{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:UZQWSGJCIAXQD2YEHP5G2KIJRE","short_pith_number":"pith:UZQWSGJC","schema_version":"1.0","canonical_sha256":"a661691922402f01eb043bfa6d2909892e93501278ded31da9dbcbba8aaa9e2d","source":{"kind":"arxiv","id":"1408.4609","version":1},"attestation_state":"computed","paper":{"title":"Spatial low-discrepancy sequences, spherical cone discrepancy, and applications in financial modeling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Johann S. Brauchart, Josef Dick, Lou Fang","submitted_at":"2014-08-20T11:26:52Z","abstract_excerpt":"In this paper we introduce a reproducing kernel Hilbert space defined on $\\mathbb{R}^{d+1}$ as the tensor product of a reproducing kernel defined on the unit sphere $\\mathbb{S}^{d}$ in $\\mathbb{R}^{d+1}$ and a reproducing kernel defined on $[0,\\infty)$. We extend Stolarsky's invariance principle to this case and prove upper and lower bounds for numerical integration in the corresponding reproducing kernel Hilbert space.\n  The idea of separating the direction from the distance from the origin can also be applied to the construction of quadrature methods. An extension of the area-preserving Lamb"},"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":"1408.4609","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-08-20T11:26:52Z","cross_cats_sorted":[],"title_canon_sha256":"c3985a30d2157bc3efb4e42ed12aad846d0e669fd5c3d5d10a18365df532792e","abstract_canon_sha256":"5b9900619f9a90036929e1a8b6c4bf4be94acdb1b72b4dfe482121b4dcbf1e10"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:50.904695Z","signature_b64":"XSocGRCf7xenwbLt4/a32DmvhhxnrOamsZuy/ri2ZBexeu2hVzbkcUfmQ2zlCyPrEhZr8qxDViUietSf8+7EAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a661691922402f01eb043bfa6d2909892e93501278ded31da9dbcbba8aaa9e2d","last_reissued_at":"2026-05-18T01:23:50.904083Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:50.904083Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spatial low-discrepancy sequences, spherical cone discrepancy, and applications in financial modeling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Johann S. Brauchart, Josef Dick, Lou Fang","submitted_at":"2014-08-20T11:26:52Z","abstract_excerpt":"In this paper we introduce a reproducing kernel Hilbert space defined on $\\mathbb{R}^{d+1}$ as the tensor product of a reproducing kernel defined on the unit sphere $\\mathbb{S}^{d}$ in $\\mathbb{R}^{d+1}$ and a reproducing kernel defined on $[0,\\infty)$. We extend Stolarsky's invariance principle to this case and prove upper and lower bounds for numerical integration in the corresponding reproducing kernel Hilbert space.\n  The idea of separating the direction from the distance from the origin can also be applied to the construction of quadrature methods. An extension of the area-preserving Lamb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.4609","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":"1408.4609","created_at":"2026-05-18T01:23:50.904167+00:00"},{"alias_kind":"arxiv_version","alias_value":"1408.4609v1","created_at":"2026-05-18T01:23:50.904167+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.4609","created_at":"2026-05-18T01:23:50.904167+00:00"},{"alias_kind":"pith_short_12","alias_value":"UZQWSGJCIAXQ","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_16","alias_value":"UZQWSGJCIAXQD2YE","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_8","alias_value":"UZQWSGJC","created_at":"2026-05-18T12:28:52.271510+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/UZQWSGJCIAXQD2YEHP5G2KIJRE","json":"https://pith.science/pith/UZQWSGJCIAXQD2YEHP5G2KIJRE.json","graph_json":"https://pith.science/api/pith-number/UZQWSGJCIAXQD2YEHP5G2KIJRE/graph.json","events_json":"https://pith.science/api/pith-number/UZQWSGJCIAXQD2YEHP5G2KIJRE/events.json","paper":"https://pith.science/paper/UZQWSGJC"},"agent_actions":{"view_html":"https://pith.science/pith/UZQWSGJCIAXQD2YEHP5G2KIJRE","download_json":"https://pith.science/pith/UZQWSGJCIAXQD2YEHP5G2KIJRE.json","view_paper":"https://pith.science/paper/UZQWSGJC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1408.4609&json=true","fetch_graph":"https://pith.science/api/pith-number/UZQWSGJCIAXQD2YEHP5G2KIJRE/graph.json","fetch_events":"https://pith.science/api/pith-number/UZQWSGJCIAXQD2YEHP5G2KIJRE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UZQWSGJCIAXQD2YEHP5G2KIJRE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UZQWSGJCIAXQD2YEHP5G2KIJRE/action/storage_attestation","attest_author":"https://pith.science/pith/UZQWSGJCIAXQD2YEHP5G2KIJRE/action/author_attestation","sign_citation":"https://pith.science/pith/UZQWSGJCIAXQD2YEHP5G2KIJRE/action/citation_signature","submit_replication":"https://pith.science/pith/UZQWSGJCIAXQD2YEHP5G2KIJRE/action/replication_record"}},"created_at":"2026-05-18T01:23:50.904167+00:00","updated_at":"2026-05-18T01:23:50.904167+00:00"}