{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:P3PZMMF24ECUFLUO52RYUGQPAZ","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":"2c5145a62a9fa2cfdab048d8f948c5c1852224ad29acf64fa0084df7d1414b5b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-08-17T08:10:08Z","title_canon_sha256":"804c0696da2dc8526dd9ea53c8ef2729f0d69bee579a72875b94deb7c89b1c8e"},"schema_version":"1.0","source":{"id":"1108.3416","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.3416","created_at":"2026-05-18T03:55:24Z"},{"alias_kind":"arxiv_version","alias_value":"1108.3416v3","created_at":"2026-05-18T03:55:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.3416","created_at":"2026-05-18T03:55:24Z"},{"alias_kind":"pith_short_12","alias_value":"P3PZMMF24ECU","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"P3PZMMF24ECUFLUO","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"P3PZMMF2","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:1d60aa02ce9383d537b3d6078be8e93f65881fe644921ae719720f16347a8a18","target":"graph","created_at":"2026-05-18T03:55:24Z","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":"Quasi-stationary, or metastable, states play an important role in two-dimensional turbulent fluid flows where they often emerge on time-scales much shorter than the viscous time scale, and then dominate the dynamics for very long time intervals. In this paper we propose a dynamical systems explanation of the metastability of an explicit family of solutions, referred to as bar states, of the two-dimensional incompressible Navier-Stokes equation on the torus. These states are physically relevant because they are associated with certain maximum entropy solutions of the Euler equations, and they h","authors_text":"C. Eugene Wayne, Margaret Beck","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-08-17T08:10:08Z","title":"Metastability and rapid convergence to quasi-stationary bar states for the 2D Navier-Stokes Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.3416","kind":"arxiv","version":3},"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:cfca2b129930d5949003ae3a364e4c28848379ef98f7b1eb879c459d09e57c69","target":"record","created_at":"2026-05-18T03:55:24Z","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":"2c5145a62a9fa2cfdab048d8f948c5c1852224ad29acf64fa0084df7d1414b5b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-08-17T08:10:08Z","title_canon_sha256":"804c0696da2dc8526dd9ea53c8ef2729f0d69bee579a72875b94deb7c89b1c8e"},"schema_version":"1.0","source":{"id":"1108.3416","kind":"arxiv","version":3}},"canonical_sha256":"7edf9630bae10542ae8eeea38a1a0f064aeb393ae173ce4fba554e70b6d2fcc3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7edf9630bae10542ae8eeea38a1a0f064aeb393ae173ce4fba554e70b6d2fcc3","first_computed_at":"2026-05-18T03:55:24.839217Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:55:24.839217Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"p8hJlA9+TDsVVRKMxFG8ZtqWLWMNrrFm1A8aKXJa8BJ0Eg9plpQSIxf++pesOfito3x6O1XIzSRfuZBYB6EyCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:55:24.839923Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.3416","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cfca2b129930d5949003ae3a364e4c28848379ef98f7b1eb879c459d09e57c69","sha256:1d60aa02ce9383d537b3d6078be8e93f65881fe644921ae719720f16347a8a18"],"state_sha256":"32133521ebba01e8961913edbcda3558063907d154ae674d14c66e8f5f89d27d"}