{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:GAKESDSK2QEY34ZHQTXGDMVPWW","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":"4dbe8805f753ddcbd6ccaac1cd906b3bc9f226bbc2554ce91ca9b8388643fe4c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-09-16T03:18:38Z","title_canon_sha256":"1a1d9ce4459ebce19ea10daf4bc0010919199cb1dfd6e0e07c5ac372d659d2a1"},"schema_version":"1.0","source":{"id":"1709.06422","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.06422","created_at":"2026-05-18T00:34:12Z"},{"alias_kind":"arxiv_version","alias_value":"1709.06422v2","created_at":"2026-05-18T00:34:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.06422","created_at":"2026-05-18T00:34:12Z"},{"alias_kind":"pith_short_12","alias_value":"GAKESDSK2QEY","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"GAKESDSK2QEY34ZH","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"GAKESDSK","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:8f5d5f54ef0c55a89f5ec0cd92a2b0e5bcfb2749d2f20bbfa1d7bb1d7a38eebb","target":"graph","created_at":"2026-05-18T00:34:12Z","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":"Partial differential equations (PDE) often involve parameters, such as viscosity or density. An analysis of the PDE may involve considering a large range of parameter values, as occurs in uncertainty quantification, control and optimization, inference, and several statistical techniques. The solution for even a single case may be quite expensive; whereas parallel computing may be applied, this reduces the total elapsed time but not the total computational effort. In the case of flows governed by the Navier-Stokes equations, a method has been devised for computing an ensemble of solutions. Rece","authors_text":"Max Gunzburger, Michael Schneier, Nan Jiang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-09-16T03:18:38Z","title":"A higher-order ensemble/proper orthogonal decomposition method for the nonstationary Navier-Stokes equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.06422","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":"sha256:0090c8614836a39775d36403c8263e7980998de0d04f44e658de63cb9a78d807","target":"record","created_at":"2026-05-18T00:34:12Z","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":"4dbe8805f753ddcbd6ccaac1cd906b3bc9f226bbc2554ce91ca9b8388643fe4c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-09-16T03:18:38Z","title_canon_sha256":"1a1d9ce4459ebce19ea10daf4bc0010919199cb1dfd6e0e07c5ac372d659d2a1"},"schema_version":"1.0","source":{"id":"1709.06422","kind":"arxiv","version":2}},"canonical_sha256":"3014490e4ad4098df32784ee61b2afb5a7071277e2551f808ab1dfb00680d1d6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3014490e4ad4098df32784ee61b2afb5a7071277e2551f808ab1dfb00680d1d6","first_computed_at":"2026-05-18T00:34:12.679012Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:34:12.679012Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"d0CJTryD636QmZllfI5AW9hODcfqCP7uqCsbpxnCstjmYFdTW7qNs4obOd3Qe05pCo/39xjjOIZxzGSMZ6K3BA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:34:12.679649Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.06422","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0090c8614836a39775d36403c8263e7980998de0d04f44e658de63cb9a78d807","sha256:8f5d5f54ef0c55a89f5ec0cd92a2b0e5bcfb2749d2f20bbfa1d7bb1d7a38eebb"],"state_sha256":"e25034e50f5a4753d2afa1017fa5d2b235fe82e8fc3ab49b7083bd06fe1b4d90"}