{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:UYZAB4GOQCRUFLWRXWMY5GPPAB","short_pith_number":"pith:UYZAB4GO","schema_version":"1.0","canonical_sha256":"a63200f0ce80a342aed1bd998e99ef00798d83270444432117e818b7c9bc5f3e","source":{"kind":"arxiv","id":"1401.7086","version":1},"attestation_state":"computed","paper":{"title":"N derivatives are necessary for order N+1 convergence in quadrature: a converse result","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Jeffrey Tsang","submitted_at":"2014-01-28T05:14:00Z","abstract_excerpt":"Results on the error bounds of quadrature methods are well known - most state that if the method has degree N, and the integrand has N derivatives, then the error is order N+1. We prove here a converse: that if the integrand fails to have N derivatives, even only at a finite number of points, no method, regardless of its degree, can guarantee convergence more than order N. Even if the integrand fails to have N derivatives at just 3 (for even N, 2) points, no method can produce order more than N+1 convergence. This is done by an adversarial proof: we explicitly construct the functions that exhi"},"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":"1401.7086","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-01-28T05:14:00Z","cross_cats_sorted":[],"title_canon_sha256":"b1903212499357debf38061727fd689eb139a3cd2be9c95df1cbae4be8d48b0a","abstract_canon_sha256":"a04a96a37b37af70b391fa2d29a1b0bc63ec1d620b84442eb0df6d2f6172523c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:00:50.902672Z","signature_b64":"kzGeYFQKGu9c9zqMUsCLuMszt1ZQRYJE1YksdZWXd5lJ03D+UhzScjIEGuEFcQZfmq1PNMnmH8SCOuyj4JimDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a63200f0ce80a342aed1bd998e99ef00798d83270444432117e818b7c9bc5f3e","last_reissued_at":"2026-05-18T03:00:50.902154Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:00:50.902154Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"N derivatives are necessary for order N+1 convergence in quadrature: a converse result","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Jeffrey Tsang","submitted_at":"2014-01-28T05:14:00Z","abstract_excerpt":"Results on the error bounds of quadrature methods are well known - most state that if the method has degree N, and the integrand has N derivatives, then the error is order N+1. We prove here a converse: that if the integrand fails to have N derivatives, even only at a finite number of points, no method, regardless of its degree, can guarantee convergence more than order N. Even if the integrand fails to have N derivatives at just 3 (for even N, 2) points, no method can produce order more than N+1 convergence. This is done by an adversarial proof: we explicitly construct the functions that exhi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.7086","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":"1401.7086","created_at":"2026-05-18T03:00:50.902230+00:00"},{"alias_kind":"arxiv_version","alias_value":"1401.7086v1","created_at":"2026-05-18T03:00:50.902230+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.7086","created_at":"2026-05-18T03:00:50.902230+00:00"},{"alias_kind":"pith_short_12","alias_value":"UYZAB4GOQCRU","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_16","alias_value":"UYZAB4GOQCRUFLWR","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_8","alias_value":"UYZAB4GO","created_at":"2026-05-18T12:28:52.271510+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/UYZAB4GOQCRUFLWRXWMY5GPPAB","json":"https://pith.science/pith/UYZAB4GOQCRUFLWRXWMY5GPPAB.json","graph_json":"https://pith.science/api/pith-number/UYZAB4GOQCRUFLWRXWMY5GPPAB/graph.json","events_json":"https://pith.science/api/pith-number/UYZAB4GOQCRUFLWRXWMY5GPPAB/events.json","paper":"https://pith.science/paper/UYZAB4GO"},"agent_actions":{"view_html":"https://pith.science/pith/UYZAB4GOQCRUFLWRXWMY5GPPAB","download_json":"https://pith.science/pith/UYZAB4GOQCRUFLWRXWMY5GPPAB.json","view_paper":"https://pith.science/paper/UYZAB4GO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1401.7086&json=true","fetch_graph":"https://pith.science/api/pith-number/UYZAB4GOQCRUFLWRXWMY5GPPAB/graph.json","fetch_events":"https://pith.science/api/pith-number/UYZAB4GOQCRUFLWRXWMY5GPPAB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UYZAB4GOQCRUFLWRXWMY5GPPAB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UYZAB4GOQCRUFLWRXWMY5GPPAB/action/storage_attestation","attest_author":"https://pith.science/pith/UYZAB4GOQCRUFLWRXWMY5GPPAB/action/author_attestation","sign_citation":"https://pith.science/pith/UYZAB4GOQCRUFLWRXWMY5GPPAB/action/citation_signature","submit_replication":"https://pith.science/pith/UYZAB4GOQCRUFLWRXWMY5GPPAB/action/replication_record"}},"created_at":"2026-05-18T03:00:50.902230+00:00","updated_at":"2026-05-18T03:00:50.902230+00:00"}