{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:W5P62HCLK5CU45ZIJWM2L7J73F","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":"4b5f29111a9264a8d660220d652f4a4251cff3082cf0290209fc6b4ab8f0975f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-06-17T06:54:16Z","title_canon_sha256":"88cef53f2ad8a8ee28b177dfc3cbe185ef315b972da9348f8535e5da07d318e2"},"schema_version":"1.0","source":{"id":"1406.4255","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.4255","created_at":"2026-05-18T02:49:38Z"},{"alias_kind":"arxiv_version","alias_value":"1406.4255v1","created_at":"2026-05-18T02:49:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.4255","created_at":"2026-05-18T02:49:38Z"},{"alias_kind":"pith_short_12","alias_value":"W5P62HCLK5CU","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"W5P62HCLK5CU45ZI","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"W5P62HCL","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:f20b3d44a47049d76771295df7e121b85d896f4211834b6bda1950f0550fdcb6","target":"graph","created_at":"2026-05-18T02:49:38Z","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 investigate two dimensional steady Euler-Poisson system which describe the motion of compressible self-gravitating flows. The unique existence and stability of subsonic flows in a duct of finite length are obtained when prescribing the entropy at the entrance and the pressure at the exit. After introducing the stream function, the Euler-Poisson system can be decomposed into several transport equations and a second order nonlinear elliptic system. We discover an energy estimate for the associated elliptic system which is a key ingredient to prove the unique existence and stability of subsoni","authors_text":"Ben Duan, Chunjing Xie, Myoungjean Bae","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-06-17T06:54:16Z","title":"Two dimensional subsonic flows with self-gravitation in bounded domain"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.4255","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":"sha256:6b44acf9134779182f077ee754d6787f5d06212c20918109aef2ee293b10b21d","target":"record","created_at":"2026-05-18T02:49:38Z","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":"4b5f29111a9264a8d660220d652f4a4251cff3082cf0290209fc6b4ab8f0975f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-06-17T06:54:16Z","title_canon_sha256":"88cef53f2ad8a8ee28b177dfc3cbe185ef315b972da9348f8535e5da07d318e2"},"schema_version":"1.0","source":{"id":"1406.4255","kind":"arxiv","version":1}},"canonical_sha256":"b75fed1c4b57454e77284d99a5fd3fd94f9b13d550948fc552f83c719a482080","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b75fed1c4b57454e77284d99a5fd3fd94f9b13d550948fc552f83c719a482080","first_computed_at":"2026-05-18T02:49:38.017343Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:49:38.017343Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Z4oy0XKMeBDJR/TugSRbYFf52At0H+AmqflDE6WIIw9tnYEEw0xlBlrM+AAEtLnR/DtCnMjPZHvucuQ8QFdkDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:49:38.017805Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.4255","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6b44acf9134779182f077ee754d6787f5d06212c20918109aef2ee293b10b21d","sha256:f20b3d44a47049d76771295df7e121b85d896f4211834b6bda1950f0550fdcb6"],"state_sha256":"9fe6afcc2af267ad95d94d2a5a38ab56ad8a9e80234cee0c8e65df99ffade673"}