{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:3PZ4IGGC2P6GI4BPDG4BPDVEQK","short_pith_number":"pith:3PZ4IGGC","canonical_record":{"source":{"id":"1806.03181","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-06-08T14:27:32Z","cross_cats_sorted":["physics.class-ph"],"title_canon_sha256":"2712368a3ff0374eb69f18938ee01090a1509082cbac632dc7fad83eb1b51faa","abstract_canon_sha256":"789776839ff03f3fa1e7f8be1c667ec81dc377b9edfb5ed315978ff9ac623abf"},"schema_version":"1.0"},"canonical_sha256":"dbf3c418c2d3fc64702f19b8178ea482918ec848636c955b9174b59258e387d0","source":{"kind":"arxiv","id":"1806.03181","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.03181","created_at":"2026-05-18T00:13:49Z"},{"alias_kind":"arxiv_version","alias_value":"1806.03181v1","created_at":"2026-05-18T00:13:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.03181","created_at":"2026-05-18T00:13:49Z"},{"alias_kind":"pith_short_12","alias_value":"3PZ4IGGC2P6G","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"3PZ4IGGC2P6GI4BP","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"3PZ4IGGC","created_at":"2026-05-18T12:32:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:3PZ4IGGC2P6GI4BPDG4BPDVEQK","target":"record","payload":{"canonical_record":{"source":{"id":"1806.03181","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-06-08T14:27:32Z","cross_cats_sorted":["physics.class-ph"],"title_canon_sha256":"2712368a3ff0374eb69f18938ee01090a1509082cbac632dc7fad83eb1b51faa","abstract_canon_sha256":"789776839ff03f3fa1e7f8be1c667ec81dc377b9edfb5ed315978ff9ac623abf"},"schema_version":"1.0"},"canonical_sha256":"dbf3c418c2d3fc64702f19b8178ea482918ec848636c955b9174b59258e387d0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:49.373801Z","signature_b64":"DGQORZ6FsgtRsi44MUFHuufIrKEXua4GUoun8XTwhmVbiCapvAay9qr7z2rSM0tjNqOBM4gEiKsRW+G1OTEDAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dbf3c418c2d3fc64702f19b8178ea482918ec848636c955b9174b59258e387d0","last_reissued_at":"2026-05-18T00:13:49.372967Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:49.372967Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.03181","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":"2026-05-18T00:13:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JOdO0DZfbMWwlu7HkwP2XrSRA17jVzDg9sgdZIS2hApZl7WS0+b/Q/wEjpeR+OTG6o62xqXCXI9JF1xVX4FoDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T01:43:52.246437Z"},"content_sha256":"d607d1d1bde743dd98ed673866f5a76d80ef0aff7e84df137f3099f770127109","schema_version":"1.0","event_id":"sha256:d607d1d1bde743dd98ed673866f5a76d80ef0aff7e84df137f3099f770127109"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:3PZ4IGGC2P6GI4BPDG4BPDVEQK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Equivalent partial differential equations of a lattice Boltzmann scheme","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.class-ph"],"primary_cat":"math.NA","authors_text":"Fran\\c{c}ois Dubois (LM-Orsay, LMSSC)","submitted_at":"2018-06-08T14:27:32Z","abstract_excerpt":"We show that when we formulate the lattice Boltzmann equation with a small time step $\\Delta$t and an associated space scale $\\Delta$x, a Taylor expansion joined with the so-called equivalent equation methodology leads to establish macroscopic fluid equations as a formal limit. We recover the Euler equations of gas dynamics at the first order and the compressible Navier-Stokes equations at the second order. 1) Discrete geometry $\\bullet$ We denote by d the dimension of space and by L a regular d-dimensional lattice. Such a lattice is composed by a set L 0 of nodes or vertices and a set L 1 of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.03181","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":"2026-05-18T00:13:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EQDfDzyE7KHIB//F/e+VpAD3Gm3D9jqrR8SdbyY5m7SrjEO63UC0QkJus8M15xsWBQ/4Ebyd6wvDyqkVi1DrCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T01:43:52.246788Z"},"content_sha256":"a30916194b4fc2c4446fcb20adfe2d09f2ed587ec74e5a7910cf1169cfed3d6b","schema_version":"1.0","event_id":"sha256:a30916194b4fc2c4446fcb20adfe2d09f2ed587ec74e5a7910cf1169cfed3d6b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3PZ4IGGC2P6GI4BPDG4BPDVEQK/bundle.json","state_url":"https://pith.science/pith/3PZ4IGGC2P6GI4BPDG4BPDVEQK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3PZ4IGGC2P6GI4BPDG4BPDVEQK/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":"2026-06-23T01:43:52Z","links":{"resolver":"https://pith.science/pith/3PZ4IGGC2P6GI4BPDG4BPDVEQK","bundle":"https://pith.science/pith/3PZ4IGGC2P6GI4BPDG4BPDVEQK/bundle.json","state":"https://pith.science/pith/3PZ4IGGC2P6GI4BPDG4BPDVEQK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3PZ4IGGC2P6GI4BPDG4BPDVEQK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:3PZ4IGGC2P6GI4BPDG4BPDVEQK","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":"789776839ff03f3fa1e7f8be1c667ec81dc377b9edfb5ed315978ff9ac623abf","cross_cats_sorted":["physics.class-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-06-08T14:27:32Z","title_canon_sha256":"2712368a3ff0374eb69f18938ee01090a1509082cbac632dc7fad83eb1b51faa"},"schema_version":"1.0","source":{"id":"1806.03181","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.03181","created_at":"2026-05-18T00:13:49Z"},{"alias_kind":"arxiv_version","alias_value":"1806.03181v1","created_at":"2026-05-18T00:13:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.03181","created_at":"2026-05-18T00:13:49Z"},{"alias_kind":"pith_short_12","alias_value":"3PZ4IGGC2P6G","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"3PZ4IGGC2P6GI4BP","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"3PZ4IGGC","created_at":"2026-05-18T12:32:02Z"}],"graph_snapshots":[{"event_id":"sha256:a30916194b4fc2c4446fcb20adfe2d09f2ed587ec74e5a7910cf1169cfed3d6b","target":"graph","created_at":"2026-05-18T00:13:49Z","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 show that when we formulate the lattice Boltzmann equation with a small time step $\\Delta$t and an associated space scale $\\Delta$x, a Taylor expansion joined with the so-called equivalent equation methodology leads to establish macroscopic fluid equations as a formal limit. We recover the Euler equations of gas dynamics at the first order and the compressible Navier-Stokes equations at the second order. 1) Discrete geometry $\\bullet$ We denote by d the dimension of space and by L a regular d-dimensional lattice. Such a lattice is composed by a set L 0 of nodes or vertices and a set L 1 of ","authors_text":"Fran\\c{c}ois Dubois (LM-Orsay, LMSSC)","cross_cats":["physics.class-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-06-08T14:27:32Z","title":"Equivalent partial differential equations of a lattice Boltzmann scheme"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.03181","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:d607d1d1bde743dd98ed673866f5a76d80ef0aff7e84df137f3099f770127109","target":"record","created_at":"2026-05-18T00:13:49Z","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":"789776839ff03f3fa1e7f8be1c667ec81dc377b9edfb5ed315978ff9ac623abf","cross_cats_sorted":["physics.class-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-06-08T14:27:32Z","title_canon_sha256":"2712368a3ff0374eb69f18938ee01090a1509082cbac632dc7fad83eb1b51faa"},"schema_version":"1.0","source":{"id":"1806.03181","kind":"arxiv","version":1}},"canonical_sha256":"dbf3c418c2d3fc64702f19b8178ea482918ec848636c955b9174b59258e387d0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dbf3c418c2d3fc64702f19b8178ea482918ec848636c955b9174b59258e387d0","first_computed_at":"2026-05-18T00:13:49.372967Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:13:49.372967Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DGQORZ6FsgtRsi44MUFHuufIrKEXua4GUoun8XTwhmVbiCapvAay9qr7z2rSM0tjNqOBM4gEiKsRW+G1OTEDAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:13:49.373801Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.03181","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d607d1d1bde743dd98ed673866f5a76d80ef0aff7e84df137f3099f770127109","sha256:a30916194b4fc2c4446fcb20adfe2d09f2ed587ec74e5a7910cf1169cfed3d6b"],"state_sha256":"4a2567fc0ad286f3ffcce1c1539934347b287fc0b140c7b73f7138f9d6170d57"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CTomO8dVkGeDaUiThQSOSFo6YhfLzLkN3AYTBX3KR8XYcSSJISSGfLuxr8lghmir9YG8/PqTfqdSs9nYfNJCCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T01:43:52.248882Z","bundle_sha256":"c9ed1dfc46f6bec0e8e957708d01fe455c480ce660ae5280548524ce3f0d6b63"}}