{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:MFW2IYR3IE6IM5UVNSL4J2L6CL","short_pith_number":"pith:MFW2IYR3","canonical_record":{"source":{"id":"1303.6463","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2013-03-26T12:53:30Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"e9ef8af1635791252303f66c57a8e30a8f546c965a878dc3fef3ad328ee57890","abstract_canon_sha256":"2f9873a5a275a7b9d063652842d1895a547443b5cdfe57d52ea6662c0eda9c0c"},"schema_version":"1.0"},"canonical_sha256":"616da4623b413c8676956c97c4e97e12f56a8c0ab4a1d9682bddc12f062d1b89","source":{"kind":"arxiv","id":"1303.6463","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.6463","created_at":"2026-05-18T02:54:21Z"},{"alias_kind":"arxiv_version","alias_value":"1303.6463v1","created_at":"2026-05-18T02:54:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.6463","created_at":"2026-05-18T02:54:21Z"},{"alias_kind":"pith_short_12","alias_value":"MFW2IYR3IE6I","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"MFW2IYR3IE6IM5UV","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"MFW2IYR3","created_at":"2026-05-18T12:27:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:MFW2IYR3IE6IM5UVNSL4J2L6CL","target":"record","payload":{"canonical_record":{"source":{"id":"1303.6463","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2013-03-26T12:53:30Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"e9ef8af1635791252303f66c57a8e30a8f546c965a878dc3fef3ad328ee57890","abstract_canon_sha256":"2f9873a5a275a7b9d063652842d1895a547443b5cdfe57d52ea6662c0eda9c0c"},"schema_version":"1.0"},"canonical_sha256":"616da4623b413c8676956c97c4e97e12f56a8c0ab4a1d9682bddc12f062d1b89","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:21.549494Z","signature_b64":"NSE/hgXU4imnWxxTpmlgM9FykBGtVjK0TUcPsjEugRmNy+8oKUqMDS8PRQ1X4OiZXDzNEHbeAKPnDtJVPVDRBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"616da4623b413c8676956c97c4e97e12f56a8c0ab4a1d9682bddc12f062d1b89","last_reissued_at":"2026-05-18T02:54:21.549078Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:21.549078Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1303.6463","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":"2026-05-18T02:54:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HdXqxkwM/Ok005LYkf1+QMUMDqjto4JrWsDl7Ew/bs4GHA47iIDulqnjUDqYk7FROrf4bj9tdrrKreV6qDS1Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T07:40:46.506712Z"},"content_sha256":"2b306aae191e9a093da8b2c1827a57ac5acab7cd4ec2843708b0157cc9d9697a","schema_version":"1.0","event_id":"sha256:2b306aae191e9a093da8b2c1827a57ac5acab7cd4ec2843708b0157cc9d9697a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:MFW2IYR3IE6IM5UVNSL4J2L6CL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Diffusion of relativistic gas mixtures in gravitational fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"gr-qc","authors_text":"Gilberto M. Kremer","submitted_at":"2013-03-26T12:53:30Z","abstract_excerpt":"A mixture of relativistic gases of non-disparate rest masses in a Schwarzschild metric is studied on the basis of a relativistic Boltzmann equation in the presence of gravitational fields. A BGK-type model equation of the collision operator of the Boltzmann equation is used in order to compute the non-equilibrium distribution functions by the Chapman-Enskog method. The main focus of this work is to obtain Fick's law without the thermal-diffusion cross-effect. Fick's law has four contributions, two of them are the usual terms proportional to the gradients of concentration and pressure. The othe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.6463","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":"2026-05-18T02:54:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rnhdZxLexDwBdOYjGULROClQsPPb+9I8mZ+SEuj3Y0qZlZPXhtYy1pxtp0kBmwqgspW4j9ydBmQFNoDR6oOfAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T07:40:46.507474Z"},"content_sha256":"eee16bcf70bcccc6e82f82f929677243c1315463fdf29ce1561c45d9e3567e8b","schema_version":"1.0","event_id":"sha256:eee16bcf70bcccc6e82f82f929677243c1315463fdf29ce1561c45d9e3567e8b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MFW2IYR3IE6IM5UVNSL4J2L6CL/bundle.json","state_url":"https://pith.science/pith/MFW2IYR3IE6IM5UVNSL4J2L6CL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MFW2IYR3IE6IM5UVNSL4J2L6CL/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":"2026-06-10T07:40:46Z","links":{"resolver":"https://pith.science/pith/MFW2IYR3IE6IM5UVNSL4J2L6CL","bundle":"https://pith.science/pith/MFW2IYR3IE6IM5UVNSL4J2L6CL/bundle.json","state":"https://pith.science/pith/MFW2IYR3IE6IM5UVNSL4J2L6CL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MFW2IYR3IE6IM5UVNSL4J2L6CL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:MFW2IYR3IE6IM5UVNSL4J2L6CL","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":"2f9873a5a275a7b9d063652842d1895a547443b5cdfe57d52ea6662c0eda9c0c","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2013-03-26T12:53:30Z","title_canon_sha256":"e9ef8af1635791252303f66c57a8e30a8f546c965a878dc3fef3ad328ee57890"},"schema_version":"1.0","source":{"id":"1303.6463","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.6463","created_at":"2026-05-18T02:54:21Z"},{"alias_kind":"arxiv_version","alias_value":"1303.6463v1","created_at":"2026-05-18T02:54:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.6463","created_at":"2026-05-18T02:54:21Z"},{"alias_kind":"pith_short_12","alias_value":"MFW2IYR3IE6I","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"MFW2IYR3IE6IM5UV","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"MFW2IYR3","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:eee16bcf70bcccc6e82f82f929677243c1315463fdf29ce1561c45d9e3567e8b","target":"graph","created_at":"2026-05-18T02:54:21Z","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":"A mixture of relativistic gases of non-disparate rest masses in a Schwarzschild metric is studied on the basis of a relativistic Boltzmann equation in the presence of gravitational fields. A BGK-type model equation of the collision operator of the Boltzmann equation is used in order to compute the non-equilibrium distribution functions by the Chapman-Enskog method. The main focus of this work is to obtain Fick's law without the thermal-diffusion cross-effect. Fick's law has four contributions, two of them are the usual terms proportional to the gradients of concentration and pressure. The othe","authors_text":"Gilberto M. Kremer","cross_cats":["cond-mat.stat-mech"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2013-03-26T12:53:30Z","title":"Diffusion of relativistic gas mixtures in gravitational fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.6463","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":"sha256:2b306aae191e9a093da8b2c1827a57ac5acab7cd4ec2843708b0157cc9d9697a","target":"record","created_at":"2026-05-18T02:54:21Z","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":"2f9873a5a275a7b9d063652842d1895a547443b5cdfe57d52ea6662c0eda9c0c","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2013-03-26T12:53:30Z","title_canon_sha256":"e9ef8af1635791252303f66c57a8e30a8f546c965a878dc3fef3ad328ee57890"},"schema_version":"1.0","source":{"id":"1303.6463","kind":"arxiv","version":1}},"canonical_sha256":"616da4623b413c8676956c97c4e97e12f56a8c0ab4a1d9682bddc12f062d1b89","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"616da4623b413c8676956c97c4e97e12f56a8c0ab4a1d9682bddc12f062d1b89","first_computed_at":"2026-05-18T02:54:21.549078Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:54:21.549078Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NSE/hgXU4imnWxxTpmlgM9FykBGtVjK0TUcPsjEugRmNy+8oKUqMDS8PRQ1X4OiZXDzNEHbeAKPnDtJVPVDRBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:54:21.549494Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.6463","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2b306aae191e9a093da8b2c1827a57ac5acab7cd4ec2843708b0157cc9d9697a","sha256:eee16bcf70bcccc6e82f82f929677243c1315463fdf29ce1561c45d9e3567e8b"],"state_sha256":"322a87ca41332d71c07ba718728d044d24cc032766918a186ef62bba411f27d0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FET0ZzKwjUnXCApQyEuWyG19dmgZdIXvEN8h3otuLb5uUFeGJx+ZJBjqPSxGdriEZxB56stOj0Zz9vIXWTWaDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T07:40:46.512115Z","bundle_sha256":"bc23347f83a81ac662a5ea9bae49fc1a41f264c6a7124c87c3e460cd89b86934"}}