{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:DUMRXT7JRIREUWWU3XKNAECC3A","short_pith_number":"pith:DUMRXT7J","canonical_record":{"source":{"id":"1405.2173","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2014-05-09T08:47:29Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"0dc1e77aef35cbc40e3b4f09791e14758317da1cd709dae7a04536597103ca52","abstract_canon_sha256":"dd6d00254086537fd7e6497941aeeb1519a128caef95d8dbcd8653e65b8bb957"},"schema_version":"1.0"},"canonical_sha256":"1d191bcfe98a224a5ad4ddd4d01042d824af03f6cbe6118a92e7474fa07ea920","source":{"kind":"arxiv","id":"1405.2173","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.2173","created_at":"2026-05-18T01:43:15Z"},{"alias_kind":"arxiv_version","alias_value":"1405.2173v2","created_at":"2026-05-18T01:43:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.2173","created_at":"2026-05-18T01:43:15Z"},{"alias_kind":"pith_short_12","alias_value":"DUMRXT7JRIRE","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"DUMRXT7JRIREUWWU","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"DUMRXT7J","created_at":"2026-05-18T12:28:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:DUMRXT7JRIREUWWU3XKNAECC3A","target":"record","payload":{"canonical_record":{"source":{"id":"1405.2173","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2014-05-09T08:47:29Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"0dc1e77aef35cbc40e3b4f09791e14758317da1cd709dae7a04536597103ca52","abstract_canon_sha256":"dd6d00254086537fd7e6497941aeeb1519a128caef95d8dbcd8653e65b8bb957"},"schema_version":"1.0"},"canonical_sha256":"1d191bcfe98a224a5ad4ddd4d01042d824af03f6cbe6118a92e7474fa07ea920","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:43:15.787237Z","signature_b64":"dVXojoFPE60Mh1WYUKwrPSTiLAiCrc3Qyf8Tfp0SLFMMuxKknLLNh460eg9sCLcl0DP+pmGg1wp+gRQdGlEZBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1d191bcfe98a224a5ad4ddd4d01042d824af03f6cbe6118a92e7474fa07ea920","last_reissued_at":"2026-05-18T01:43:15.786647Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:43:15.786647Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.2173","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:43:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WG0y1suc2LM4FL2gv4vkqn6rzwHSLPM43JKPH4HhxkWv8J6IyY21myQFeM+lVRhy8T5UR84iyEZiSuhoqcfdAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T11:15:47.271616Z"},"content_sha256":"35a4101ac083d7f9da11f55ca13878dc7bf3b1ef235f99c91f2d267b45996499","schema_version":"1.0","event_id":"sha256:35a4101ac083d7f9da11f55ca13878dc7bf3b1ef235f99c91f2d267b45996499"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:DUMRXT7JRIREUWWU3XKNAECC3A","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The evolution of a spatially homogeneous and isotropic universe filled with a collisionless gas","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"gr-qc","authors_text":"Francisco Astorga, Olivier Sarbach, Thomas Zannias","submitted_at":"2014-05-09T08:47:29Z","abstract_excerpt":"We review the evolution of a spatially homogeneous and isotropic universe described by a Friedmann-Robertson-Walker spacetime filled with a collisionless, neutral, simple, massive gas. The gas is described by a one-particle distribution function which satisfies the Liouville equation and is assumed to be homogeneous and isotropic. Making use of the isometries of the spacetime, we define precisely the homogeneity and isotropicity property of the distribution function, and based on this definition we give a concise derivation of the most general family of such distribution functions. For this fa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.2173","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:43:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tojtqWDmFH5E0hWHSc7P9Mt/AfXPKxb2d4aFMx1dW4aNRcgO54HoGjsz+0V4jY+E+6TVqh03TNbG+HasaDSHDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T11:15:47.272301Z"},"content_sha256":"b4a65e453c0e03a36767c13f3c0ef2087ebf9711fc49545f1d03e24b1f0a558c","schema_version":"1.0","event_id":"sha256:b4a65e453c0e03a36767c13f3c0ef2087ebf9711fc49545f1d03e24b1f0a558c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DUMRXT7JRIREUWWU3XKNAECC3A/bundle.json","state_url":"https://pith.science/pith/DUMRXT7JRIREUWWU3XKNAECC3A/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DUMRXT7JRIREUWWU3XKNAECC3A/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":"2026-05-26T11:15:47Z","links":{"resolver":"https://pith.science/pith/DUMRXT7JRIREUWWU3XKNAECC3A","bundle":"https://pith.science/pith/DUMRXT7JRIREUWWU3XKNAECC3A/bundle.json","state":"https://pith.science/pith/DUMRXT7JRIREUWWU3XKNAECC3A/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DUMRXT7JRIREUWWU3XKNAECC3A/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:DUMRXT7JRIREUWWU3XKNAECC3A","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":"dd6d00254086537fd7e6497941aeeb1519a128caef95d8dbcd8653e65b8bb957","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2014-05-09T08:47:29Z","title_canon_sha256":"0dc1e77aef35cbc40e3b4f09791e14758317da1cd709dae7a04536597103ca52"},"schema_version":"1.0","source":{"id":"1405.2173","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.2173","created_at":"2026-05-18T01:43:15Z"},{"alias_kind":"arxiv_version","alias_value":"1405.2173v2","created_at":"2026-05-18T01:43:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.2173","created_at":"2026-05-18T01:43:15Z"},{"alias_kind":"pith_short_12","alias_value":"DUMRXT7JRIRE","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"DUMRXT7JRIREUWWU","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"DUMRXT7J","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:b4a65e453c0e03a36767c13f3c0ef2087ebf9711fc49545f1d03e24b1f0a558c","target":"graph","created_at":"2026-05-18T01:43:15Z","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 review the evolution of a spatially homogeneous and isotropic universe described by a Friedmann-Robertson-Walker spacetime filled with a collisionless, neutral, simple, massive gas. The gas is described by a one-particle distribution function which satisfies the Liouville equation and is assumed to be homogeneous and isotropic. Making use of the isometries of the spacetime, we define precisely the homogeneity and isotropicity property of the distribution function, and based on this definition we give a concise derivation of the most general family of such distribution functions. For this fa","authors_text":"Francisco Astorga, Olivier Sarbach, Thomas Zannias","cross_cats":["cond-mat.stat-mech"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2014-05-09T08:47:29Z","title":"The evolution of a spatially homogeneous and isotropic universe filled with a collisionless gas"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.2173","kind":"arxiv","version":2},"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":"sha256:35a4101ac083d7f9da11f55ca13878dc7bf3b1ef235f99c91f2d267b45996499","target":"record","created_at":"2026-05-18T01:43:15Z","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":"dd6d00254086537fd7e6497941aeeb1519a128caef95d8dbcd8653e65b8bb957","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2014-05-09T08:47:29Z","title_canon_sha256":"0dc1e77aef35cbc40e3b4f09791e14758317da1cd709dae7a04536597103ca52"},"schema_version":"1.0","source":{"id":"1405.2173","kind":"arxiv","version":2}},"canonical_sha256":"1d191bcfe98a224a5ad4ddd4d01042d824af03f6cbe6118a92e7474fa07ea920","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1d191bcfe98a224a5ad4ddd4d01042d824af03f6cbe6118a92e7474fa07ea920","first_computed_at":"2026-05-18T01:43:15.786647Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:43:15.786647Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dVXojoFPE60Mh1WYUKwrPSTiLAiCrc3Qyf8Tfp0SLFMMuxKknLLNh460eg9sCLcl0DP+pmGg1wp+gRQdGlEZBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:43:15.787237Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.2173","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:35a4101ac083d7f9da11f55ca13878dc7bf3b1ef235f99c91f2d267b45996499","sha256:b4a65e453c0e03a36767c13f3c0ef2087ebf9711fc49545f1d03e24b1f0a558c"],"state_sha256":"3214786cfa8a98453b78f8d9f14f5a9cb3a5e5d3fa825da0ebea0f1ee426bb31"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tTuABYvy+g2oomd/sXN01r91PzYf7Ibk3GJCiXuCqADCeVubgzGvOXs+akalecLV5O+zJ6tbmBvKWfdtEisTCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T11:15:47.275191Z","bundle_sha256":"ccf479e8332a7398bc892041e485b3736b888c444104e5a948a4dba362352552"}}