{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:J3UC72MUSKJYY5Q43ZLB6RXV4K","short_pith_number":"pith:J3UC72MU","schema_version":"1.0","canonical_sha256":"4ee82fe99492938c761cde561f46f5e29cb263c0f00752eff54ca715fa4b136d","source":{"kind":"arxiv","id":"1209.2754","version":1},"attestation_state":"computed","paper":{"title":"New derivation of the Lagrangian of a perfect fluid with a barotropic equation of state","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.CO","math-ph","math.MP"],"primary_cat":"gr-qc","authors_text":"Olivier Minazzoli, Tiberiu Harko","submitted_at":"2012-09-12T23:45:32Z","abstract_excerpt":"In this paper we give a simple proof that when the particle number is conserved, the Lagrangian of a barotropic perfect fluid is $\\mathcal{L}_m=-\\rho [c^2 +\\int P(\\rho)/\\rho^2 d\\rho]$, where $\\rho$ is the \\textit{rest mass} density and $P(\\rho)$ is the pressure. To prove this result nor additional fields neither Lagrange multipliers are needed. Besides, the result is applicable to a wide range of theories of gravitation. The only assumptions used in the derivation are: 1) the matter part of the Lagrangian does not depend on the derivatives of the metric, and 2) the particle number of the fluid"},"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":"1209.2754","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2012-09-12T23:45:32Z","cross_cats_sorted":["astro-ph.CO","math-ph","math.MP"],"title_canon_sha256":"f2a3633bedbadcdc0fe0576ccfa37143f0649c9669a269c76554e07beaf60a63","abstract_canon_sha256":"9e52f6cb940d4aa68f8082adfa176a42504951e2b8a228c80c74676725a51699"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:43:39.843538Z","signature_b64":"YxSXJTmtoGZA/nFAQaA8Ag/ZT2zWFTRJLQENKPEhuF9XfvgJ3dJl0Z2ouGmEZeeYc6Ee4hfhkFTbKFus/iIeCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4ee82fe99492938c761cde561f46f5e29cb263c0f00752eff54ca715fa4b136d","last_reissued_at":"2026-05-18T03:43:39.842870Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:43:39.842870Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"New derivation of the Lagrangian of a perfect fluid with a barotropic equation of state","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.CO","math-ph","math.MP"],"primary_cat":"gr-qc","authors_text":"Olivier Minazzoli, Tiberiu Harko","submitted_at":"2012-09-12T23:45:32Z","abstract_excerpt":"In this paper we give a simple proof that when the particle number is conserved, the Lagrangian of a barotropic perfect fluid is $\\mathcal{L}_m=-\\rho [c^2 +\\int P(\\rho)/\\rho^2 d\\rho]$, where $\\rho$ is the \\textit{rest mass} density and $P(\\rho)$ is the pressure. To prove this result nor additional fields neither Lagrange multipliers are needed. Besides, the result is applicable to a wide range of theories of gravitation. The only assumptions used in the derivation are: 1) the matter part of the Lagrangian does not depend on the derivatives of the metric, and 2) the particle number of the fluid"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.2754","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1209.2754","created_at":"2026-05-18T03:43:39.842974+00:00"},{"alias_kind":"arxiv_version","alias_value":"1209.2754v1","created_at":"2026-05-18T03:43:39.842974+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.2754","created_at":"2026-05-18T03:43:39.842974+00:00"},{"alias_kind":"pith_short_12","alias_value":"J3UC72MUSKJY","created_at":"2026-05-18T12:27:09.501522+00:00"},{"alias_kind":"pith_short_16","alias_value":"J3UC72MUSKJYY5Q4","created_at":"2026-05-18T12:27:09.501522+00:00"},{"alias_kind":"pith_short_8","alias_value":"J3UC72MU","created_at":"2026-05-18T12:27:09.501522+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/J3UC72MUSKJYY5Q43ZLB6RXV4K","json":"https://pith.science/pith/J3UC72MUSKJYY5Q43ZLB6RXV4K.json","graph_json":"https://pith.science/api/pith-number/J3UC72MUSKJYY5Q43ZLB6RXV4K/graph.json","events_json":"https://pith.science/api/pith-number/J3UC72MUSKJYY5Q43ZLB6RXV4K/events.json","paper":"https://pith.science/paper/J3UC72MU"},"agent_actions":{"view_html":"https://pith.science/pith/J3UC72MUSKJYY5Q43ZLB6RXV4K","download_json":"https://pith.science/pith/J3UC72MUSKJYY5Q43ZLB6RXV4K.json","view_paper":"https://pith.science/paper/J3UC72MU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1209.2754&json=true","fetch_graph":"https://pith.science/api/pith-number/J3UC72MUSKJYY5Q43ZLB6RXV4K/graph.json","fetch_events":"https://pith.science/api/pith-number/J3UC72MUSKJYY5Q43ZLB6RXV4K/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/J3UC72MUSKJYY5Q43ZLB6RXV4K/action/timestamp_anchor","attest_storage":"https://pith.science/pith/J3UC72MUSKJYY5Q43ZLB6RXV4K/action/storage_attestation","attest_author":"https://pith.science/pith/J3UC72MUSKJYY5Q43ZLB6RXV4K/action/author_attestation","sign_citation":"https://pith.science/pith/J3UC72MUSKJYY5Q43ZLB6RXV4K/action/citation_signature","submit_replication":"https://pith.science/pith/J3UC72MUSKJYY5Q43ZLB6RXV4K/action/replication_record"}},"created_at":"2026-05-18T03:43:39.842974+00:00","updated_at":"2026-05-18T03:43:39.842974+00:00"}