{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:LUNGCJIHPM4EQ2UV6G6PKIGPHX","short_pith_number":"pith:LUNGCJIH","schema_version":"1.0","canonical_sha256":"5d1a6125077b38486a95f1bcf520cf3de3ddc1b452571281522bf6b837c40414","source":{"kind":"arxiv","id":"1706.09161","version":2},"attestation_state":"computed","paper":{"title":"Multiple-Relaxation-Time Lattice Boltzmann scheme for Fractional Advection-Diffusion Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"physics.comp-ph","authors_text":"Alain Cartalade, Amina Younsi, Marie-Christine N\\'eel","submitted_at":"2017-06-28T08:07:21Z","abstract_excerpt":"Partial differential equations (p.d.e) equipped of spatial derivatives of fractional order capture anomalous transport behaviors observed in diverse fields of Science. A number of numerical methods approximate their solutions in dimension one. Focusing our effort on such p.d.e. in higher dimension with Dirichlet boundary conditions, we present an approximation based on Lattice Boltzmann Method with Bhatnagar-Gross-Krook (BGK) or Multiple-Relaxation-Time (MRT) collision operators. First, an equilibrium distribution function is defined for simulating space-fractional diffusion equations in dimen"},"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":"1706.09161","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2017-06-28T08:07:21Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"75749917220972f5863fc7ac9d5947d0eb98e116030f0b1fcfdcf8e07f457ff0","abstract_canon_sha256":"5e8d652bda3f61ac2a779f7613f537fe29103b4abf1a65f12b414d5baf37b13d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:07:50.755557Z","signature_b64":"/0lxSKc/6N9b9t1hhp3jT3ZI2BJCMY8GhmbYEo/uZsQAGNUDYis+SXJ5tjNAsmXYLcpZtalhEdP4bOouRcCXBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5d1a6125077b38486a95f1bcf520cf3de3ddc1b452571281522bf6b837c40414","last_reissued_at":"2026-05-18T00:07:50.754680Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:07:50.754680Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Multiple-Relaxation-Time Lattice Boltzmann scheme for Fractional Advection-Diffusion Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"physics.comp-ph","authors_text":"Alain Cartalade, Amina Younsi, Marie-Christine N\\'eel","submitted_at":"2017-06-28T08:07:21Z","abstract_excerpt":"Partial differential equations (p.d.e) equipped of spatial derivatives of fractional order capture anomalous transport behaviors observed in diverse fields of Science. A number of numerical methods approximate their solutions in dimension one. Focusing our effort on such p.d.e. in higher dimension with Dirichlet boundary conditions, we present an approximation based on Lattice Boltzmann Method with Bhatnagar-Gross-Krook (BGK) or Multiple-Relaxation-Time (MRT) collision operators. First, an equilibrium distribution function is defined for simulating space-fractional diffusion equations in dimen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.09161","kind":"arxiv","version":2},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1706.09161","created_at":"2026-05-18T00:07:50.754779+00:00"},{"alias_kind":"arxiv_version","alias_value":"1706.09161v2","created_at":"2026-05-18T00:07:50.754779+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.09161","created_at":"2026-05-18T00:07:50.754779+00:00"},{"alias_kind":"pith_short_12","alias_value":"LUNGCJIHPM4E","created_at":"2026-05-18T12:31:28.150371+00:00"},{"alias_kind":"pith_short_16","alias_value":"LUNGCJIHPM4EQ2UV","created_at":"2026-05-18T12:31:28.150371+00:00"},{"alias_kind":"pith_short_8","alias_value":"LUNGCJIH","created_at":"2026-05-18T12:31:28.150371+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/LUNGCJIHPM4EQ2UV6G6PKIGPHX","json":"https://pith.science/pith/LUNGCJIHPM4EQ2UV6G6PKIGPHX.json","graph_json":"https://pith.science/api/pith-number/LUNGCJIHPM4EQ2UV6G6PKIGPHX/graph.json","events_json":"https://pith.science/api/pith-number/LUNGCJIHPM4EQ2UV6G6PKIGPHX/events.json","paper":"https://pith.science/paper/LUNGCJIH"},"agent_actions":{"view_html":"https://pith.science/pith/LUNGCJIHPM4EQ2UV6G6PKIGPHX","download_json":"https://pith.science/pith/LUNGCJIHPM4EQ2UV6G6PKIGPHX.json","view_paper":"https://pith.science/paper/LUNGCJIH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1706.09161&json=true","fetch_graph":"https://pith.science/api/pith-number/LUNGCJIHPM4EQ2UV6G6PKIGPHX/graph.json","fetch_events":"https://pith.science/api/pith-number/LUNGCJIHPM4EQ2UV6G6PKIGPHX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LUNGCJIHPM4EQ2UV6G6PKIGPHX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LUNGCJIHPM4EQ2UV6G6PKIGPHX/action/storage_attestation","attest_author":"https://pith.science/pith/LUNGCJIHPM4EQ2UV6G6PKIGPHX/action/author_attestation","sign_citation":"https://pith.science/pith/LUNGCJIHPM4EQ2UV6G6PKIGPHX/action/citation_signature","submit_replication":"https://pith.science/pith/LUNGCJIHPM4EQ2UV6G6PKIGPHX/action/replication_record"}},"created_at":"2026-05-18T00:07:50.754779+00:00","updated_at":"2026-05-18T00:07:50.754779+00:00"}