{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:NNY725VFLX3U3SCKSSMB4TOIE2","short_pith_number":"pith:NNY725VF","canonical_record":{"source":{"id":"2210.15572","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2022-10-27T16:05:54Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"cef63e7302b25bd30b63fc1d417b5c5b27a0c0ff6292b60f2684065ae85d24f0","abstract_canon_sha256":"4f159d3b01fc0111b77d482066a6533420bff5db8fd7e9b94c1b63014c96ed63"},"schema_version":"1.0"},"canonical_sha256":"6b71fd76a55df74dc84a94981e4dc8269d151a25abcd20c53d3a8114673b9257","source":{"kind":"arxiv","id":"2210.15572","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2210.15572","created_at":"2026-07-05T09:57:17Z"},{"alias_kind":"arxiv_version","alias_value":"2210.15572v3","created_at":"2026-07-05T09:57:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2210.15572","created_at":"2026-07-05T09:57:17Z"},{"alias_kind":"pith_short_12","alias_value":"NNY725VFLX3U","created_at":"2026-07-05T09:57:17Z"},{"alias_kind":"pith_short_16","alias_value":"NNY725VFLX3U3SCK","created_at":"2026-07-05T09:57:17Z"},{"alias_kind":"pith_short_8","alias_value":"NNY725VF","created_at":"2026-07-05T09:57:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:NNY725VFLX3U3SCKSSMB4TOIE2","target":"record","payload":{"canonical_record":{"source":{"id":"2210.15572","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2022-10-27T16:05:54Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"cef63e7302b25bd30b63fc1d417b5c5b27a0c0ff6292b60f2684065ae85d24f0","abstract_canon_sha256":"4f159d3b01fc0111b77d482066a6533420bff5db8fd7e9b94c1b63014c96ed63"},"schema_version":"1.0"},"canonical_sha256":"6b71fd76a55df74dc84a94981e4dc8269d151a25abcd20c53d3a8114673b9257","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:57:17.813907Z","signature_b64":"uFkCtfn4OJo4Q77LHyTkc3n4L0urBpkgPc9YfhN1jvKldmxiLznu8qHKt29tgnFl+N/qWtSZcIHLmhRRzimbDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6b71fd76a55df74dc84a94981e4dc8269d151a25abcd20c53d3a8114673b9257","last_reissued_at":"2026-07-05T09:57:17.813354Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:57:17.813354Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2210.15572","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:57:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2nrr/5d7/yXjX3JQnpmhqhbJ85ap2Q4bexHkfa5eJigSzayAnyQo3iZUpRNzmkSR30DbUaGqMvPgqSnEp9SbCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T10:47:21.166976Z"},"content_sha256":"ab4234444fde825fd0954df6a88a522278d989e47365bc949ac15a5ca0d3fb45","schema_version":"1.0","event_id":"sha256:ab4234444fde825fd0954df6a88a522278d989e47365bc949ac15a5ca0d3fb45"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:NNY725VFLX3U3SCKSSMB4TOIE2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quasi-Monte Carlo finite element approximation of the Navier-Stokes equations with initial data modeled by log-normal random fields","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Guanglian Li, Seungchan Ko, Yi Yu","submitted_at":"2022-10-27T16:05:54Z","abstract_excerpt":"In this paper, we analyze the numerical approximation of the Navier-Stokes problem over a bounded polygonal domain in $\\mathbb{R}^2$, where the initial condition is modeled by a log-normal random field. This problem usually arises in the area of uncertainty quantification. We aim to compute the expectation value of linear functionals of the solution to the Navier-Stokes equations and perform a rigorous error analysis for the problem. In particular, our method includes the finite element, fully-discrete discretizations, truncated Karhunen-Lo\\'eve expansion for the realizations of the initial co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.15572","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2210.15572/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:57:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zYy+dA4YFRu8eq33Tu4pJoxjPxtew/K3QRjvQwtUyCs8GWf+EXeZVbdbm+W17H8Rwfd29Rez24Wit0c6Fx5mBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T10:47:21.167507Z"},"content_sha256":"dcab3b81f1dc685e31aadf133375d38175eaf521be8aa510316e62edb4cb8f2f","schema_version":"1.0","event_id":"sha256:dcab3b81f1dc685e31aadf133375d38175eaf521be8aa510316e62edb4cb8f2f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NNY725VFLX3U3SCKSSMB4TOIE2/bundle.json","state_url":"https://pith.science/pith/NNY725VFLX3U3SCKSSMB4TOIE2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NNY725VFLX3U3SCKSSMB4TOIE2/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-19T10:47:21Z","links":{"resolver":"https://pith.science/pith/NNY725VFLX3U3SCKSSMB4TOIE2","bundle":"https://pith.science/pith/NNY725VFLX3U3SCKSSMB4TOIE2/bundle.json","state":"https://pith.science/pith/NNY725VFLX3U3SCKSSMB4TOIE2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NNY725VFLX3U3SCKSSMB4TOIE2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:NNY725VFLX3U3SCKSSMB4TOIE2","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":"4f159d3b01fc0111b77d482066a6533420bff5db8fd7e9b94c1b63014c96ed63","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2022-10-27T16:05:54Z","title_canon_sha256":"cef63e7302b25bd30b63fc1d417b5c5b27a0c0ff6292b60f2684065ae85d24f0"},"schema_version":"1.0","source":{"id":"2210.15572","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2210.15572","created_at":"2026-07-05T09:57:17Z"},{"alias_kind":"arxiv_version","alias_value":"2210.15572v3","created_at":"2026-07-05T09:57:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2210.15572","created_at":"2026-07-05T09:57:17Z"},{"alias_kind":"pith_short_12","alias_value":"NNY725VFLX3U","created_at":"2026-07-05T09:57:17Z"},{"alias_kind":"pith_short_16","alias_value":"NNY725VFLX3U3SCK","created_at":"2026-07-05T09:57:17Z"},{"alias_kind":"pith_short_8","alias_value":"NNY725VF","created_at":"2026-07-05T09:57:17Z"}],"graph_snapshots":[{"event_id":"sha256:dcab3b81f1dc685e31aadf133375d38175eaf521be8aa510316e62edb4cb8f2f","target":"graph","created_at":"2026-07-05T09:57:17Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2210.15572/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we analyze the numerical approximation of the Navier-Stokes problem over a bounded polygonal domain in $\\mathbb{R}^2$, where the initial condition is modeled by a log-normal random field. This problem usually arises in the area of uncertainty quantification. We aim to compute the expectation value of linear functionals of the solution to the Navier-Stokes equations and perform a rigorous error analysis for the problem. In particular, our method includes the finite element, fully-discrete discretizations, truncated Karhunen-Lo\\'eve expansion for the realizations of the initial co","authors_text":"Guanglian Li, Seungchan Ko, Yi Yu","cross_cats":["cs.NA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2022-10-27T16:05:54Z","title":"Quasi-Monte Carlo finite element approximation of the Navier-Stokes equations with initial data modeled by log-normal random fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.15572","kind":"arxiv","version":3},"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:ab4234444fde825fd0954df6a88a522278d989e47365bc949ac15a5ca0d3fb45","target":"record","created_at":"2026-07-05T09:57:17Z","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":"4f159d3b01fc0111b77d482066a6533420bff5db8fd7e9b94c1b63014c96ed63","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2022-10-27T16:05:54Z","title_canon_sha256":"cef63e7302b25bd30b63fc1d417b5c5b27a0c0ff6292b60f2684065ae85d24f0"},"schema_version":"1.0","source":{"id":"2210.15572","kind":"arxiv","version":3}},"canonical_sha256":"6b71fd76a55df74dc84a94981e4dc8269d151a25abcd20c53d3a8114673b9257","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6b71fd76a55df74dc84a94981e4dc8269d151a25abcd20c53d3a8114673b9257","first_computed_at":"2026-07-05T09:57:17.813354Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:57:17.813354Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uFkCtfn4OJo4Q77LHyTkc3n4L0urBpkgPc9YfhN1jvKldmxiLznu8qHKt29tgnFl+N/qWtSZcIHLmhRRzimbDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:57:17.813907Z","signed_message":"canonical_sha256_bytes"},"source_id":"2210.15572","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ab4234444fde825fd0954df6a88a522278d989e47365bc949ac15a5ca0d3fb45","sha256:dcab3b81f1dc685e31aadf133375d38175eaf521be8aa510316e62edb4cb8f2f"],"state_sha256":"c7c0e770d87af9786ab85ebdb29e00445dc59a81ec911168abf9d803bfa80a48"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xqDPNBFw6uKl1r4kT2vqEzG75HFdgisrDEeLg6uBsb0VrmgEgwgNAoIQ8IzSa05ZaSf4ot8XWB02xfFV97vXDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-19T10:47:21.172731Z","bundle_sha256":"0717229046f5915a4446018e040b4e66075277d6103dabef2edea70d8cecf33c"}}