{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:R67ML2EII4XVN7M4UAJXP436CI","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":"4515225bc55d48bf0dc748e993a58650ba5927b53af5f14957ddb547e66fea4a","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.NA","submitted_at":"2022-03-22T13:41:43Z","title_canon_sha256":"eba04f378ec14f2184f14e469be8b2b84c9fec45507bef86be64c81ca80ac8f9"},"schema_version":"1.0","source":{"id":"2203.11735","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2203.11735","created_at":"2026-07-05T04:07:15Z"},{"alias_kind":"arxiv_version","alias_value":"2203.11735v1","created_at":"2026-07-05T04:07:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.11735","created_at":"2026-07-05T04:07:15Z"},{"alias_kind":"pith_short_12","alias_value":"R67ML2EII4XV","created_at":"2026-07-05T04:07:15Z"},{"alias_kind":"pith_short_16","alias_value":"R67ML2EII4XVN7M4","created_at":"2026-07-05T04:07:15Z"},{"alias_kind":"pith_short_8","alias_value":"R67ML2EI","created_at":"2026-07-05T04:07:15Z"}],"graph_snapshots":[{"event_id":"sha256:5c2e27e8b348b52f9ef61a4837a05dcdc4901963c13d9bc024e3f5554904798b","target":"graph","created_at":"2026-07-05T04:07:15Z","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/2203.11735/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we propose a local model reduction approach for subsurface flow problems in stochastic and highly heterogeneous media. To guarantee the mass conservation, we consider the mixed formulation of the flow problem and aim to solve the problem in a coarse grid to reduce the complexity of a large-scale system. We decompose the entire problem into a training and a testing stage, namely the offline coarse-grid multiscale basis generation stage and online simulation stage with different parameters. In the training stage, a parameter-independent and small-dimensional multiscale basis funct","authors_text":"Eric Chung, Shubin Fu, Yiran Wang","cross_cats":["cs.NA"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.NA","submitted_at":"2022-03-22T13:41:43Z","title":"A conservative multiscale method for stochastic highly heterogeneous flow"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.11735","kind":"arxiv","version":1},"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":"sha256:0d568981da90d267633aa223077219a130758c366442889f6664c4d827dfe812","target":"record","created_at":"2026-07-05T04:07:15Z","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":"4515225bc55d48bf0dc748e993a58650ba5927b53af5f14957ddb547e66fea4a","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.NA","submitted_at":"2022-03-22T13:41:43Z","title_canon_sha256":"eba04f378ec14f2184f14e469be8b2b84c9fec45507bef86be64c81ca80ac8f9"},"schema_version":"1.0","source":{"id":"2203.11735","kind":"arxiv","version":1}},"canonical_sha256":"8fbec5e888472f56fd9ca01377f37e120f0f7df4e83de16e44feb14cca7ad715","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8fbec5e888472f56fd9ca01377f37e120f0f7df4e83de16e44feb14cca7ad715","first_computed_at":"2026-07-05T04:07:15.105049Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:07:15.105049Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9PLFzEDEk47HE6uHb4sO/6ewSGiMjv8NGf5QClnxCxjno+F1vyt3k9hVCXtdansRwMKsWNwRuM0I2lpKj/tzAA==","signature_status":"signed_v1","signed_at":"2026-07-05T04:07:15.105550Z","signed_message":"canonical_sha256_bytes"},"source_id":"2203.11735","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0d568981da90d267633aa223077219a130758c366442889f6664c4d827dfe812","sha256:5c2e27e8b348b52f9ef61a4837a05dcdc4901963c13d9bc024e3f5554904798b"],"state_sha256":"d019bca1ef4c9b31b8e68794e068c2f0c676d2126a403b382f15dd4f226b62d3"}