{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:GY5HOUZSMQKG4GLEVBGFUGVTGZ","short_pith_number":"pith:GY5HOUZS","schema_version":"1.0","canonical_sha256":"363a77533264146e1964a84c5a1ab336685f70cec6af579442d24f2696bef603","source":{"kind":"arxiv","id":"1908.05943","version":2},"attestation_state":"computed","paper":{"title":"Algorithms and Complexity for Functions on General Domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.NA"],"primary_cat":"math.NA","authors_text":"Erich Novak","submitted_at":"2019-08-16T12:07:35Z","abstract_excerpt":"Error bounds and complexity bounds in numerical analysis and information-based complexity are often proved for functions that are defined on very simple domains, such as a cube, a torus, or a sphere. We study optimal error bounds for the approximation or integration of functions defined on $D_d \\subset R^d$ and only assume that $D_d$ is a bounded Lipschitz domain. Some results are even more general. We study three different concepts to measure the complexity: order of convergence, asymptotic constant, and explicit uniform bounds, i.e., bounds that hold for all $n$ (number of pieces of informat"},"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":"1908.05943","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-08-16T12:07:35Z","cross_cats_sorted":["cs.CC","cs.NA"],"title_canon_sha256":"ad5af3eb4c3803d260893273ad139957820e03f17763642edbf4fa715b545cea","abstract_canon_sha256":"c3fce620ef3aa66cb831c93a881e80fb6945fc2048a9b4417b73ad7916c1564a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:33:02.731583Z","signature_b64":"6LlKJpWouk6muqt3FsQeEAFKlnKWJvj6TsC9y2EcE+P/NScrs0f5hpJr5g+DYAbigz5E9e6x4Uh0wF9tFcA/Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"363a77533264146e1964a84c5a1ab336685f70cec6af579442d24f2696bef603","last_reissued_at":"2026-07-05T00:33:02.731100Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:33:02.731100Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Algorithms and Complexity for Functions on General Domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.NA"],"primary_cat":"math.NA","authors_text":"Erich Novak","submitted_at":"2019-08-16T12:07:35Z","abstract_excerpt":"Error bounds and complexity bounds in numerical analysis and information-based complexity are often proved for functions that are defined on very simple domains, such as a cube, a torus, or a sphere. We study optimal error bounds for the approximation or integration of functions defined on $D_d \\subset R^d$ and only assume that $D_d$ is a bounded Lipschitz domain. Some results are even more general. We study three different concepts to measure the complexity: order of convergence, asymptotic constant, and explicit uniform bounds, i.e., bounds that hold for all $n$ (number of pieces of informat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.05943","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.05943/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1908.05943","created_at":"2026-07-05T00:33:02.731160+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.05943v2","created_at":"2026-07-05T00:33:02.731160+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.05943","created_at":"2026-07-05T00:33:02.731160+00:00"},{"alias_kind":"pith_short_12","alias_value":"GY5HOUZSMQKG","created_at":"2026-07-05T00:33:02.731160+00:00"},{"alias_kind":"pith_short_16","alias_value":"GY5HOUZSMQKG4GLE","created_at":"2026-07-05T00:33:02.731160+00:00"},{"alias_kind":"pith_short_8","alias_value":"GY5HOUZS","created_at":"2026-07-05T00:33:02.731160+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/GY5HOUZSMQKG4GLEVBGFUGVTGZ","json":"https://pith.science/pith/GY5HOUZSMQKG4GLEVBGFUGVTGZ.json","graph_json":"https://pith.science/api/pith-number/GY5HOUZSMQKG4GLEVBGFUGVTGZ/graph.json","events_json":"https://pith.science/api/pith-number/GY5HOUZSMQKG4GLEVBGFUGVTGZ/events.json","paper":"https://pith.science/paper/GY5HOUZS"},"agent_actions":{"view_html":"https://pith.science/pith/GY5HOUZSMQKG4GLEVBGFUGVTGZ","download_json":"https://pith.science/pith/GY5HOUZSMQKG4GLEVBGFUGVTGZ.json","view_paper":"https://pith.science/paper/GY5HOUZS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.05943&json=true","fetch_graph":"https://pith.science/api/pith-number/GY5HOUZSMQKG4GLEVBGFUGVTGZ/graph.json","fetch_events":"https://pith.science/api/pith-number/GY5HOUZSMQKG4GLEVBGFUGVTGZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GY5HOUZSMQKG4GLEVBGFUGVTGZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GY5HOUZSMQKG4GLEVBGFUGVTGZ/action/storage_attestation","attest_author":"https://pith.science/pith/GY5HOUZSMQKG4GLEVBGFUGVTGZ/action/author_attestation","sign_citation":"https://pith.science/pith/GY5HOUZSMQKG4GLEVBGFUGVTGZ/action/citation_signature","submit_replication":"https://pith.science/pith/GY5HOUZSMQKG4GLEVBGFUGVTGZ/action/replication_record"}},"created_at":"2026-07-05T00:33:02.731160+00:00","updated_at":"2026-07-05T00:33:02.731160+00:00"}