{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:CGQGRAE7PBW4CLXWMG3J4GSEKA","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":"d122dc1facf9367974396dd542ac399b79e467c6e233bd3da40195a87e503f20","cross_cats_sorted":["cond-mat.stat-mech","gr-qc","hep-th"],"license":"","primary_cat":"astro-ph","submitted_at":"2006-01-26T14:27:17Z","title_canon_sha256":"68c783a7489429365a790842ec7f69fbb159bb211f9c4e660f835d6b378dc3cb"},"schema_version":"1.0","source":{"id":"astro-ph/0601600","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"astro-ph/0601600","created_at":"2026-05-18T01:40:32Z"},{"alias_kind":"arxiv_version","alias_value":"astro-ph/0601600v1","created_at":"2026-05-18T01:40:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.astro-ph/0601600","created_at":"2026-05-18T01:40:32Z"},{"alias_kind":"pith_short_12","alias_value":"CGQGRAE7PBW4","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"CGQGRAE7PBW4CLXW","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"CGQGRAE7","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:7859ec3988086e6e33d8a2d8e0226acfd8582781a0a72666816547c72ae28944","target":"graph","created_at":"2026-05-18T01:40:32Z","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 show that the self-gravitating gas at thermal equilibrium has an infinite volume limit in the three ensembles (GCE, CE, MCE) when (N, V) -> infty, keeping N/V^{1/3} fixed, that is, with eta = G m^2 N/[ V^{1/3} T] fixed. We develop MonteCarlo simulations, analytic mean field methods (MF) and low density expansions. We compute the equation of state and find it to be locally p(r) = T rho_V(r), that is a local ideal gas equation of state. The system is in a gaseous phase for eta < eta_T = 1.51024...and collapses into a very dense object for eta > eta_T in the CE with the pressure becoming large","authors_text":"H. J. de Vega, N. G. Sanchez","cross_cats":["cond-mat.stat-mech","gr-qc","hep-th"],"headline":"","license":"","primary_cat":"astro-ph","submitted_at":"2006-01-26T14:27:17Z","title":"Statistical Mechanics of the Self-Gravitating Gas: Thermodynamic Limit, Unstabilities and Phase Diagrams"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"astro-ph/0601600","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:e229fce7edb8997860429959299b713edce2f052148f35c645dee6193dd4ad03","target":"record","created_at":"2026-05-18T01:40:32Z","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":"d122dc1facf9367974396dd542ac399b79e467c6e233bd3da40195a87e503f20","cross_cats_sorted":["cond-mat.stat-mech","gr-qc","hep-th"],"license":"","primary_cat":"astro-ph","submitted_at":"2006-01-26T14:27:17Z","title_canon_sha256":"68c783a7489429365a790842ec7f69fbb159bb211f9c4e660f835d6b378dc3cb"},"schema_version":"1.0","source":{"id":"astro-ph/0601600","kind":"arxiv","version":1}},"canonical_sha256":"11a068809f786dc12ef661b69e1a445012ec51e2c423ab504039b8981a62c816","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"11a068809f786dc12ef661b69e1a445012ec51e2c423ab504039b8981a62c816","first_computed_at":"2026-05-18T01:40:32.634734Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:40:32.634734Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yBkDb3sswSmVy1xw0NwbWpby8+u6hU4F/LGnnKDA05dUhgb0aa9AR2vYWx9ik49ZjGJAkzQ37k6Z3BWuUJkhBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:40:32.635347Z","signed_message":"canonical_sha256_bytes"},"source_id":"astro-ph/0601600","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e229fce7edb8997860429959299b713edce2f052148f35c645dee6193dd4ad03","sha256:7859ec3988086e6e33d8a2d8e0226acfd8582781a0a72666816547c72ae28944"],"state_sha256":"6abed805c5bcb0af94bb050a5ef9b14f80f4ffd418e5148c5353a69e48713e28"}