{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:GBMURW6Q5FUIUF5SKWFRS5FRLL","short_pith_number":"pith:GBMURW6Q","canonical_record":{"source":{"id":"1104.5262","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2011-04-27T22:31:22Z","cross_cats_sorted":["astro-ph.GA","astro-ph.SR"],"title_canon_sha256":"dbeb40db041d0c850b22f31c5a00fc1ee89f51fbf5807ba86dcdc9f8ef1eb3c5","abstract_canon_sha256":"3031db6e8bb791816f7cfe99ad6ecfc7fb6ea77d4ca38af7540577b258a25cb1"},"schema_version":"1.0"},"canonical_sha256":"305948dbd0e9688a17b2558b1974b15ae9418c6233260cd585b5fd46ad372187","source":{"kind":"arxiv","id":"1104.5262","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.5262","created_at":"2026-05-18T04:18:55Z"},{"alias_kind":"arxiv_version","alias_value":"1104.5262v1","created_at":"2026-05-18T04:18:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.5262","created_at":"2026-05-18T04:18:55Z"},{"alias_kind":"pith_short_12","alias_value":"GBMURW6Q5FUI","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"GBMURW6Q5FUIUF5S","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"GBMURW6Q","created_at":"2026-05-18T12:26:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:GBMURW6Q5FUIUF5SKWFRS5FRLL","target":"record","payload":{"canonical_record":{"source":{"id":"1104.5262","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2011-04-27T22:31:22Z","cross_cats_sorted":["astro-ph.GA","astro-ph.SR"],"title_canon_sha256":"dbeb40db041d0c850b22f31c5a00fc1ee89f51fbf5807ba86dcdc9f8ef1eb3c5","abstract_canon_sha256":"3031db6e8bb791816f7cfe99ad6ecfc7fb6ea77d4ca38af7540577b258a25cb1"},"schema_version":"1.0"},"canonical_sha256":"305948dbd0e9688a17b2558b1974b15ae9418c6233260cd585b5fd46ad372187","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:18:55.235847Z","signature_b64":"BoM0sf63Xvhs1CYJBEf42potpVHGAcyDzNk77HzLLRkkbLQ2hG8CEE5DiAllTUntFhV5zLxbfkOdtlwGl/PJDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"305948dbd0e9688a17b2558b1974b15ae9418c6233260cd585b5fd46ad372187","last_reissued_at":"2026-05-18T04:18:55.235308Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:18:55.235308Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1104.5262","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":"2026-05-18T04:18:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dblh3whYPjEIZjnsxgPJD8c3iyzwtx9GYOcFT6a0zDb3tbgiPhrDm/ao2LvP1CzIbt2Tnv+4d9Mtd1jjOlK9Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T18:47:22.860365Z"},"content_sha256":"29c2f63d05fd197e79a3ef8e5f9c745a9a7be876fff51c3b9ff9790001c68eb4","schema_version":"1.0","event_id":"sha256:29c2f63d05fd197e79a3ef8e5f9c745a9a7be876fff51c3b9ff9790001c68eb4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:GBMURW6Q5FUIUF5SKWFRS5FRLL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Kinetic Theory of Collisionless Self-Gravitating Gases: Post-Newtonian Polytropes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.GA","astro-ph.SR"],"primary_cat":"gr-qc","authors_text":"C. A. Ag\\'on, J. F. Pedraza, J. Ramos-Caro","submitted_at":"2011-04-27T22:31:22Z","abstract_excerpt":"In this paper we study the kinetic theory of many-particle astrophysical systems and we present a consistent version of the collisionless Boltzmann equation in the 1PN approximation. We argue that the equation presented by Rezania and Sobouti in A&A 354 1110 (2000) is not the correct expression to describe the evolution of a collisionless self-gravitating gas. One of the reasons that account for the previous statement is that the energy of a free-falling test particle, obeying the 1PN equations of motion for static gravitational fields, is not a static solution of the mentioned equation. The s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.5262","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":"2026-05-18T04:18:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3+H12NSLg39atjcic0ocv9lHlj5OnM7GMjqll5LJ5F5PHDeswBLnhTv20OaCBaWbIvGX+xyJU7/3l+u8XyMqCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T18:47:22.860722Z"},"content_sha256":"ea0c6a28e54c872f3e8e8be84d943c31274688f2f15167d67198df835c99796a","schema_version":"1.0","event_id":"sha256:ea0c6a28e54c872f3e8e8be84d943c31274688f2f15167d67198df835c99796a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GBMURW6Q5FUIUF5SKWFRS5FRLL/bundle.json","state_url":"https://pith.science/pith/GBMURW6Q5FUIUF5SKWFRS5FRLL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GBMURW6Q5FUIUF5SKWFRS5FRLL/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":"2026-06-10T18:47:22Z","links":{"resolver":"https://pith.science/pith/GBMURW6Q5FUIUF5SKWFRS5FRLL","bundle":"https://pith.science/pith/GBMURW6Q5FUIUF5SKWFRS5FRLL/bundle.json","state":"https://pith.science/pith/GBMURW6Q5FUIUF5SKWFRS5FRLL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GBMURW6Q5FUIUF5SKWFRS5FRLL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:GBMURW6Q5FUIUF5SKWFRS5FRLL","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":"3031db6e8bb791816f7cfe99ad6ecfc7fb6ea77d4ca38af7540577b258a25cb1","cross_cats_sorted":["astro-ph.GA","astro-ph.SR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2011-04-27T22:31:22Z","title_canon_sha256":"dbeb40db041d0c850b22f31c5a00fc1ee89f51fbf5807ba86dcdc9f8ef1eb3c5"},"schema_version":"1.0","source":{"id":"1104.5262","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.5262","created_at":"2026-05-18T04:18:55Z"},{"alias_kind":"arxiv_version","alias_value":"1104.5262v1","created_at":"2026-05-18T04:18:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.5262","created_at":"2026-05-18T04:18:55Z"},{"alias_kind":"pith_short_12","alias_value":"GBMURW6Q5FUI","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"GBMURW6Q5FUIUF5S","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"GBMURW6Q","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:ea0c6a28e54c872f3e8e8be84d943c31274688f2f15167d67198df835c99796a","target":"graph","created_at":"2026-05-18T04:18:55Z","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":"In this paper we study the kinetic theory of many-particle astrophysical systems and we present a consistent version of the collisionless Boltzmann equation in the 1PN approximation. We argue that the equation presented by Rezania and Sobouti in A&A 354 1110 (2000) is not the correct expression to describe the evolution of a collisionless self-gravitating gas. One of the reasons that account for the previous statement is that the energy of a free-falling test particle, obeying the 1PN equations of motion for static gravitational fields, is not a static solution of the mentioned equation. The s","authors_text":"C. A. Ag\\'on, J. F. Pedraza, J. Ramos-Caro","cross_cats":["astro-ph.GA","astro-ph.SR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2011-04-27T22:31:22Z","title":"Kinetic Theory of Collisionless Self-Gravitating Gases: Post-Newtonian Polytropes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.5262","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":"sha256:29c2f63d05fd197e79a3ef8e5f9c745a9a7be876fff51c3b9ff9790001c68eb4","target":"record","created_at":"2026-05-18T04:18:55Z","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":"3031db6e8bb791816f7cfe99ad6ecfc7fb6ea77d4ca38af7540577b258a25cb1","cross_cats_sorted":["astro-ph.GA","astro-ph.SR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2011-04-27T22:31:22Z","title_canon_sha256":"dbeb40db041d0c850b22f31c5a00fc1ee89f51fbf5807ba86dcdc9f8ef1eb3c5"},"schema_version":"1.0","source":{"id":"1104.5262","kind":"arxiv","version":1}},"canonical_sha256":"305948dbd0e9688a17b2558b1974b15ae9418c6233260cd585b5fd46ad372187","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"305948dbd0e9688a17b2558b1974b15ae9418c6233260cd585b5fd46ad372187","first_computed_at":"2026-05-18T04:18:55.235308Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:18:55.235308Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BoM0sf63Xvhs1CYJBEf42potpVHGAcyDzNk77HzLLRkkbLQ2hG8CEE5DiAllTUntFhV5zLxbfkOdtlwGl/PJDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:18:55.235847Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.5262","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:29c2f63d05fd197e79a3ef8e5f9c745a9a7be876fff51c3b9ff9790001c68eb4","sha256:ea0c6a28e54c872f3e8e8be84d943c31274688f2f15167d67198df835c99796a"],"state_sha256":"133fcce0a80e91e1b2a99789937c753a7737703b5d89fdd721864ba3cda86612"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PqFcRNn+Qj5x12IB5ee4w4+eco32g4l0BW95PGuiZSn3RiRuFG/KcHuQw0aRXpa89q/b/RG21hrzGTpJoaVDCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T18:47:22.862740Z","bundle_sha256":"fd4e0de6fcb5d5d4d8cfc514984c718e9bd9b7e2d0a222a78c6da4ce452d65c9"}}