https://pith.science/pith/P5QDXAWJVXWSIDKTD3XDUECWO6/action/replication_record"}},"created_at":"2026-05-17T23:49:28.502875+00:00","updated_at":"2026-05-17T23:49:28.502875+00:00"}