{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:6GKEWYSU6Y6OVIF6VG4DPLKKBE","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":"69e0e424b9434a7ddd5d811460f1ef89bc3478b7bc4bcdc97eec4eee4730da24","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2019-08-28T16:36:58Z","title_canon_sha256":"8e6c24584682d6165ecc65236bd8c39000fbc792d0632bc0990e48a9f30b49ef"},"schema_version":"1.0","source":{"id":"1908.10817","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.10817","created_at":"2026-07-05T02:01:28Z"},{"alias_kind":"arxiv_version","alias_value":"1908.10817v1","created_at":"2026-07-05T02:01:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.10817","created_at":"2026-07-05T02:01:28Z"},{"alias_kind":"pith_short_12","alias_value":"6GKEWYSU6Y6O","created_at":"2026-07-05T02:01:28Z"},{"alias_kind":"pith_short_16","alias_value":"6GKEWYSU6Y6OVIF6","created_at":"2026-07-05T02:01:28Z"},{"alias_kind":"pith_short_8","alias_value":"6GKEWYSU","created_at":"2026-07-05T02:01:28Z"}],"graph_snapshots":[{"event_id":"sha256:d01d3f974dd990f2876336a874abb45e03b0f2575749483cc41395ef5be88e01","target":"graph","created_at":"2026-07-05T02:01:28Z","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/1908.10817/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the statistical mechanics of classical self-gravitating systems confined within a box of radius $R$ in general relativity. It has been found that the caloric curve $T_{\\infty}(E)$ has the form of a double spiral whose shape depends on the compactness parameter $\\nu=GNm/Rc^2$. The double spiral shrinks as $\\nu$ increases and finally disappears when $\\nu_{\\rm max}=0.1764$. Therefore, general relativistic effects render the system more unstable. On the other hand, the cold spiral and the hot spiral move away from each other as $\\nu$ decreases. Using a normalization $\\Lambda=-ER/GN^2m^2$ ","authors_text":"Pierre-Henri Chavanis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2019-08-28T16:36:58Z","title":"Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.10817","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:ed8087340e1e70cab9a6abb4985abeea3611d5001251565919acb54dd169ca12","target":"record","created_at":"2026-07-05T02:01:28Z","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":"69e0e424b9434a7ddd5d811460f1ef89bc3478b7bc4bcdc97eec4eee4730da24","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2019-08-28T16:36:58Z","title_canon_sha256":"8e6c24584682d6165ecc65236bd8c39000fbc792d0632bc0990e48a9f30b49ef"},"schema_version":"1.0","source":{"id":"1908.10817","kind":"arxiv","version":1}},"canonical_sha256":"f1944b6254f63ceaa0bea9b837ad4a093b70187a6e09cb4288ba0e5bbfcf8c8a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f1944b6254f63ceaa0bea9b837ad4a093b70187a6e09cb4288ba0e5bbfcf8c8a","first_computed_at":"2026-07-05T02:01:28.051028Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:01:28.051028Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PUparjxD/PkW7B+f6QMWU91/m3/kuGkNE9pQfos7PF30v1tWGySdDUwsFB5jNSvUWwrWunKrZdJQgvmJ/BvgAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T02:01:28.051452Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.10817","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ed8087340e1e70cab9a6abb4985abeea3611d5001251565919acb54dd169ca12","sha256:d01d3f974dd990f2876336a874abb45e03b0f2575749483cc41395ef5be88e01"],"state_sha256":"be51305941ca3dfe20718d753221dd7d839e2fb4cd31127cd187f89bddd1d5d8"}