{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2001:HP2MPO66VV3TFV4WON25LHZUM3","short_pith_number":"pith:HP2MPO66","canonical_record":{"source":{"id":"astro-ph/0103159","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"astro-ph","submitted_at":"2001-03-11T16:30:35Z","cross_cats_sorted":["cond-mat.stat-mech","nlin.CD","physics.flu-dyn"],"title_canon_sha256":"c5f167a6d0f67b36aa697ed5a3a53a239d9038822f3d5c5c8e44ae6145b65be6","abstract_canon_sha256":"31b879ae87fb67fa66fa1119e084d8a2d2d2b571eabbc87c0f83c40348172003"},"schema_version":"1.0"},"canonical_sha256":"3bf4c7bbdead7732d7967375d59f3466c74ef665aa65c260d6983b336bf57395","source":{"kind":"arxiv","id":"astro-ph/0103159","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"astro-ph/0103159","created_at":"2026-07-04T16:22:51Z"},{"alias_kind":"arxiv_version","alias_value":"astro-ph/0103159v2","created_at":"2026-07-04T16:22:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.astro-ph/0103159","created_at":"2026-07-04T16:22:51Z"},{"alias_kind":"pith_short_12","alias_value":"HP2MPO66VV3T","created_at":"2026-07-04T16:22:51Z"},{"alias_kind":"pith_short_16","alias_value":"HP2MPO66VV3TFV4W","created_at":"2026-07-04T16:22:51Z"},{"alias_kind":"pith_short_8","alias_value":"HP2MPO66","created_at":"2026-07-04T16:22:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2001:HP2MPO66VV3TFV4WON25LHZUM3","target":"record","payload":{"canonical_record":{"source":{"id":"astro-ph/0103159","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"astro-ph","submitted_at":"2001-03-11T16:30:35Z","cross_cats_sorted":["cond-mat.stat-mech","nlin.CD","physics.flu-dyn"],"title_canon_sha256":"c5f167a6d0f67b36aa697ed5a3a53a239d9038822f3d5c5c8e44ae6145b65be6","abstract_canon_sha256":"31b879ae87fb67fa66fa1119e084d8a2d2d2b571eabbc87c0f83c40348172003"},"schema_version":"1.0"},"canonical_sha256":"3bf4c7bbdead7732d7967375d59f3466c74ef665aa65c260d6983b336bf57395","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T16:22:51.240808Z","signature_b64":"Aao/wROHPU894zdNf6dF8hvUCUo/eo4C9FeE5uGT6v2Prw5A0Ki84gPUoaC17K7bbWXnlzbV296iVYpbJobsCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3bf4c7bbdead7732d7967375d59f3466c74ef665aa65c260d6983b336bf57395","last_reissued_at":"2026-07-04T16:22:51.240395Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T16:22:51.240395Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"astro-ph/0103159","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":"2026-07-04T16:22:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O5O0Au1g+/aco5e2lKmMlBsXkfs6o0Dl2aGJaedBiJt3o1buBSBUItG2GDWZMS/rpsNy8k3gS4KdlR85pP8OCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-01T07:43:36.970518Z"},"content_sha256":"7ec5a20791e4d0023e0b936b0d21e05c50f4a09f4c1232f9e59b50e860492432","schema_version":"1.0","event_id":"sha256:7ec5a20791e4d0023e0b936b0d21e05c50f4a09f4c1232f9e59b50e860492432"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2001:HP2MPO66VV3TFV4WON25LHZUM3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Gravitational instability of finite isothermal spheres","license":"","headline":"","cross_cats":["cond-mat.stat-mech","nlin.CD","physics.flu-dyn"],"primary_cat":"astro-ph","authors_text":"P.-H. Chavanis","submitted_at":"2001-03-11T16:30:35Z","abstract_excerpt":"We investigate the stability of bounded self-gravitating systems in the canonical ensemble by using a thermodynamical approach. Our study extends the earlier work of Padmanabhan [Astrophys. J. Supp. 71, 651 (1989)] in the microcanonical ensemble. By studying the second variations of the free energy, we find that instability sets in precisely at the point of minimum temperature in agreement with the theorem of Katz [ Mon. Not. R. astr. Soc. 183, 765 (1978)]. The perturbation that induces instability at this point is calculated explicitly; it has not a ``core-halo'' structure contrary to what ha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"astro-ph/0103159","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/astro-ph/0103159/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T16:22:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RttW4fX3zrR+xzXjRSC4xU2QqheQuyOnTj55iW6dVFMTn9xsn70fpqlRGZf/Kx2xdq2VexD5aiZB4Ijd9SmkAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-01T07:43:36.970903Z"},"content_sha256":"99d35b67c21ef1e1e8f45c96319fc4fd518be3b4e941a6268256764fe3704406","schema_version":"1.0","event_id":"sha256:99d35b67c21ef1e1e8f45c96319fc4fd518be3b4e941a6268256764fe3704406"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HP2MPO66VV3TFV4WON25LHZUM3/bundle.json","state_url":"https://pith.science/pith/HP2MPO66VV3TFV4WON25LHZUM3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HP2MPO66VV3TFV4WON25LHZUM3/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":"2026-08-01T07:43:36Z","links":{"resolver":"https://pith.science/pith/HP2MPO66VV3TFV4WON25LHZUM3","bundle":"https://pith.science/pith/HP2MPO66VV3TFV4WON25LHZUM3/bundle.json","state":"https://pith.science/pith/HP2MPO66VV3TFV4WON25LHZUM3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HP2MPO66VV3TFV4WON25LHZUM3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:HP2MPO66VV3TFV4WON25LHZUM3","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":"31b879ae87fb67fa66fa1119e084d8a2d2d2b571eabbc87c0f83c40348172003","cross_cats_sorted":["cond-mat.stat-mech","nlin.CD","physics.flu-dyn"],"license":"","primary_cat":"astro-ph","submitted_at":"2001-03-11T16:30:35Z","title_canon_sha256":"c5f167a6d0f67b36aa697ed5a3a53a239d9038822f3d5c5c8e44ae6145b65be6"},"schema_version":"1.0","source":{"id":"astro-ph/0103159","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"astro-ph/0103159","created_at":"2026-07-04T16:22:51Z"},{"alias_kind":"arxiv_version","alias_value":"astro-ph/0103159v2","created_at":"2026-07-04T16:22:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.astro-ph/0103159","created_at":"2026-07-04T16:22:51Z"},{"alias_kind":"pith_short_12","alias_value":"HP2MPO66VV3T","created_at":"2026-07-04T16:22:51Z"},{"alias_kind":"pith_short_16","alias_value":"HP2MPO66VV3TFV4W","created_at":"2026-07-04T16:22:51Z"},{"alias_kind":"pith_short_8","alias_value":"HP2MPO66","created_at":"2026-07-04T16:22:51Z"}],"graph_snapshots":[{"event_id":"sha256:99d35b67c21ef1e1e8f45c96319fc4fd518be3b4e941a6268256764fe3704406","target":"graph","created_at":"2026-07-04T16:22:51Z","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/astro-ph/0103159/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We investigate the stability of bounded self-gravitating systems in the canonical ensemble by using a thermodynamical approach. Our study extends the earlier work of Padmanabhan [Astrophys. J. Supp. 71, 651 (1989)] in the microcanonical ensemble. By studying the second variations of the free energy, we find that instability sets in precisely at the point of minimum temperature in agreement with the theorem of Katz [ Mon. Not. R. astr. Soc. 183, 765 (1978)]. The perturbation that induces instability at this point is calculated explicitly; it has not a ``core-halo'' structure contrary to what ha","authors_text":"P.-H. Chavanis","cross_cats":["cond-mat.stat-mech","nlin.CD","physics.flu-dyn"],"headline":"","license":"","primary_cat":"astro-ph","submitted_at":"2001-03-11T16:30:35Z","title":"Gravitational instability of finite isothermal spheres"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"astro-ph/0103159","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":"sha256:7ec5a20791e4d0023e0b936b0d21e05c50f4a09f4c1232f9e59b50e860492432","target":"record","created_at":"2026-07-04T16:22:51Z","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":"31b879ae87fb67fa66fa1119e084d8a2d2d2b571eabbc87c0f83c40348172003","cross_cats_sorted":["cond-mat.stat-mech","nlin.CD","physics.flu-dyn"],"license":"","primary_cat":"astro-ph","submitted_at":"2001-03-11T16:30:35Z","title_canon_sha256":"c5f167a6d0f67b36aa697ed5a3a53a239d9038822f3d5c5c8e44ae6145b65be6"},"schema_version":"1.0","source":{"id":"astro-ph/0103159","kind":"arxiv","version":2}},"canonical_sha256":"3bf4c7bbdead7732d7967375d59f3466c74ef665aa65c260d6983b336bf57395","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3bf4c7bbdead7732d7967375d59f3466c74ef665aa65c260d6983b336bf57395","first_computed_at":"2026-07-04T16:22:51.240395Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:22:51.240395Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Aao/wROHPU894zdNf6dF8hvUCUo/eo4C9FeE5uGT6v2Prw5A0Ki84gPUoaC17K7bbWXnlzbV296iVYpbJobsCA==","signature_status":"signed_v1","signed_at":"2026-07-04T16:22:51.240808Z","signed_message":"canonical_sha256_bytes"},"source_id":"astro-ph/0103159","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7ec5a20791e4d0023e0b936b0d21e05c50f4a09f4c1232f9e59b50e860492432","sha256:99d35b67c21ef1e1e8f45c96319fc4fd518be3b4e941a6268256764fe3704406"],"state_sha256":"701b18397759b94f5ee1929d8e0d38e3f3ed5a5565b3d444fd91488d45135e4b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qnzWkXNwJdW9ycP6hZiYbYugxpbtNggPJ5+DjlRI0gWXdV4RvpQWWR4utZB4VoV2N/BpGd7XXVKdnQCHm+TWAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-01T07:43:36.973543Z","bundle_sha256":"89540739d819f16b62f4605267d765197130a62d4f670b699746e83e50ccb39d"}}