{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:7IUJDIG2VTJXGGCOPSQKE5LBTG","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":"18c55006041306780c9793950f7b221a21cd20a94870d8a06693943037afa32f","cross_cats_sorted":["astro-ph"],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2002-04-14T14:04:43Z","title_canon_sha256":"95fa48cc190482f983572c904bae936c550b26de15bbbac6931054cb0a4d6ec0"},"schema_version":"1.0","source":{"id":"cond-mat/0204303","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0204303","created_at":"2026-07-04T16:32:05Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0204303v1","created_at":"2026-07-04T16:32:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0204303","created_at":"2026-07-04T16:32:05Z"},{"alias_kind":"pith_short_12","alias_value":"7IUJDIG2VTJX","created_at":"2026-07-04T16:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"7IUJDIG2VTJXGGCO","created_at":"2026-07-04T16:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"7IUJDIG2","created_at":"2026-07-04T16:32:05Z"}],"graph_snapshots":[{"event_id":"sha256:3edbd16c39b56c1fd128b89e89e8da9192ca375941fc406513533e17967c36eb","target":"graph","created_at":"2026-07-04T16:32:05Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/cond-mat/0204303/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We address the thermodynamics (equilibrium density profiles, phase diagram, instability analysis...) and the collapse of a self-gravitating gas of Brownian particles in D dimensions, in both canonical and microcanonical ensembles. In the canonical ensemble, we derive the analytic form of the density scaling profile which decays as f(x)=x^{-\\alpha}, with alpha=2. In the microcanonical ensemble, we show that f decays as f(x)=x^{-\\alpha_{max}}, where \\alpha_{max} is a non-trivial exponent. We derive exact expansions for alpha_{max} and f in the limit of large D. Finally, we solve the problem in D","authors_text":"C. Sire, P.-H. Chavanis","cross_cats":["astro-ph"],"headline":"","license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2002-04-14T14:04:43Z","title":"Thermodynamics and collapse of self-gravitating Brownian particles in D dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0204303","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":"sha256:8b06a555a7a3226c2a3fa3ac0e159412b3c28578bfba6dce44f90db3bb3370f1","target":"record","created_at":"2026-07-04T16:32:05Z","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":"18c55006041306780c9793950f7b221a21cd20a94870d8a06693943037afa32f","cross_cats_sorted":["astro-ph"],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2002-04-14T14:04:43Z","title_canon_sha256":"95fa48cc190482f983572c904bae936c550b26de15bbbac6931054cb0a4d6ec0"},"schema_version":"1.0","source":{"id":"cond-mat/0204303","kind":"arxiv","version":1}},"canonical_sha256":"fa2891a0daacd373184e7ca0a2756199b8903171f13f8f281736d31fc88f8728","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fa2891a0daacd373184e7ca0a2756199b8903171f13f8f281736d31fc88f8728","first_computed_at":"2026-07-04T16:32:05.258487Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:32:05.258487Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MpwHLvhq3xiyWx2etvJu1ot+O9M6ac4+9vtc+AclA9rkylomJiMhxZCKSV0F0ZIA/n0ROWliYLgW36lUGW8LBg==","signature_status":"signed_v1","signed_at":"2026-07-04T16:32:05.258899Z","signed_message":"canonical_sha256_bytes"},"source_id":"cond-mat/0204303","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8b06a555a7a3226c2a3fa3ac0e159412b3c28578bfba6dce44f90db3bb3370f1","sha256:3edbd16c39b56c1fd128b89e89e8da9192ca375941fc406513533e17967c36eb"],"state_sha256":"2bc6fe705707d8781e2866bec850f035031377fc0aac3a8b0fa7fe61af017e5d"}