{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:7SJXJ5ATH7GMHFZ4LXT3TA42TY","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":"41387f4239678ae54cc848748c8eb6bed422d22773ce512a5f9efc9a3afe2e73","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.GA","submitted_at":"2011-10-20T17:29:39Z","title_canon_sha256":"4381988eb94925d2cf3bc48469bcd2f9377d2c043ab3cd015ed35e56adf54d31"},"schema_version":"1.0","source":{"id":"1110.4588","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.4588","created_at":"2026-05-18T02:00:07Z"},{"alias_kind":"arxiv_version","alias_value":"1110.4588v2","created_at":"2026-05-18T02:00:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.4588","created_at":"2026-05-18T02:00:07Z"},{"alias_kind":"pith_short_12","alias_value":"7SJXJ5ATH7GM","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7SJXJ5ATH7GMHFZ4","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7SJXJ5AT","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:a59209bcb61fb3ee4bb435facb869b87384224960ce9d81cc336ba57b069e1ab","target":"graph","created_at":"2026-05-18T02:00:07Z","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 formulate the collisionless Boltzmann equation (CBE) for dense star clusters that lie within the radius of influence of a massive black hole in galactic nuclei. Our approach to these nearly Keplerian systems follows that of Sridhar and Touma (1999): Delaunay canonical variables are used to describe stellar orbits and we average over the fast Keplerian orbital phases. The stellar distribution function (DF) evolves on the longer time scale of precessional motions, whose dynamics is governed by a Hamiltonian, given by the orbit-averaged self-gravitational potential of the cluster. We specializ","authors_text":"Jihad R. Touma, S. Sridhar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.GA","submitted_at":"2011-10-20T17:29:39Z","title":"Counter-rotating stellar discs around a massive black hole: self-consistent, time-dependent dynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.4588","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:c01d5119c07d5c4db71369903c4660e0fab54062398d8ce9a6672d33547cc0a1","target":"record","created_at":"2026-05-18T02:00:07Z","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":"41387f4239678ae54cc848748c8eb6bed422d22773ce512a5f9efc9a3afe2e73","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.GA","submitted_at":"2011-10-20T17:29:39Z","title_canon_sha256":"4381988eb94925d2cf3bc48469bcd2f9377d2c043ab3cd015ed35e56adf54d31"},"schema_version":"1.0","source":{"id":"1110.4588","kind":"arxiv","version":2}},"canonical_sha256":"fc9374f4133fccc3973c5de7b9839a9e0358284d73814c8b39237bf79de51b8d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc9374f4133fccc3973c5de7b9839a9e0358284d73814c8b39237bf79de51b8d","first_computed_at":"2026-05-18T02:00:07.772718Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:00:07.772718Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NjYWJ3AyFIq7o/G7gL9bW5ZmeJ7GEz8WwG1Y57fs3p87rkQ0ut7NcFhxOoB3fNVDvq6MnwFqMNm2Gube6fGuBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:00:07.773334Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.4588","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c01d5119c07d5c4db71369903c4660e0fab54062398d8ce9a6672d33547cc0a1","sha256:a59209bcb61fb3ee4bb435facb869b87384224960ce9d81cc336ba57b069e1ab"],"state_sha256":"431f913e86a60c4464ace2794bdc6004f72a0bbe24cfb5c94bb2312388c95fb4"}