{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:O6FI5TBPD5DYIPJSO5JRDQ7YDG","short_pith_number":"pith:O6FI5TBP","canonical_record":{"source":{"id":"1101.4315","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-01-22T20:00:50Z","cross_cats_sorted":["physics.comp-ph"],"title_canon_sha256":"76f9aea81acb3c502e1d6e1f379dc766ba135b181147bd34c16f2358f18b1150","abstract_canon_sha256":"ddf71dbf45c8920fc5084a1cc1fd632a0baae04c7179da128edd75e5409c32c1"},"schema_version":"1.0"},"canonical_sha256":"778a8ecc2f1f47843d32775311c3f8199d2a5560b09cf0bc1dd1db7a16a8819c","source":{"kind":"arxiv","id":"1101.4315","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.4315","created_at":"2026-05-18T04:31:11Z"},{"alias_kind":"arxiv_version","alias_value":"1101.4315v1","created_at":"2026-05-18T04:31:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.4315","created_at":"2026-05-18T04:31:11Z"},{"alias_kind":"pith_short_12","alias_value":"O6FI5TBPD5DY","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"O6FI5TBPD5DYIPJS","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"O6FI5TBP","created_at":"2026-05-18T12:26:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:O6FI5TBPD5DYIPJSO5JRDQ7YDG","target":"record","payload":{"canonical_record":{"source":{"id":"1101.4315","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-01-22T20:00:50Z","cross_cats_sorted":["physics.comp-ph"],"title_canon_sha256":"76f9aea81acb3c502e1d6e1f379dc766ba135b181147bd34c16f2358f18b1150","abstract_canon_sha256":"ddf71dbf45c8920fc5084a1cc1fd632a0baae04c7179da128edd75e5409c32c1"},"schema_version":"1.0"},"canonical_sha256":"778a8ecc2f1f47843d32775311c3f8199d2a5560b09cf0bc1dd1db7a16a8819c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:31:11.203249Z","signature_b64":"y3o9MKmdugY6GEKRuynYG+S+iqG67Q6C5pKM5RS6STnMA1bxSZqsqY1OTF0LitGeN6JbKyx+d8htlWYsPHenDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"778a8ecc2f1f47843d32775311c3f8199d2a5560b09cf0bc1dd1db7a16a8819c","last_reissued_at":"2026-05-18T04:31:11.202790Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:31:11.202790Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1101.4315","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:31:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SQoSLZLTRgacz5zmRYMJQOgaVHZLE6muzDDWcs21p4IdhD6tBjNwWFWw8UlLz/vlqiY2otMmHsoSb9LNmSQ+AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T21:50:01.759267Z"},"content_sha256":"bc0ea46d7f03977a9c5a01589a718d3db13d388c80379174f708a186903bfa14","schema_version":"1.0","event_id":"sha256:bc0ea46d7f03977a9c5a01589a718d3db13d388c80379174f708a186903bfa14"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:O6FI5TBPD5DYIPJSO5JRDQ7YDG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An introduction to finite volumes for gas dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.comp-ph"],"primary_cat":"math.NA","authors_text":"Fran\\c{c}ois Dubois (LM-Orsay)","submitted_at":"2011-01-22T20:00:50Z","abstract_excerpt":"We propose an elementary introduction to the finite volume method in the context of gas dynamics conservation laws. Our approach is founded on the advection equation, the exact integration of the associated Cauchy problem, and the so-called upwind scheme in one space dimension. It is then extended in three directions: hyperbolic linear systems and particularily the system of acoustics, gas dynamics with the help of the Roe matrix and two space dimensions by following the approach proposed by Van Leer. A special emphasis on boundary conditions is proposed all along the text."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.4315","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":""},"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":"2026-05-18T04:31:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WtIAojTTdcJCUkSH2ZUwbT5H1UwQxe8R0Bxwu7krDaBrsxqHVwIIzVzlY/T7Lj0ehAz6sVJuCfIlRhnj/XsNCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T21:50:01.759639Z"},"content_sha256":"b9fcfb2fba3e05c82ee089a7903c9bef1de555cc26a19fa98d71e67ebe27c0d6","schema_version":"1.0","event_id":"sha256:b9fcfb2fba3e05c82ee089a7903c9bef1de555cc26a19fa98d71e67ebe27c0d6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O6FI5TBPD5DYIPJSO5JRDQ7YDG/bundle.json","state_url":"https://pith.science/pith/O6FI5TBPD5DYIPJSO5JRDQ7YDG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O6FI5TBPD5DYIPJSO5JRDQ7YDG/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":"2026-06-04T21:50:01Z","links":{"resolver":"https://pith.science/pith/O6FI5TBPD5DYIPJSO5JRDQ7YDG","bundle":"https://pith.science/pith/O6FI5TBPD5DYIPJSO5JRDQ7YDG/bundle.json","state":"https://pith.science/pith/O6FI5TBPD5DYIPJSO5JRDQ7YDG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O6FI5TBPD5DYIPJSO5JRDQ7YDG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:O6FI5TBPD5DYIPJSO5JRDQ7YDG","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":"ddf71dbf45c8920fc5084a1cc1fd632a0baae04c7179da128edd75e5409c32c1","cross_cats_sorted":["physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-01-22T20:00:50Z","title_canon_sha256":"76f9aea81acb3c502e1d6e1f379dc766ba135b181147bd34c16f2358f18b1150"},"schema_version":"1.0","source":{"id":"1101.4315","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.4315","created_at":"2026-05-18T04:31:11Z"},{"alias_kind":"arxiv_version","alias_value":"1101.4315v1","created_at":"2026-05-18T04:31:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.4315","created_at":"2026-05-18T04:31:11Z"},{"alias_kind":"pith_short_12","alias_value":"O6FI5TBPD5DY","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"O6FI5TBPD5DYIPJS","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"O6FI5TBP","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:b9fcfb2fba3e05c82ee089a7903c9bef1de555cc26a19fa98d71e67ebe27c0d6","target":"graph","created_at":"2026-05-18T04:31:11Z","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":"We propose an elementary introduction to the finite volume method in the context of gas dynamics conservation laws. Our approach is founded on the advection equation, the exact integration of the associated Cauchy problem, and the so-called upwind scheme in one space dimension. It is then extended in three directions: hyperbolic linear systems and particularily the system of acoustics, gas dynamics with the help of the Roe matrix and two space dimensions by following the approach proposed by Van Leer. A special emphasis on boundary conditions is proposed all along the text.","authors_text":"Fran\\c{c}ois Dubois (LM-Orsay)","cross_cats":["physics.comp-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-01-22T20:00:50Z","title":"An introduction to finite volumes for gas dynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.4315","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:bc0ea46d7f03977a9c5a01589a718d3db13d388c80379174f708a186903bfa14","target":"record","created_at":"2026-05-18T04:31:11Z","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":"ddf71dbf45c8920fc5084a1cc1fd632a0baae04c7179da128edd75e5409c32c1","cross_cats_sorted":["physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-01-22T20:00:50Z","title_canon_sha256":"76f9aea81acb3c502e1d6e1f379dc766ba135b181147bd34c16f2358f18b1150"},"schema_version":"1.0","source":{"id":"1101.4315","kind":"arxiv","version":1}},"canonical_sha256":"778a8ecc2f1f47843d32775311c3f8199d2a5560b09cf0bc1dd1db7a16a8819c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"778a8ecc2f1f47843d32775311c3f8199d2a5560b09cf0bc1dd1db7a16a8819c","first_computed_at":"2026-05-18T04:31:11.202790Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:31:11.202790Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"y3o9MKmdugY6GEKRuynYG+S+iqG67Q6C5pKM5RS6STnMA1bxSZqsqY1OTF0LitGeN6JbKyx+d8htlWYsPHenDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:31:11.203249Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.4315","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bc0ea46d7f03977a9c5a01589a718d3db13d388c80379174f708a186903bfa14","sha256:b9fcfb2fba3e05c82ee089a7903c9bef1de555cc26a19fa98d71e67ebe27c0d6"],"state_sha256":"4439481c113e198349cdd114a9c2969a5ed053b28bd9cf465e87ed8c9bdd76d6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/VtAPG7y4YobrREEFmfbsB6MY3HwSNC4MYCY5TSnEWpFtv3sTI82WrjHM3onSmbM0lEDtkVuwYJ+h304KQPMBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T21:50:01.761719Z","bundle_sha256":"1baf6026a3105ab6a9d6fcd1ebf062f309c7911655066572894c11dc7aeb3b31"}}