{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:KUIJBM4RMGLJVWRLGO7H7XSIZK","short_pith_number":"pith:KUIJBM4R","canonical_record":{"source":{"id":"1005.5575","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-05-31T03:39:06Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"7886e43612629365213f86724bf7cc7158377ef0ae655ae754e3bfa5162bc17b","abstract_canon_sha256":"c3e90058102018b3fdbb322a4bfe2655a43fc475466b501e69ad1c62706971f7"},"schema_version":"1.0"},"canonical_sha256":"551090b39161969ada2b33be7fde48cab559fc30b1f33c995f80fe704ad6c80c","source":{"kind":"arxiv","id":"1005.5575","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.5575","created_at":"2026-05-18T04:34:27Z"},{"alias_kind":"arxiv_version","alias_value":"1005.5575v3","created_at":"2026-05-18T04:34:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.5575","created_at":"2026-05-18T04:34:27Z"},{"alias_kind":"pith_short_12","alias_value":"KUIJBM4RMGLJ","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"KUIJBM4RMGLJVWRL","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"KUIJBM4R","created_at":"2026-05-18T12:26:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:KUIJBM4RMGLJVWRLGO7H7XSIZK","target":"record","payload":{"canonical_record":{"source":{"id":"1005.5575","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-05-31T03:39:06Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"7886e43612629365213f86724bf7cc7158377ef0ae655ae754e3bfa5162bc17b","abstract_canon_sha256":"c3e90058102018b3fdbb322a4bfe2655a43fc475466b501e69ad1c62706971f7"},"schema_version":"1.0"},"canonical_sha256":"551090b39161969ada2b33be7fde48cab559fc30b1f33c995f80fe704ad6c80c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:34:27.475368Z","signature_b64":"WH/Hwvg+/5FU5dFdP/qI+hx1ywBTXz4eI+O5npXXOBtjNdIAH2YrTiet7O2OkxhCpML7QeCIh1IgzEV8xV6fAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"551090b39161969ada2b33be7fde48cab559fc30b1f33c995f80fe704ad6c80c","last_reissued_at":"2026-05-18T04:34:27.474727Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:34:27.474727Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1005.5575","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:34:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EHx68K2lorqL5hRZhf9xfNxqd93vEx+OiTJigobErdBYYJFuIEEXcE2Q9rYkk9D+n0qi5Kjk1dHLP6SOcHRZAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T14:59:39.415625Z"},"content_sha256":"87465597fdce3e34c1626eb5cc128eb81dc3da210ab0ae1b114972888e27d5fb","schema_version":"1.0","event_id":"sha256:87465597fdce3e34c1626eb5cc128eb81dc3da210ab0ae1b114972888e27d5fb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:KUIJBM4RMGLJVWRLGO7H7XSIZK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Error bounds for quasi-Monte Carlo integration for \\mathscr{L}^{\\infty} with uniform point sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"math.NT","authors_text":"Su Hu, Yan Li","submitted_at":"2010-05-31T03:39:06Z","abstract_excerpt":"Niederreiter [H.Niederreiter, Error bounds for quasi-Monte Carlo integration with uniform point sets, Journal of computational and applied mathematics 150 (2003), 283-292] established new bounds for quasi-Monte Carlo integration for nodes sets with a special kind of uniformity property. Let (X,\\mathscr{A},\\mu) be an arbitrary probability space, i.e., X is an arbitrary nonempty set, \\mathscr{A} a \\sigma-algebra of subsets of X, and \\mu a probability measure defined on \\mathscr{A}. The functions considered in Niederreiter's paper are bounded \\mu-integrable functions on X. In this note, we extend"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.5575","kind":"arxiv","version":3},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:34:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mk/+sHmkIIry+7kQQ2/Ccs6J88p09QWOQ0r4bLGpOL5x+delG0Hd0Kkfesb2nMyVp2iT2UOALqTulDyqhixJAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T14:59:39.415968Z"},"content_sha256":"549c70a71e6743f61494247a8d7faa1a1dcc2b4bd937dc4e03394fee370ed8ae","schema_version":"1.0","event_id":"sha256:549c70a71e6743f61494247a8d7faa1a1dcc2b4bd937dc4e03394fee370ed8ae"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KUIJBM4RMGLJVWRLGO7H7XSIZK/bundle.json","state_url":"https://pith.science/pith/KUIJBM4RMGLJVWRLGO7H7XSIZK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KUIJBM4RMGLJVWRLGO7H7XSIZK/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-08T14:59:39Z","links":{"resolver":"https://pith.science/pith/KUIJBM4RMGLJVWRLGO7H7XSIZK","bundle":"https://pith.science/pith/KUIJBM4RMGLJVWRLGO7H7XSIZK/bundle.json","state":"https://pith.science/pith/KUIJBM4RMGLJVWRLGO7H7XSIZK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KUIJBM4RMGLJVWRLGO7H7XSIZK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:KUIJBM4RMGLJVWRLGO7H7XSIZK","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":"c3e90058102018b3fdbb322a4bfe2655a43fc475466b501e69ad1c62706971f7","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-05-31T03:39:06Z","title_canon_sha256":"7886e43612629365213f86724bf7cc7158377ef0ae655ae754e3bfa5162bc17b"},"schema_version":"1.0","source":{"id":"1005.5575","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.5575","created_at":"2026-05-18T04:34:27Z"},{"alias_kind":"arxiv_version","alias_value":"1005.5575v3","created_at":"2026-05-18T04:34:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.5575","created_at":"2026-05-18T04:34:27Z"},{"alias_kind":"pith_short_12","alias_value":"KUIJBM4RMGLJ","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"KUIJBM4RMGLJVWRL","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"KUIJBM4R","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:549c70a71e6743f61494247a8d7faa1a1dcc2b4bd937dc4e03394fee370ed8ae","target":"graph","created_at":"2026-05-18T04:34:27Z","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":"Niederreiter [H.Niederreiter, Error bounds for quasi-Monte Carlo integration with uniform point sets, Journal of computational and applied mathematics 150 (2003), 283-292] established new bounds for quasi-Monte Carlo integration for nodes sets with a special kind of uniformity property. Let (X,\\mathscr{A},\\mu) be an arbitrary probability space, i.e., X is an arbitrary nonempty set, \\mathscr{A} a \\sigma-algebra of subsets of X, and \\mu a probability measure defined on \\mathscr{A}. The functions considered in Niederreiter's paper are bounded \\mu-integrable functions on X. In this note, we extend","authors_text":"Su Hu, Yan Li","cross_cats":["math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-05-31T03:39:06Z","title":"Error bounds for quasi-Monte Carlo integration for \\mathscr{L}^{\\infty} with uniform point sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.5575","kind":"arxiv","version":3},"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":"sha256:87465597fdce3e34c1626eb5cc128eb81dc3da210ab0ae1b114972888e27d5fb","target":"record","created_at":"2026-05-18T04:34:27Z","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":"c3e90058102018b3fdbb322a4bfe2655a43fc475466b501e69ad1c62706971f7","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-05-31T03:39:06Z","title_canon_sha256":"7886e43612629365213f86724bf7cc7158377ef0ae655ae754e3bfa5162bc17b"},"schema_version":"1.0","source":{"id":"1005.5575","kind":"arxiv","version":3}},"canonical_sha256":"551090b39161969ada2b33be7fde48cab559fc30b1f33c995f80fe704ad6c80c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"551090b39161969ada2b33be7fde48cab559fc30b1f33c995f80fe704ad6c80c","first_computed_at":"2026-05-18T04:34:27.474727Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:34:27.474727Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WH/Hwvg+/5FU5dFdP/qI+hx1ywBTXz4eI+O5npXXOBtjNdIAH2YrTiet7O2OkxhCpML7QeCIh1IgzEV8xV6fAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:34:27.475368Z","signed_message":"canonical_sha256_bytes"},"source_id":"1005.5575","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:87465597fdce3e34c1626eb5cc128eb81dc3da210ab0ae1b114972888e27d5fb","sha256:549c70a71e6743f61494247a8d7faa1a1dcc2b4bd937dc4e03394fee370ed8ae"],"state_sha256":"e66c7bfcd9acfa6bc178aae7e0a2d51aecd9a63ab6181ebbde7e00b042664bd3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3JAkwgHg2NIEuFAz6R4OozepHpkfQ07qsgZQV9EzDKJpQFDv9ZDmgqXzH7A3ARDocqvifviS3RySj9ZyCnb2CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T14:59:39.417812Z","bundle_sha256":"bdb0509622c335a3eaeaa042420659140a4661b907e94074fb955fbbc4cf43b4"}}