{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:GY5HOUZSMQKG4GLEVBGFUGVTGZ","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":"c3fce620ef3aa66cb831c93a881e80fb6945fc2048a9b4417b73ad7916c1564a","cross_cats_sorted":["cs.CC","cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-08-16T12:07:35Z","title_canon_sha256":"ad5af3eb4c3803d260893273ad139957820e03f17763642edbf4fa715b545cea"},"schema_version":"1.0","source":{"id":"1908.05943","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.05943","created_at":"2026-07-05T00:33:02Z"},{"alias_kind":"arxiv_version","alias_value":"1908.05943v2","created_at":"2026-07-05T00:33:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.05943","created_at":"2026-07-05T00:33:02Z"},{"alias_kind":"pith_short_12","alias_value":"GY5HOUZSMQKG","created_at":"2026-07-05T00:33:02Z"},{"alias_kind":"pith_short_16","alias_value":"GY5HOUZSMQKG4GLE","created_at":"2026-07-05T00:33:02Z"},{"alias_kind":"pith_short_8","alias_value":"GY5HOUZS","created_at":"2026-07-05T00:33:02Z"}],"graph_snapshots":[{"event_id":"sha256:e37d5bacfb00e34ab347b59f59dce615d4f584515d2007ffed8ca7a55259f5dd","target":"graph","created_at":"2026-07-05T00:33:02Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1908.05943/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Erich Novak","cross_cats":["cs.CC","cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-08-16T12:07:35Z","title":"Algorithms and Complexity for Functions on General Domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.05943","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":"sha256:15b9a54133d530178a8eeb1c870e6cd93c7568f1f093d1301b9648c32d92ba8c","target":"record","created_at":"2026-07-05T00:33:02Z","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":"c3fce620ef3aa66cb831c93a881e80fb6945fc2048a9b4417b73ad7916c1564a","cross_cats_sorted":["cs.CC","cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-08-16T12:07:35Z","title_canon_sha256":"ad5af3eb4c3803d260893273ad139957820e03f17763642edbf4fa715b545cea"},"schema_version":"1.0","source":{"id":"1908.05943","kind":"arxiv","version":2}},"canonical_sha256":"363a77533264146e1964a84c5a1ab336685f70cec6af579442d24f2696bef603","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"363a77533264146e1964a84c5a1ab336685f70cec6af579442d24f2696bef603","first_computed_at":"2026-07-05T00:33:02.731100Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:33:02.731100Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6LlKJpWouk6muqt3FsQeEAFKlnKWJvj6TsC9y2EcE+P/NScrs0f5hpJr5g+DYAbigz5E9e6x4Uh0wF9tFcA/Ag==","signature_status":"signed_v1","signed_at":"2026-07-05T00:33:02.731583Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.05943","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:15b9a54133d530178a8eeb1c870e6cd93c7568f1f093d1301b9648c32d92ba8c","sha256:e37d5bacfb00e34ab347b59f59dce615d4f584515d2007ffed8ca7a55259f5dd"],"state_sha256":"f334ab706e87bc5df4d1e965be8924303856b3b9e7b6d725dd4983eb152c8065"}