{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:CG6FDRDVVTYDHTGEO5KWFRG7RB","short_pith_number":"pith:CG6FDRDV","schema_version":"1.0","canonical_sha256":"11bc51c475acf033ccc4775562c4df887217ea5cb4476fc210cb24a0308d2d9e","source":{"kind":"arxiv","id":"1401.0372","version":1},"attestation_state":"computed","paper":{"title":"Is $2k$-Conjecture valid for finite volume methods?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Qingsong Zou, Waixiang Cao, Zhimin Zhang","submitted_at":"2014-01-02T06:43:44Z","abstract_excerpt":"This paper is concerned with superconvergence properties of a class of finite volume methods of arbitrary order over rectangular meshes. Our main result is to prove {\\it 2k-conjecture}: at each vertex of the underlying rectangular mesh, the bi-$k$ degree finite volume solution approximates the exact solution with an order\n  $ O(h^{2k})$, where $h$ is the mesh size. As byproducts, superconvergence properties for finite volume discretization errors at Lobatto and Gauss points are also obtained. All theoretical findings are confirmed by numerical experiments."},"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":"1401.0372","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-01-02T06:43:44Z","cross_cats_sorted":[],"title_canon_sha256":"acd34b9e68cc3e17324944e01d6d4255ce7f9c53a528305957c3d1b992c832e3","abstract_canon_sha256":"09f71772d964b7a813c6a57155df97f600ad8532bac457d66d1c8152cad6dd38"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:03:23.414887Z","signature_b64":"qiyAUVCIou+PWqSWgqXnbLMgV4rTR4ifJdWUO1No3KZOCFAsrT56Z9ymDCIooD0KwV7a/HOTMAT4AvlOKYdOAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"11bc51c475acf033ccc4775562c4df887217ea5cb4476fc210cb24a0308d2d9e","last_reissued_at":"2026-05-18T03:03:23.414231Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:03:23.414231Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Is $2k$-Conjecture valid for finite volume methods?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Qingsong Zou, Waixiang Cao, Zhimin Zhang","submitted_at":"2014-01-02T06:43:44Z","abstract_excerpt":"This paper is concerned with superconvergence properties of a class of finite volume methods of arbitrary order over rectangular meshes. Our main result is to prove {\\it 2k-conjecture}: at each vertex of the underlying rectangular mesh, the bi-$k$ degree finite volume solution approximates the exact solution with an order\n  $ O(h^{2k})$, where $h$ is the mesh size. As byproducts, superconvergence properties for finite volume discretization errors at Lobatto and Gauss points are also obtained. All theoretical findings are confirmed by numerical experiments."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0372","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":"1401.0372","created_at":"2026-05-18T03:03:23.414335+00:00"},{"alias_kind":"arxiv_version","alias_value":"1401.0372v1","created_at":"2026-05-18T03:03:23.414335+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.0372","created_at":"2026-05-18T03:03:23.414335+00:00"},{"alias_kind":"pith_short_12","alias_value":"CG6FDRDVVTYD","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_16","alias_value":"CG6FDRDVVTYDHTGE","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_8","alias_value":"CG6FDRDV","created_at":"2026-05-18T12:28:22.404517+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/CG6FDRDVVTYDHTGEO5KWFRG7RB","json":"https://pith.science/pith/CG6FDRDVVTYDHTGEO5KWFRG7RB.json","graph_json":"https://pith.science/api/pith-number/CG6FDRDVVTYDHTGEO5KWFRG7RB/graph.json","events_json":"https://pith.science/api/pith-number/CG6FDRDVVTYDHTGEO5KWFRG7RB/events.json","paper":"https://pith.science/paper/CG6FDRDV"},"agent_actions":{"view_html":"https://pith.science/pith/CG6FDRDVVTYDHTGEO5KWFRG7RB","download_json":"https://pith.science/pith/CG6FDRDVVTYDHTGEO5KWFRG7RB.json","view_paper":"https://pith.science/paper/CG6FDRDV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1401.0372&json=true","fetch_graph":"https://pith.science/api/pith-number/CG6FDRDVVTYDHTGEO5KWFRG7RB/graph.json","fetch_events":"https://pith.science/api/pith-number/CG6FDRDVVTYDHTGEO5KWFRG7RB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CG6FDRDVVTYDHTGEO5KWFRG7RB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CG6FDRDVVTYDHTGEO5KWFRG7RB/action/storage_attestation","attest_author":"https://pith.science/pith/CG6FDRDVVTYDHTGEO5KWFRG7RB/action/author_attestation","sign_citation":"https://pith.science/pith/CG6FDRDVVTYDHTGEO5KWFRG7RB/action/citation_signature","submit_replication":"https://pith.science/pith/CG6FDRDVVTYDHTGEO5KWFRG7RB/action/replication_record"}},"created_at":"2026-05-18T03:03:23.414335+00:00","updated_at":"2026-05-18T03:03:23.414335+00:00"}