{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:D77ZVBEDER3YZQARBKSMTBMLGM","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":"d8a682448a000be01a2dfd5797df07d48507b8e67d7b0a2c0ae917f980ace0ed","cross_cats_sorted":["cs.NA","physics.flu-dyn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-06-06T11:53:14Z","title_canon_sha256":"793680f3265edcc376a95f906bd85c73ab5594a6b7952130b9913ecc34d5245a"},"schema_version":"1.0","source":{"id":"1906.02536","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.02536","created_at":"2026-07-05T09:09:44Z"},{"alias_kind":"arxiv_version","alias_value":"1906.02536v1","created_at":"2026-07-05T09:09:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.02536","created_at":"2026-07-05T09:09:44Z"},{"alias_kind":"pith_short_12","alias_value":"D77ZVBEDER3Y","created_at":"2026-07-05T09:09:44Z"},{"alias_kind":"pith_short_16","alias_value":"D77ZVBEDER3YZQAR","created_at":"2026-07-05T09:09:44Z"},{"alias_kind":"pith_short_8","alias_value":"D77ZVBED","created_at":"2026-07-05T09:09:44Z"}],"graph_snapshots":[{"event_id":"sha256:a3fbc22fe72e23f9debbc5f67008b46ee41d4defd9c5accd717d0b67fbe59216","target":"graph","created_at":"2026-07-05T09:09:44Z","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/1906.02536/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Statistical solutions are time-parameterized probability measures on spaces of integrable functions, that have been proposed recently as a framework for global solutions and uncertainty quantification for multi-dimensional hyperbolic system of conservation laws. By combining high-resolution finite volume methods with a Monte Carlo sampling procedure, we present a numerical algorithm to approximate statistical solutions. Under verifiable assumptions on the finite volume method, we prove that the approximations, generated by the proposed algorithm, converge in an appropriate topology to a statis","authors_text":"Franziska Weber, Kjetil Lye, Siddhartha Mishra, Ulrik Skre Fjordholm","cross_cats":["cs.NA","physics.flu-dyn"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-06-06T11:53:14Z","title":"Statistical solutions of hyperbolic systems of conservation laws: numerical approximation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.02536","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:d6bdae8c6875826ed9b9424654214634b0fba4f66269754f6b707a3c90815b45","target":"record","created_at":"2026-07-05T09:09:44Z","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":"d8a682448a000be01a2dfd5797df07d48507b8e67d7b0a2c0ae917f980ace0ed","cross_cats_sorted":["cs.NA","physics.flu-dyn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-06-06T11:53:14Z","title_canon_sha256":"793680f3265edcc376a95f906bd85c73ab5594a6b7952130b9913ecc34d5245a"},"schema_version":"1.0","source":{"id":"1906.02536","kind":"arxiv","version":1}},"canonical_sha256":"1fff9a848324778cc0110aa4c9858b3334859b197bed420477e6cff042f8b6b6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1fff9a848324778cc0110aa4c9858b3334859b197bed420477e6cff042f8b6b6","first_computed_at":"2026-07-05T09:09:44.965978Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:09:44.965978Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"I2TH16y4E5BxI6tOKneJS5AIg6frf1QRaKYiuy4q5f2zoOrPMdzHjiS6kep5ZYsYjUULmMEQSqBOD9kWIxS7Cw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:09:44.966399Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.02536","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d6bdae8c6875826ed9b9424654214634b0fba4f66269754f6b707a3c90815b45","sha256:a3fbc22fe72e23f9debbc5f67008b46ee41d4defd9c5accd717d0b67fbe59216"],"state_sha256":"7f02a8cf393317db6213135e0877bc6709b5a7af471dee4eb0faf8c13a3abbf6"}