{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:4SWBWUGXBYPCDK6ELDSV7N4RZV","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":"1306d684508a95c62df23c25ca67d007704cd6aa88165762e4755facbc7e8e12","cross_cats_sorted":[],"license":"","primary_cat":"astro-ph","submitted_at":"2005-08-13T15:03:01Z","title_canon_sha256":"391e26916b0c23c533b7e560e0f182da1fabda0a7a1e0d959052941ea42d42ef"},"schema_version":"1.0","source":{"id":"astro-ph/0508308","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"astro-ph/0508308","created_at":"2026-07-04T17:15:00Z"},{"alias_kind":"arxiv_version","alias_value":"astro-ph/0508308v2","created_at":"2026-07-04T17:15:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.astro-ph/0508308","created_at":"2026-07-04T17:15:00Z"},{"alias_kind":"pith_short_12","alias_value":"4SWBWUGXBYPC","created_at":"2026-07-04T17:15:00Z"},{"alias_kind":"pith_short_16","alias_value":"4SWBWUGXBYPCDK6E","created_at":"2026-07-04T17:15:00Z"},{"alias_kind":"pith_short_8","alias_value":"4SWBWUGX","created_at":"2026-07-04T17:15:00Z"}],"graph_snapshots":[{"event_id":"sha256:7ccbb1b5e089f79f993d090e00ddb4f92f417492090bf21760c1c848c0d056f4","target":"graph","created_at":"2026-07-04T17:15:00Z","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/0508308/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The collisionless quasi-equilibrium state realized after the cold collapse of self-gravitating systems has two remarkable characters. One of them is the linear temperature-mass (TM) relation, which yields a characteristic non-Gaussian velocity distribution. Another is the local virial (LV) relation, the virial relation which holds even locally in collisionless systems through phase mixing such as cold-collapse. A family of polytropes are examined from a view point of these two characters. The LV relation imposes a strong constraint on these models: only polytropes with index $n \\sim 5$ with a ","authors_text":"A.Nakamichi, M.Morikawa, O.Iguchi, Y.Sota","cross_cats":[],"headline":"","license":"","primary_cat":"astro-ph","submitted_at":"2005-08-13T15:03:01Z","title":"Local virial relation and velocity anisotropy for collisionless self-gravitating systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"astro-ph/0508308","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:f7aad13ba02ed1b41ec11a4a1f201b97f31d508f59f99c77f19ba81010dc58c9","target":"record","created_at":"2026-07-04T17:15:00Z","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":"1306d684508a95c62df23c25ca67d007704cd6aa88165762e4755facbc7e8e12","cross_cats_sorted":[],"license":"","primary_cat":"astro-ph","submitted_at":"2005-08-13T15:03:01Z","title_canon_sha256":"391e26916b0c23c533b7e560e0f182da1fabda0a7a1e0d959052941ea42d42ef"},"schema_version":"1.0","source":{"id":"astro-ph/0508308","kind":"arxiv","version":2}},"canonical_sha256":"e4ac1b50d70e1e21abc458e55fb791cd57323ad32971c3a1161151d030d408b3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e4ac1b50d70e1e21abc458e55fb791cd57323ad32971c3a1161151d030d408b3","first_computed_at":"2026-07-04T17:15:00.708709Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T17:15:00.708709Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cMuE28u93ZQjLaA1zSP6C04BEDUithrKJidvca8hfVlaM3uLPLVPZE0fBBPuV67kbWaP2FhmnkSxNXgwsU9KBg==","signature_status":"signed_v1","signed_at":"2026-07-04T17:15:00.709199Z","signed_message":"canonical_sha256_bytes"},"source_id":"astro-ph/0508308","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f7aad13ba02ed1b41ec11a4a1f201b97f31d508f59f99c77f19ba81010dc58c9","sha256:7ccbb1b5e089f79f993d090e00ddb4f92f417492090bf21760c1c848c0d056f4"],"state_sha256":"0dba80c0e0b46f37b7a5dc3b5787e40a99fc34c4c3f955d23d7c7b27a2475c1f"}