{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:WWCX6TQYZZ55YGOO3FOMCSA4LJ","short_pith_number":"pith:WWCX6TQY","schema_version":"1.0","canonical_sha256":"b5857f4e18ce7bdc19ced95cc1481c5a4d725ed09cae6890221908d2316690ec","source":{"kind":"arxiv","id":"1705.03181","version":1},"attestation_state":"computed","paper":{"title":"Asymptotic Normality of Extensible Grid Sampling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.NA","authors_text":"Lingjiong Zhu, Zhijian He","submitted_at":"2017-05-09T05:26:57Z","abstract_excerpt":"Recently, He and Owen (2016) proposed the use of Hilbert's space filling curve (HSFC) in numerical integration as a way of reducing the dimension from $d>1$ to $d=1$. This paper studies the asymptotic normality of the HSFC-based estimate when using scrambled van der Corput sequence as input. We show that the estimate has an asymptotic normal distribution for functions in $C^1([0,1]^d)$, excluding the trivial case of constant functions. The asymptotic normality also holds for discontinuous functions under mild conditions. It was previously known only that scrambled $(0,m,d)$-net quadratures enj"},"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":"1705.03181","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-05-09T05:26:57Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"cd93ce1dec31d9e9da0461ca42f97b7bf2e6edd93fc689df9baf2e6d7c34c595","abstract_canon_sha256":"f09ada63b9ec582db5b90beed178e980ff9182a81da2ccb0729efb87cda4e48c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:34.633452Z","signature_b64":"Nb68FeHf3eyoKewaxozrTnoN8yixGwDRKp1enQQMjAuu6eBPbZfUYOQBUg3hofA8oCCAET2svf1DqVAUzUh9CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b5857f4e18ce7bdc19ced95cc1481c5a4d725ed09cae6890221908d2316690ec","last_reissued_at":"2026-05-17T23:51:34.632715Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:34.632715Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Asymptotic Normality of Extensible Grid Sampling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.NA","authors_text":"Lingjiong Zhu, Zhijian He","submitted_at":"2017-05-09T05:26:57Z","abstract_excerpt":"Recently, He and Owen (2016) proposed the use of Hilbert's space filling curve (HSFC) in numerical integration as a way of reducing the dimension from $d>1$ to $d=1$. This paper studies the asymptotic normality of the HSFC-based estimate when using scrambled van der Corput sequence as input. We show that the estimate has an asymptotic normal distribution for functions in $C^1([0,1]^d)$, excluding the trivial case of constant functions. The asymptotic normality also holds for discontinuous functions under mild conditions. It was previously known only that scrambled $(0,m,d)$-net quadratures enj"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.03181","kind":"arxiv","version":1},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1705.03181","created_at":"2026-05-17T23:51:34.632843+00:00"},{"alias_kind":"arxiv_version","alias_value":"1705.03181v1","created_at":"2026-05-17T23:51:34.632843+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.03181","created_at":"2026-05-17T23:51:34.632843+00:00"},{"alias_kind":"pith_short_12","alias_value":"WWCX6TQYZZ55","created_at":"2026-05-18T12:31:53.515858+00:00"},{"alias_kind":"pith_short_16","alias_value":"WWCX6TQYZZ55YGOO","created_at":"2026-05-18T12:31:53.515858+00:00"},{"alias_kind":"pith_short_8","alias_value":"WWCX6TQY","created_at":"2026-05-18T12:31:53.515858+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/WWCX6TQYZZ55YGOO3FOMCSA4LJ","json":"https://pith.science/pith/WWCX6TQYZZ55YGOO3FOMCSA4LJ.json","graph_json":"https://pith.science/api/pith-number/WWCX6TQYZZ55YGOO3FOMCSA4LJ/graph.json","events_json":"https://pith.science/api/pith-number/WWCX6TQYZZ55YGOO3FOMCSA4LJ/events.json","paper":"https://pith.science/paper/WWCX6TQY"},"agent_actions":{"view_html":"https://pith.science/pith/WWCX6TQYZZ55YGOO3FOMCSA4LJ","download_json":"https://pith.science/pith/WWCX6TQYZZ55YGOO3FOMCSA4LJ.json","view_paper":"https://pith.science/paper/WWCX6TQY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1705.03181&json=true","fetch_graph":"https://pith.science/api/pith-number/WWCX6TQYZZ55YGOO3FOMCSA4LJ/graph.json","fetch_events":"https://pith.science/api/pith-number/WWCX6TQYZZ55YGOO3FOMCSA4LJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WWCX6TQYZZ55YGOO3FOMCSA4LJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WWCX6TQYZZ55YGOO3FOMCSA4LJ/action/storage_attestation","attest_author":"https://pith.science/pith/WWCX6TQYZZ55YGOO3FOMCSA4LJ/action/author_attestation","sign_citation":"https://pith.science/pith/WWCX6TQYZZ55YGOO3FOMCSA4LJ/action/citation_signature","submit_replication":"https://pith.science/pith/WWCX6TQYZZ55YGOO3FOMCSA4LJ/action/replication_record"}},"created_at":"2026-05-17T23:51:34.632843+00:00","updated_at":"2026-05-17T23:51:34.632843+00:00"}