{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:NJYK5E4CVJSYP3PTV6PHQPJSJG","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":"0aa8d7d85edf8a09ce00a8e734fc17b0bf8401eea5cb78e1a0d27f082ea75129","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-12-11T19:43:38Z","title_canon_sha256":"8c1081ced61ae9e2dde012d7e879f1e56ebfff5237796e728c446caf5773734b"},"schema_version":"1.0","source":{"id":"1312.3290","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.3290","created_at":"2026-05-18T02:32:38Z"},{"alias_kind":"arxiv_version","alias_value":"1312.3290v1","created_at":"2026-05-18T02:32:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.3290","created_at":"2026-05-18T02:32:38Z"},{"alias_kind":"pith_short_12","alias_value":"NJYK5E4CVJSY","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"NJYK5E4CVJSYP3PT","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"NJYK5E4C","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:c5a8a69871add235baac994184824e20a27f20f5c432f8bf09192e73d1e70ea8","target":"graph","created_at":"2026-05-18T02:32:38Z","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"},"paper":{"abstract_excerpt":"We study the complexity of Banach space valued integration in the randomized setting. We are concerned with $r$-times continuously differentiable functions on the $d$-dimensional unit cube $Q$, with values in a Banach space $X$, and investigate the relation of the optimal convergence rate to the geometry of $X$. It turns out that the $n$-th minimal errors are bounded by $cn^{-r/d-1+1/p}$ if and only if $X$ is of equal norm type $p$.","authors_text":"Aicke Hinrichs, Stefan Heinrich","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-12-11T19:43:38Z","title":"On the randomized complexity of Banach space valued integration"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.3290","kind":"arxiv","version":1},"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":"sha256:2ee54ff675804f18c5965f271d7696f2fe34a002d548e6d93a4f68d875703f4a","target":"record","created_at":"2026-05-18T02:32:38Z","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":"0aa8d7d85edf8a09ce00a8e734fc17b0bf8401eea5cb78e1a0d27f082ea75129","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-12-11T19:43:38Z","title_canon_sha256":"8c1081ced61ae9e2dde012d7e879f1e56ebfff5237796e728c446caf5773734b"},"schema_version":"1.0","source":{"id":"1312.3290","kind":"arxiv","version":1}},"canonical_sha256":"6a70ae9382aa6587edf3af9e783d3249946f9cb85f4de5265a5315f97cea8b1b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6a70ae9382aa6587edf3af9e783d3249946f9cb85f4de5265a5315f97cea8b1b","first_computed_at":"2026-05-18T02:32:38.954941Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:32:38.954941Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qdCyZ85Y3kvCTKyycH29W7TYX9dlJcgbPvhisVFPfSkQp+F/ibLIqeZ6WVFbNZx/096p2ry81SNazFcmmKIxDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:32:38.955489Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.3290","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2ee54ff675804f18c5965f271d7696f2fe34a002d548e6d93a4f68d875703f4a","sha256:c5a8a69871add235baac994184824e20a27f20f5c432f8bf09192e73d1e70ea8"],"state_sha256":"4edde4d67a4f3a6cbfcdce1c6d41238ee7c3ef16a03e78102728581fe9f336fb"}