{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:D77ZVBEDER3YZQARBKSMTBMLGM","short_pith_number":"pith:D77ZVBED","schema_version":"1.0","canonical_sha256":"1fff9a848324778cc0110aa4c9858b3334859b197bed420477e6cff042f8b6b6","source":{"kind":"arxiv","id":"1906.02536","version":1},"attestation_state":"computed","paper":{"title":"Statistical solutions of hyperbolic systems of conservation laws: numerical approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","physics.flu-dyn"],"primary_cat":"math.NA","authors_text":"Franziska Weber, Kjetil Lye, Siddhartha Mishra, Ulrik Skre Fjordholm","submitted_at":"2019-06-06T11:53:14Z","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1906.02536","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-06-06T11:53:14Z","cross_cats_sorted":["cs.NA","physics.flu-dyn"],"title_canon_sha256":"793680f3265edcc376a95f906bd85c73ab5594a6b7952130b9913ecc34d5245a","abstract_canon_sha256":"d8a682448a000be01a2dfd5797df07d48507b8e67d7b0a2c0ae917f980ace0ed"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:09:44.966399Z","signature_b64":"I2TH16y4E5BxI6tOKneJS5AIg6frf1QRaKYiuy4q5f2zoOrPMdzHjiS6kep5ZYsYjUULmMEQSqBOD9kWIxS7Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1fff9a848324778cc0110aa4c9858b3334859b197bed420477e6cff042f8b6b6","last_reissued_at":"2026-07-05T09:09:44.965978Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:09:44.965978Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Statistical solutions of hyperbolic systems of conservation laws: numerical approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","physics.flu-dyn"],"primary_cat":"math.NA","authors_text":"Franziska Weber, Kjetil Lye, Siddhartha Mishra, Ulrik Skre Fjordholm","submitted_at":"2019-06-06T11:53:14Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.02536","kind":"arxiv","version":1},"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/1906.02536/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1906.02536","created_at":"2026-07-05T09:09:44.966027+00:00"},{"alias_kind":"arxiv_version","alias_value":"1906.02536v1","created_at":"2026-07-05T09:09:44.966027+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.02536","created_at":"2026-07-05T09:09:44.966027+00:00"},{"alias_kind":"pith_short_12","alias_value":"D77ZVBEDER3Y","created_at":"2026-07-05T09:09:44.966027+00:00"},{"alias_kind":"pith_short_16","alias_value":"D77ZVBEDER3YZQAR","created_at":"2026-07-05T09:09:44.966027+00:00"},{"alias_kind":"pith_short_8","alias_value":"D77ZVBED","created_at":"2026-07-05T09:09:44.966027+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/D77ZVBEDER3YZQARBKSMTBMLGM","json":"https://pith.science/pith/D77ZVBEDER3YZQARBKSMTBMLGM.json","graph_json":"https://pith.science/api/pith-number/D77ZVBEDER3YZQARBKSMTBMLGM/graph.json","events_json":"https://pith.science/api/pith-number/D77ZVBEDER3YZQARBKSMTBMLGM/events.json","paper":"https://pith.science/paper/D77ZVBED"},"agent_actions":{"view_html":"https://pith.science/pith/D77ZVBEDER3YZQARBKSMTBMLGM","download_json":"https://pith.science/pith/D77ZVBEDER3YZQARBKSMTBMLGM.json","view_paper":"https://pith.science/paper/D77ZVBED","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1906.02536&json=true","fetch_graph":"https://pith.science/api/pith-number/D77ZVBEDER3YZQARBKSMTBMLGM/graph.json","fetch_events":"https://pith.science/api/pith-number/D77ZVBEDER3YZQARBKSMTBMLGM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/D77ZVBEDER3YZQARBKSMTBMLGM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/D77ZVBEDER3YZQARBKSMTBMLGM/action/storage_attestation","attest_author":"https://pith.science/pith/D77ZVBEDER3YZQARBKSMTBMLGM/action/author_attestation","sign_citation":"https://pith.science/pith/D77ZVBEDER3YZQARBKSMTBMLGM/action/citation_signature","submit_replication":"https://pith.science/pith/D77ZVBEDER3YZQARBKSMTBMLGM/action/replication_record"}},"created_at":"2026-07-05T09:09:44.966027+00:00","updated_at":"2026-07-05T09:09:44.966027+00:00"}