{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:ZUNBO5TE5ZNQK4N26J7L6BSLP2","short_pith_number":"pith:ZUNBO5TE","schema_version":"1.0","canonical_sha256":"cd1a177664ee5b0571baf27ebf064b7ead3715bbb2fa79a6d015354966ca0122","source":{"kind":"arxiv","id":"1701.05974","version":1},"attestation_state":"computed","paper":{"title":"Quasi-Monte Carlo integration with product weights for elliptic PDEs with log-normal coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Yoshihito Kazashi","submitted_at":"2017-01-21T03:13:21Z","abstract_excerpt":"Quasi-Monte Carlo (QMC) integration of output functionals of solutions of the diffusion problem with a log-normal random coefficient is considered. The random coefficient is assumed to be given by an exponential of a Gaussian random field that is represented by a series expansion of some system of functions. Graham et al. [16] developed a lattice-based QMC theory for this problem and established a quadrature error decay rate $\\approx 1$ with respect to the number of quadrature points. The key assumption there was a suitable summability condition on the aforementioned system of functions. As a "},"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":"1701.05974","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-01-21T03:13:21Z","cross_cats_sorted":[],"title_canon_sha256":"bebeef4937de9f8faa751504e7639f7174f4303d672af408b6a10ad30dfe7533","abstract_canon_sha256":"f3308297d42a5138f0d36fc0325b5a91c4eca1e61c96e9eedc285d29908d1186"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:19.716370Z","signature_b64":"5Pm4OJQI9utqebHva4aE0ueMWzTXikKDGEzatZ/jzuvyD3XnZjCfMKsK/GZH8lbDzU99dfK5qvAYXMNAipb0Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cd1a177664ee5b0571baf27ebf064b7ead3715bbb2fa79a6d015354966ca0122","last_reissued_at":"2026-05-18T00:52:19.715695Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:19.715695Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quasi-Monte Carlo integration with product weights for elliptic PDEs with log-normal coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Yoshihito Kazashi","submitted_at":"2017-01-21T03:13:21Z","abstract_excerpt":"Quasi-Monte Carlo (QMC) integration of output functionals of solutions of the diffusion problem with a log-normal random coefficient is considered. The random coefficient is assumed to be given by an exponential of a Gaussian random field that is represented by a series expansion of some system of functions. Graham et al. [16] developed a lattice-based QMC theory for this problem and established a quadrature error decay rate $\\approx 1$ with respect to the number of quadrature points. The key assumption there was a suitable summability condition on the aforementioned system of functions. As a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.05974","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":"1701.05974","created_at":"2026-05-18T00:52:19.715800+00:00"},{"alias_kind":"arxiv_version","alias_value":"1701.05974v1","created_at":"2026-05-18T00:52:19.715800+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.05974","created_at":"2026-05-18T00:52:19.715800+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZUNBO5TE5ZNQ","created_at":"2026-05-18T12:31:59.375834+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZUNBO5TE5ZNQK4N2","created_at":"2026-05-18T12:31:59.375834+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZUNBO5TE","created_at":"2026-05-18T12:31:59.375834+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/ZUNBO5TE5ZNQK4N26J7L6BSLP2","json":"https://pith.science/pith/ZUNBO5TE5ZNQK4N26J7L6BSLP2.json","graph_json":"https://pith.science/api/pith-number/ZUNBO5TE5ZNQK4N26J7L6BSLP2/graph.json","events_json":"https://pith.science/api/pith-number/ZUNBO5TE5ZNQK4N26J7L6BSLP2/events.json","paper":"https://pith.science/paper/ZUNBO5TE"},"agent_actions":{"view_html":"https://pith.science/pith/ZUNBO5TE5ZNQK4N26J7L6BSLP2","download_json":"https://pith.science/pith/ZUNBO5TE5ZNQK4N26J7L6BSLP2.json","view_paper":"https://pith.science/paper/ZUNBO5TE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1701.05974&json=true","fetch_graph":"https://pith.science/api/pith-number/ZUNBO5TE5ZNQK4N26J7L6BSLP2/graph.json","fetch_events":"https://pith.science/api/pith-number/ZUNBO5TE5ZNQK4N26J7L6BSLP2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZUNBO5TE5ZNQK4N26J7L6BSLP2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZUNBO5TE5ZNQK4N26J7L6BSLP2/action/storage_attestation","attest_author":"https://pith.science/pith/ZUNBO5TE5ZNQK4N26J7L6BSLP2/action/author_attestation","sign_citation":"https://pith.science/pith/ZUNBO5TE5ZNQK4N26J7L6BSLP2/action/citation_signature","submit_replication":"https://pith.science/pith/ZUNBO5TE5ZNQK4N26J7L6BSLP2/action/replication_record"}},"created_at":"2026-05-18T00:52:19.715800+00:00","updated_at":"2026-05-18T00:52:19.715800+00:00"}