{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:SAY3PDUEE6TS4EQTUZLS2NCKN2","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":"30360416d2614f106fd51492d780b65823201fcb5eafca4852da91224cd020fc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-12-04T12:22:50Z","title_canon_sha256":"90ffd51cd6708e9c3bb914fec19670b9c506b96aa306b8b7b77b664af9c80559"},"schema_version":"1.0","source":{"id":"1312.1135","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.1135","created_at":"2026-05-18T02:56:34Z"},{"alias_kind":"arxiv_version","alias_value":"1312.1135v2","created_at":"2026-05-18T02:56:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.1135","created_at":"2026-05-18T02:56:34Z"},{"alias_kind":"pith_short_12","alias_value":"SAY3PDUEE6TS","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"SAY3PDUEE6TS4EQT","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"SAY3PDUE","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:98ccea8f536d5855831f29f8dffd794dcd9931c13df92f19a31c1f6d2361ae52","target":"graph","created_at":"2026-05-18T02:56:34Z","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 introduce quasi-Monte Carlo rules for the numerical integration of functions $f$ defined on $[0,1]^s$, $s \\ge 1$, which satisfy the following properties: the Fourier-, Fourier cosine- or Walsh coefficients of $f$ are absolutely summable and $f$ satisfies a H\\\"older condition of order $\\alpha$, for some $0 < \\alpha \\le 1$. We show a convergent rate of the integration error of order $\\max((s-1) N^{-1/2}, s^{\\alpha/2} N^{-\\alpha} )$. The construction of the quadrature points is explicit and is based on Weil sums.","authors_text":"Josef Dick","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-12-04T12:22:50Z","title":"Numerical integration of H\\\"older continuous, absolutely convergent Fourier-, Fourier cosine-, and Walsh series"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1135","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:b46b69361c0cce4902a3d2651b55a26650c334c6909a353fcd0df73c1638c688","target":"record","created_at":"2026-05-18T02:56:34Z","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":"30360416d2614f106fd51492d780b65823201fcb5eafca4852da91224cd020fc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-12-04T12:22:50Z","title_canon_sha256":"90ffd51cd6708e9c3bb914fec19670b9c506b96aa306b8b7b77b664af9c80559"},"schema_version":"1.0","source":{"id":"1312.1135","kind":"arxiv","version":2}},"canonical_sha256":"9031b78e8427a72e1213a6572d344a6e82f430ee55fbc1f5fd617009097f9f06","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9031b78e8427a72e1213a6572d344a6e82f430ee55fbc1f5fd617009097f9f06","first_computed_at":"2026-05-18T02:56:34.819583Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:56:34.819583Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fB9rSR43hprCQCBXpCB6jboT9wLNSo0Ou6k0JyLaUJFyWqLl89CvpO3dnUG8eWd85TYOWnMVimfOsa/QxQ1MDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:56:34.821002Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.1135","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b46b69361c0cce4902a3d2651b55a26650c334c6909a353fcd0df73c1638c688","sha256:98ccea8f536d5855831f29f8dffd794dcd9931c13df92f19a31c1f6d2361ae52"],"state_sha256":"c0b65183953bc67bc4130a554131ed35b01d46da3534cd032cf0654f2c60ddfe"}