{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:ULFVX3TY7ZDK3KGEPKUCCXKEXB","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":"756a897de3993ed3727528565972ca29b845f4a5e6ce060bd8d1a258abe91e04","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-06-17T17:15:10Z","title_canon_sha256":"158c4d06ca848695032377da2d86b910b49f5963f3ba8e2c4cc6c47159835302"},"schema_version":"1.0","source":{"id":"1406.4432","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.4432","created_at":"2026-05-18T01:35:35Z"},{"alias_kind":"arxiv_version","alias_value":"1406.4432v2","created_at":"2026-05-18T01:35:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.4432","created_at":"2026-05-18T01:35:35Z"},{"alias_kind":"pith_short_12","alias_value":"ULFVX3TY7ZDK","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"ULFVX3TY7ZDK3KGE","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"ULFVX3TY","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:d664115930745e9a33b867923153ea0296911ce5499ff79581633f264f8565ad","target":"graph","created_at":"2026-05-18T01:35:35Z","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":"We develop a convergence analysis of a multi-level algorithm combining higher order quasi-Monte Carlo (QMC) quadratures with general Petrov-Galerkin discretizations of countably affine parametric operator equations of elliptic and parabolic type, extending both the multi-level first order analysis in [\\emph{F.Y.~Kuo, Ch.~Schwab, and I.H.~Sloan, Multi-level quasi-Monte Carlo finite element methods for a class of elliptic partial differential equations with random coefficient} (in review)] and the single level higher order analysis in [\\emph{J.~Dick, F.Y.~Kuo, Q.T.~Le~Gia, D.~Nuyens, and Ch.~Sch","authors_text":"Christoph Schwab, Frances Kuo, Josef Dick, Quoc Thong Le Gia","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-06-17T17:15:10Z","title":"Multi-level higher order QMC Galerkin discretization for affine parametric operator equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.4432","kind":"arxiv","version":2},"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":"sha256:2d55279b21e9ac174d6be66ebf92f5081b406a8bafbdc98a5e5164011f265453","target":"record","created_at":"2026-05-18T01:35:35Z","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":"756a897de3993ed3727528565972ca29b845f4a5e6ce060bd8d1a258abe91e04","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-06-17T17:15:10Z","title_canon_sha256":"158c4d06ca848695032377da2d86b910b49f5963f3ba8e2c4cc6c47159835302"},"schema_version":"1.0","source":{"id":"1406.4432","kind":"arxiv","version":2}},"canonical_sha256":"a2cb5bee78fe46ada8c47aa8215d44b85dc0ca7dc215ace16d0fb8955550c445","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a2cb5bee78fe46ada8c47aa8215d44b85dc0ca7dc215ace16d0fb8955550c445","first_computed_at":"2026-05-18T01:35:35.394759Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:35:35.394759Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sCinyK0CfKdz0rbrAZzlhGl7Cm8Zpl0J9qNQM8W1WtwVuh52EJhrVK6Uaz3hUjHlMCGfQGu2WdtrPYKRHmEjBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:35:35.395483Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.4432","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2d55279b21e9ac174d6be66ebf92f5081b406a8bafbdc98a5e5164011f265453","sha256:d664115930745e9a33b867923153ea0296911ce5499ff79581633f264f8565ad"],"state_sha256":"5101a6887364a33387c330645cd7042f31c70cfa93cc939278c2885a899bb6fb"}