{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:X2CH3ZGXPRO43V42LQRUZSO53U","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":"c1936195dd29f837fa2f7e322798f4a48e9a1e2f7cbfc1906d8da4938d01c7ae","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph","submitted_at":"2008-08-19T15:10:15Z","title_canon_sha256":"aa7e1e7073dae92ac8eb3f0186798318db2c3721a7c3d85afa2a018ce25315df"},"schema_version":"1.0","source":{"id":"0808.2612","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0808.2612","created_at":"2026-05-18T04:14:36Z"},{"alias_kind":"arxiv_version","alias_value":"0808.2612v2","created_at":"2026-05-18T04:14:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0808.2612","created_at":"2026-05-18T04:14:36Z"},{"alias_kind":"pith_short_12","alias_value":"X2CH3ZGXPRO4","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"X2CH3ZGXPRO43V42","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"X2CH3ZGX","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:7b5cd752f1a0bc8a8d74c3554828910834a5e561ab795a03415e143da8135b80","target":"graph","created_at":"2026-05-18T04:14:36Z","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":"An analytical method is presented for treating the problem of a uniformly rotating, self-gravitating ring without a central body in Newtonian gravity. The method is based on an expansion about the thin ring limit, where the cross-section of the ring tends to a circle. The iterative scheme developed here is applied to homogeneous rings up to the 20th order and to polytropes with the index n=1 up to the third order. For other polytropic indices no analytic solutions are obtainable, but one can apply the method numerically. However, it is possible to derive a simple formula relating mass to the i","authors_text":"David Petroff, Stefan Horatschek","cross_cats":["gr-qc"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph","submitted_at":"2008-08-19T15:10:15Z","title":"Uniformly Rotating Homogeneous and Polytropic Rings in Newtonian Gravity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0808.2612","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":"sha256:6ad299dcfe825a4feae99136d89c2ea7ba01dac6295aa125cbe61b4a186c759b","target":"record","created_at":"2026-05-18T04:14:36Z","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":"c1936195dd29f837fa2f7e322798f4a48e9a1e2f7cbfc1906d8da4938d01c7ae","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph","submitted_at":"2008-08-19T15:10:15Z","title_canon_sha256":"aa7e1e7073dae92ac8eb3f0186798318db2c3721a7c3d85afa2a018ce25315df"},"schema_version":"1.0","source":{"id":"0808.2612","kind":"arxiv","version":2}},"canonical_sha256":"be847de4d77c5dcdd79a5c234cc9dddd2cf52aff22ebed5443cad535d06f4245","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"be847de4d77c5dcdd79a5c234cc9dddd2cf52aff22ebed5443cad535d06f4245","first_computed_at":"2026-05-18T04:14:36.405215Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:14:36.405215Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gDXKTSVhuUem7Mb2JiOxeTCr603Rrwf+pgCKzmAOFwkBqVkmTLbCrsgso8Fe5me3t6vhr7D/NOC0rS68ZGsmCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:14:36.405751Z","signed_message":"canonical_sha256_bytes"},"source_id":"0808.2612","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6ad299dcfe825a4feae99136d89c2ea7ba01dac6295aa125cbe61b4a186c759b","sha256:7b5cd752f1a0bc8a8d74c3554828910834a5e561ab795a03415e143da8135b80"],"state_sha256":"8942014592dadc3764497e2b7a6e7378d3c09f38a383158bfc157af556e9fd9e"}