{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:YWYQYPOBXD6QMSMNYCJNYG63ZQ","short_pith_number":"pith:YWYQYPOB","canonical_record":{"source":{"id":"0710.3150","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"gr-qc","submitted_at":"2007-10-16T18:39:48Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"d6f0587202e274b30a7aadb998c5e739e20e9be945e5d370679c62b1fe68c1ee","abstract_canon_sha256":"210e595b8c08953889a4e708ec75de7c5136b8cca0f8013f4d04ebeaf98ac016"},"schema_version":"1.0"},"canonical_sha256":"c5b10c3dc1b8fd06498dc092dc1bdbcc0a063773409208f78d1b4e6c74e3325b","source":{"kind":"arxiv","id":"0710.3150","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0710.3150","created_at":"2026-05-18T02:46:04Z"},{"alias_kind":"arxiv_version","alias_value":"0710.3150v1","created_at":"2026-05-18T02:46:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0710.3150","created_at":"2026-05-18T02:46:04Z"},{"alias_kind":"pith_short_12","alias_value":"YWYQYPOBXD6Q","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"YWYQYPOBXD6QMSMN","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"YWYQYPOB","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:YWYQYPOBXD6QMSMNYCJNYG63ZQ","target":"record","payload":{"canonical_record":{"source":{"id":"0710.3150","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"gr-qc","submitted_at":"2007-10-16T18:39:48Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"d6f0587202e274b30a7aadb998c5e739e20e9be945e5d370679c62b1fe68c1ee","abstract_canon_sha256":"210e595b8c08953889a4e708ec75de7c5136b8cca0f8013f4d04ebeaf98ac016"},"schema_version":"1.0"},"canonical_sha256":"c5b10c3dc1b8fd06498dc092dc1bdbcc0a063773409208f78d1b4e6c74e3325b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:46:04.875631Z","signature_b64":"FfNGwoPqyn4/n5qhLVmVbPlKxvGIgbF8z4dsUDSzCbqpkF6Ox0oop5In3JsrAgnTJXhAt4D6aV/qG3eeD+vJCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c5b10c3dc1b8fd06498dc092dc1bdbcc0a063773409208f78d1b4e6c74e3325b","last_reissued_at":"2026-05-18T02:46:04.875088Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:46:04.875088Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0710.3150","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:46:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OqJwCDTjTijkwjv/A3QRASCS0ocCWuh2N01U4Gh2nWR6KPreNojQaWkc+FMh09c0Q5kLpebOXrS0n1Gg4+wyCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T22:20:20.451683Z"},"content_sha256":"94d1d534c87a4ccd96dfacfc9ff7b57dd3879e29b0e65bb3b84a51ef0a61d488","schema_version":"1.0","event_id":"sha256:94d1d534c87a4ccd96dfacfc9ff7b57dd3879e29b0e65bb3b84a51ef0a61d488"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:YWYQYPOBXD6QMSMNYCJNYG63ZQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nonlinear Dynamical Stability of Newtonian Rotating White Dwarfs and Supermassive Stars","license":"","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"gr-qc","authors_text":"Joel Smoller, Tao Luo","submitted_at":"2007-10-16T18:39:48Z","abstract_excerpt":"We prove general nonlinear stability and existence theorems for rotating star solutions which are axi-symmetric steady-state solutions of the compressible isentropic Euler-Poisson equations in 3 spatial dimensions. We apply our results to rotating and non-rotating white dwarf, and rotating high density supermassive (extreme relativistic) stars, stars which are in convective equilibrium and have uniform chemical composition. This paper is a continuation of our earlier work ([28])."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0710.3150","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T02:46:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SZADvbmGywJ0nNCMCalb6j8Rkzf/7NJxTQShzZB01QCDW866X8pCbDkerBoiiHUXo0pw1Mwoy6mN7EWHp/O8Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T22:20:20.452621Z"},"content_sha256":"1c1a8ef23a76b0a094a97d29a95aa61f4ede25363599c9712e2cb76604db464c","schema_version":"1.0","event_id":"sha256:1c1a8ef23a76b0a094a97d29a95aa61f4ede25363599c9712e2cb76604db464c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YWYQYPOBXD6QMSMNYCJNYG63ZQ/bundle.json","state_url":"https://pith.science/pith/YWYQYPOBXD6QMSMNYCJNYG63ZQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YWYQYPOBXD6QMSMNYCJNYG63ZQ/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":"2026-05-26T22:20:20Z","links":{"resolver":"https://pith.science/pith/YWYQYPOBXD6QMSMNYCJNYG63ZQ","bundle":"https://pith.science/pith/YWYQYPOBXD6QMSMNYCJNYG63ZQ/bundle.json","state":"https://pith.science/pith/YWYQYPOBXD6QMSMNYCJNYG63ZQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YWYQYPOBXD6QMSMNYCJNYG63ZQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:YWYQYPOBXD6QMSMNYCJNYG63ZQ","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":"210e595b8c08953889a4e708ec75de7c5136b8cca0f8013f4d04ebeaf98ac016","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"gr-qc","submitted_at":"2007-10-16T18:39:48Z","title_canon_sha256":"d6f0587202e274b30a7aadb998c5e739e20e9be945e5d370679c62b1fe68c1ee"},"schema_version":"1.0","source":{"id":"0710.3150","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0710.3150","created_at":"2026-05-18T02:46:04Z"},{"alias_kind":"arxiv_version","alias_value":"0710.3150v1","created_at":"2026-05-18T02:46:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0710.3150","created_at":"2026-05-18T02:46:04Z"},{"alias_kind":"pith_short_12","alias_value":"YWYQYPOBXD6Q","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"YWYQYPOBXD6QMSMN","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"YWYQYPOB","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:1c1a8ef23a76b0a094a97d29a95aa61f4ede25363599c9712e2cb76604db464c","target":"graph","created_at":"2026-05-18T02:46:04Z","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 prove general nonlinear stability and existence theorems for rotating star solutions which are axi-symmetric steady-state solutions of the compressible isentropic Euler-Poisson equations in 3 spatial dimensions. We apply our results to rotating and non-rotating white dwarf, and rotating high density supermassive (extreme relativistic) stars, stars which are in convective equilibrium and have uniform chemical composition. This paper is a continuation of our earlier work ([28]).","authors_text":"Joel Smoller, Tao Luo","cross_cats":["math-ph","math.MP"],"headline":"","license":"","primary_cat":"gr-qc","submitted_at":"2007-10-16T18:39:48Z","title":"Nonlinear Dynamical Stability of Newtonian Rotating White Dwarfs and Supermassive Stars"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0710.3150","kind":"arxiv","version":1},"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":"sha256:94d1d534c87a4ccd96dfacfc9ff7b57dd3879e29b0e65bb3b84a51ef0a61d488","target":"record","created_at":"2026-05-18T02:46:04Z","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":"210e595b8c08953889a4e708ec75de7c5136b8cca0f8013f4d04ebeaf98ac016","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"gr-qc","submitted_at":"2007-10-16T18:39:48Z","title_canon_sha256":"d6f0587202e274b30a7aadb998c5e739e20e9be945e5d370679c62b1fe68c1ee"},"schema_version":"1.0","source":{"id":"0710.3150","kind":"arxiv","version":1}},"canonical_sha256":"c5b10c3dc1b8fd06498dc092dc1bdbcc0a063773409208f78d1b4e6c74e3325b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c5b10c3dc1b8fd06498dc092dc1bdbcc0a063773409208f78d1b4e6c74e3325b","first_computed_at":"2026-05-18T02:46:04.875088Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:46:04.875088Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FfNGwoPqyn4/n5qhLVmVbPlKxvGIgbF8z4dsUDSzCbqpkF6Ox0oop5In3JsrAgnTJXhAt4D6aV/qG3eeD+vJCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:46:04.875631Z","signed_message":"canonical_sha256_bytes"},"source_id":"0710.3150","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:94d1d534c87a4ccd96dfacfc9ff7b57dd3879e29b0e65bb3b84a51ef0a61d488","sha256:1c1a8ef23a76b0a094a97d29a95aa61f4ede25363599c9712e2cb76604db464c"],"state_sha256":"81a6182e5c4c16666f6d0f18a215092fcc4b6cc4a44abd6d237306eb0d9855d1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hYWH4KPUZ6+xE7EZDGvpK15kQED1hv1FUxhfadF1My7abuANX2T3XHBg2mCMl3XVN/Gb9qBNXLrsnj3ZwBYrDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T22:20:20.455813Z","bundle_sha256":"0bba53b048f3d58f991887f93b2f321ec437bd0859b776ed032e00bfaffe8b77"}}