{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:DVBO76V6HWRXRU653O5YHIOLGA","short_pith_number":"pith:DVBO76V6","schema_version":"1.0","canonical_sha256":"1d42effabe3da378d3dddbbb83a1cb3012fcf59eafd83378d22d69878a8aa46e","source":{"kind":"arxiv","id":"1507.01090","version":2},"attestation_state":"computed","paper":{"title":"Multilevel Quasi-Monte Carlo Methods for Lognormal Diffusion Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Christoph Schwab, Elisabeth Ullmann, Frances Y. Kuo, Ian H. Sloan, Robert Scheichl","submitted_at":"2015-07-04T09:36:33Z","abstract_excerpt":"In this paper we present a rigorous cost and error analysis of a multilevel estimator based on randomly shifted Quasi-Monte Carlo (QMC) lattice rules for lognormal diffusion problems. These problems are motivated by uncertainty quantification problems in subsurface flow. We extend the convergence analysis in [Graham et al., Numer. Math. 2014] to multilevel Quasi-Monte Carlo finite element discretizations and give a constructive proof of the dimension-independent convergence of the QMC rules. More precisely, we provide suitable parameters for the construction of such rules that yield the requir"},"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":"1507.01090","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-07-04T09:36:33Z","cross_cats_sorted":[],"title_canon_sha256":"01f55afe8ea486c434deb1201b0735799ada620c04972c83bf2a83cc83eaa20e","abstract_canon_sha256":"07ebb86bc447715728e2012f38fc8d55f76edcda294a126a3e9e69d8368e6cb6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:06:24.652640Z","signature_b64":"inVovwXeuy/gctCcsFvy2ZQjLd60xEnDqeDMtSF1Aot33iadM9wpESsWd+mIYSpLdb8eaKVJKe+sSwZglWMQBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1d42effabe3da378d3dddbbb83a1cb3012fcf59eafd83378d22d69878a8aa46e","last_reissued_at":"2026-05-18T01:06:24.652238Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:06:24.652238Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Multilevel Quasi-Monte Carlo Methods for Lognormal Diffusion Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Christoph Schwab, Elisabeth Ullmann, Frances Y. Kuo, Ian H. Sloan, Robert Scheichl","submitted_at":"2015-07-04T09:36:33Z","abstract_excerpt":"In this paper we present a rigorous cost and error analysis of a multilevel estimator based on randomly shifted Quasi-Monte Carlo (QMC) lattice rules for lognormal diffusion problems. These problems are motivated by uncertainty quantification problems in subsurface flow. We extend the convergence analysis in [Graham et al., Numer. Math. 2014] to multilevel Quasi-Monte Carlo finite element discretizations and give a constructive proof of the dimension-independent convergence of the QMC rules. More precisely, we provide suitable parameters for the construction of such rules that yield the requir"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.01090","kind":"arxiv","version":2},"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":"1507.01090","created_at":"2026-05-18T01:06:24.652293+00:00"},{"alias_kind":"arxiv_version","alias_value":"1507.01090v2","created_at":"2026-05-18T01:06:24.652293+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.01090","created_at":"2026-05-18T01:06:24.652293+00:00"},{"alias_kind":"pith_short_12","alias_value":"DVBO76V6HWRX","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_16","alias_value":"DVBO76V6HWRXRU65","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_8","alias_value":"DVBO76V6","created_at":"2026-05-18T12:29:17.054201+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/DVBO76V6HWRXRU653O5YHIOLGA","json":"https://pith.science/pith/DVBO76V6HWRXRU653O5YHIOLGA.json","graph_json":"https://pith.science/api/pith-number/DVBO76V6HWRXRU653O5YHIOLGA/graph.json","events_json":"https://pith.science/api/pith-number/DVBO76V6HWRXRU653O5YHIOLGA/events.json","paper":"https://pith.science/paper/DVBO76V6"},"agent_actions":{"view_html":"https://pith.science/pith/DVBO76V6HWRXRU653O5YHIOLGA","download_json":"https://pith.science/pith/DVBO76V6HWRXRU653O5YHIOLGA.json","view_paper":"https://pith.science/paper/DVBO76V6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1507.01090&json=true","fetch_graph":"https://pith.science/api/pith-number/DVBO76V6HWRXRU653O5YHIOLGA/graph.json","fetch_events":"https://pith.science/api/pith-number/DVBO76V6HWRXRU653O5YHIOLGA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DVBO76V6HWRXRU653O5YHIOLGA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DVBO76V6HWRXRU653O5YHIOLGA/action/storage_attestation","attest_author":"https://pith.science/pith/DVBO76V6HWRXRU653O5YHIOLGA/action/author_attestation","sign_citation":"https://pith.science/pith/DVBO76V6HWRXRU653O5YHIOLGA/action/citation_signature","submit_replication":"https://pith.science/pith/DVBO76V6HWRXRU653O5YHIOLGA/action/replication_record"}},"created_at":"2026-05-18T01:06:24.652293+00:00","updated_at":"2026-05-18T01:06:24.652293+00:00"}