{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:226STT64E4YK2RQ7S2ML4N6N2U","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":"f737f11e669391d74f46da3b4a06d6038db1e9cf3868a959be04c405159590f1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2016-03-17T09:39:41Z","title_canon_sha256":"a87955a91ae18f013012412601c7afd523d58dbd5925b9bb5f80379650120e82"},"schema_version":"1.0","source":{"id":"1603.05404","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.05404","created_at":"2026-05-18T00:18:54Z"},{"alias_kind":"arxiv_version","alias_value":"1603.05404v2","created_at":"2026-05-18T00:18:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.05404","created_at":"2026-05-18T00:18:54Z"},{"alias_kind":"pith_short_12","alias_value":"226STT64E4YK","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"226STT64E4YK2RQ7","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"226STT64","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:669ffc9f1538e2552212bf458af152b4d637f4ef9e9b5538769fda4fccfd1b30","target":"graph","created_at":"2026-05-18T00:18:54Z","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":"Axisymmetric and stationary solutions are constructed to the Einstein--Vlasov and Vlasov--Poisson systems. These solutions are constructed numerically, using finite element methods and a fixed-point iteration in which the total mass is fixed at each step. A variety of axisymmetric stationary solutions are exhibited, including solutions with toroidal, disk-like, spindle-like, and composite spatial density configurations, as are solutions with non-vanishing net angular momentum. In the case of toroidal solutions, we show for the first time, solutions of the Einstein--Vlasov system which contain ","authors_text":"Anders Logg, Ellery Ames, H{\\aa}kan Andr\\'easson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2016-03-17T09:39:41Z","title":"On Axisymmetric and Stationary Solutions of the Self-Gravitating Vlasov System"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.05404","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:f5b8352ed87b6cc28fa7aba3103f58db98a36587f25f7d174410adcf3c87693c","target":"record","created_at":"2026-05-18T00:18:54Z","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":"f737f11e669391d74f46da3b4a06d6038db1e9cf3868a959be04c405159590f1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2016-03-17T09:39:41Z","title_canon_sha256":"a87955a91ae18f013012412601c7afd523d58dbd5925b9bb5f80379650120e82"},"schema_version":"1.0","source":{"id":"1603.05404","kind":"arxiv","version":2}},"canonical_sha256":"d6bd29cfdc2730ad461f9698be37cdd51e70355ab47846ac0c2f61b5b9d27510","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d6bd29cfdc2730ad461f9698be37cdd51e70355ab47846ac0c2f61b5b9d27510","first_computed_at":"2026-05-18T00:18:54.247485Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:54.247485Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"S8W4qdmNT69a56X9lzb7b7NxOzcyCucPAkYGS+IYTrOjHswaOLHVOR4bRkViJBfoUmMPBZVRZ1dCV1EG3PwOCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:54.247920Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.05404","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f5b8352ed87b6cc28fa7aba3103f58db98a36587f25f7d174410adcf3c87693c","sha256:669ffc9f1538e2552212bf458af152b4d637f4ef9e9b5538769fda4fccfd1b30"],"state_sha256":"071b8672a7a18815792bd7e51875f43df532b21a722ea175b10048be5ca0faab"}