{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:2EM6G5Z4HDHMQMKDAGENXUUGIB","short_pith_number":"pith:2EM6G5Z4","schema_version":"1.0","canonical_sha256":"d119e3773c38cec831430188dbd286404e1b19d4ff8206fa144cf91c1cf70617","source":{"kind":"arxiv","id":"1108.5561","version":2},"attestation_state":"computed","paper":{"title":"Relativistic (Lattice) Boltzmann Equation with Non-Ideal Equation of State","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","nucl-th","physics.flu-dyn"],"primary_cat":"gr-qc","authors_text":"Paul Romatschke","submitted_at":"2011-08-29T14:21:55Z","abstract_excerpt":"The relativistic Boltzmann equation for a single particle species generally implies a fixed, unchangeable equation of state that corresponds to that of an ideal gas. Real-world systems typically have more complicated equation of state which cannot be described by the Boltzmann equation. The present work derives a 'Boltzmann-like' equation that gives rise to a conserved energy-momentum tensor with an arbitrary (but thermodynamically consistent) equation of state. Using this, a Lattice Boltzmann scheme for diagonal metric tensors and arbitrary equations of state is constructed. The scheme is ver"},"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":"1108.5561","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2011-08-29T14:21:55Z","cross_cats_sorted":["hep-th","nucl-th","physics.flu-dyn"],"title_canon_sha256":"13fe854c1ca8c4da4e0a9944e1a6b0e5f33ecef8e554b6892d06977438d5a644","abstract_canon_sha256":"0e6ef24ea47b34da7f4d17dcfc385662378ceaccb1f29e7744ef120fb11235cb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:23:02.316826Z","signature_b64":"5OMb8e+UPDFNuS7sJ7IndV1KT7Ec+6U37zsX35mnOQ2bsUEooCMnwJEvNmGhrU11IjShqfX0KcrrTfoglqBDBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d119e3773c38cec831430188dbd286404e1b19d4ff8206fa144cf91c1cf70617","last_reissued_at":"2026-05-18T03:23:02.316308Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:23:02.316308Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Relativistic (Lattice) Boltzmann Equation with Non-Ideal Equation of State","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","nucl-th","physics.flu-dyn"],"primary_cat":"gr-qc","authors_text":"Paul Romatschke","submitted_at":"2011-08-29T14:21:55Z","abstract_excerpt":"The relativistic Boltzmann equation for a single particle species generally implies a fixed, unchangeable equation of state that corresponds to that of an ideal gas. Real-world systems typically have more complicated equation of state which cannot be described by the Boltzmann equation. The present work derives a 'Boltzmann-like' equation that gives rise to a conserved energy-momentum tensor with an arbitrary (but thermodynamically consistent) equation of state. Using this, a Lattice Boltzmann scheme for diagonal metric tensors and arbitrary equations of state is constructed. The scheme is ver"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.5561","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":"1108.5561","created_at":"2026-05-18T03:23:02.316399+00:00"},{"alias_kind":"arxiv_version","alias_value":"1108.5561v2","created_at":"2026-05-18T03:23:02.316399+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.5561","created_at":"2026-05-18T03:23:02.316399+00:00"},{"alias_kind":"pith_short_12","alias_value":"2EM6G5Z4HDHM","created_at":"2026-05-18T12:26:18.847500+00:00"},{"alias_kind":"pith_short_16","alias_value":"2EM6G5Z4HDHMQMKD","created_at":"2026-05-18T12:26:18.847500+00:00"},{"alias_kind":"pith_short_8","alias_value":"2EM6G5Z4","created_at":"2026-05-18T12:26:18.847500+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2604.22352","citing_title":"Four-dimensional QCD equation of state from a quasi-parton model with physics-informed neural networks","ref_index":37,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2EM6G5Z4HDHMQMKDAGENXUUGIB","json":"https://pith.science/pith/2EM6G5Z4HDHMQMKDAGENXUUGIB.json","graph_json":"https://pith.science/api/pith-number/2EM6G5Z4HDHMQMKDAGENXUUGIB/graph.json","events_json":"https://pith.science/api/pith-number/2EM6G5Z4HDHMQMKDAGENXUUGIB/events.json","paper":"https://pith.science/paper/2EM6G5Z4"},"agent_actions":{"view_html":"https://pith.science/pith/2EM6G5Z4HDHMQMKDAGENXUUGIB","download_json":"https://pith.science/pith/2EM6G5Z4HDHMQMKDAGENXUUGIB.json","view_paper":"https://pith.science/paper/2EM6G5Z4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1108.5561&json=true","fetch_graph":"https://pith.science/api/pith-number/2EM6G5Z4HDHMQMKDAGENXUUGIB/graph.json","fetch_events":"https://pith.science/api/pith-number/2EM6G5Z4HDHMQMKDAGENXUUGIB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2EM6G5Z4HDHMQMKDAGENXUUGIB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2EM6G5Z4HDHMQMKDAGENXUUGIB/action/storage_attestation","attest_author":"https://pith.science/pith/2EM6G5Z4HDHMQMKDAGENXUUGIB/action/author_attestation","sign_citation":"https://pith.science/pith/2EM6G5Z4HDHMQMKDAGENXUUGIB/action/citation_signature","submit_replication":"https://pith.science/pith/2EM6G5Z4HDHMQMKDAGENXUUGIB/action/replication_record"}},"created_at":"2026-05-18T03:23:02.316399+00:00","updated_at":"2026-05-18T03:23:02.316399+00:00"}