{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:XHJMMYN3KASVNBWDIAGZ7H2LMW","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":"9f1f0191a9c559658469639483bc27dff4fd1518c9376c50fb6519afc225955f","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-07-06T17:09:20Z","title_canon_sha256":"657b79b7f1591a64ac4db16300990a3d6d2f9389f34c5ca76ce9873aa98657a0"},"schema_version":"1.0","source":{"id":"1007.0957","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.0957","created_at":"2026-05-18T01:09:23Z"},{"alias_kind":"arxiv_version","alias_value":"1007.0957v1","created_at":"2026-05-18T01:09:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.0957","created_at":"2026-05-18T01:09:23Z"},{"alias_kind":"pith_short_12","alias_value":"XHJMMYN3KASV","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"XHJMMYN3KASVNBWD","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"XHJMMYN3","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:0dc46a781ad37bfd5d403a1aa2e76f227eb0e67111bffed891bfdefd816b22ed","target":"graph","created_at":"2026-05-18T01:09:23Z","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 a steady flow of incompressible fluid in the plane. The motion is governed by the Navier-Stokes equations with prescribed velocity $u_\\infty$ at infinity. The main result shows the existence of unique solutions for arbitrary force, provided sufficient largeness of $u_\\infty$. Furthermore a spacial structure of the solution is obtained in comparison with the Oseen flow. A key element of our new approach is based on a setting which treats the directino of the flow as \\emph{time} direction. The analysis is done in framework of the Fourier transform taken in one (perpendicular) dire","authors_text":"Pawe{\\l} Konieczny, Piotr Bogus{\\l}aw Mucha","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-07-06T17:09:20Z","title":"Directional approach to spatial structure of solutions to the Navier-Stokes equations in the plane"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.0957","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:c88c0a43d5c2a4e0edbdf3d982a94696df01498d6a6adcc9ebfba32902de6cb6","target":"record","created_at":"2026-05-18T01:09:23Z","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":"9f1f0191a9c559658469639483bc27dff4fd1518c9376c50fb6519afc225955f","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-07-06T17:09:20Z","title_canon_sha256":"657b79b7f1591a64ac4db16300990a3d6d2f9389f34c5ca76ce9873aa98657a0"},"schema_version":"1.0","source":{"id":"1007.0957","kind":"arxiv","version":1}},"canonical_sha256":"b9d2c661bb50255686c3400d9f9f4b658e73d3bf5a67c3eb9b6edc3723b63625","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b9d2c661bb50255686c3400d9f9f4b658e73d3bf5a67c3eb9b6edc3723b63625","first_computed_at":"2026-05-18T01:09:23.819801Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:23.819801Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Waua8lEOfRUG3t+4RMbqllu5YTGHZxN8/Jfj4iSqgRDkF+wLI5WwcSJgeG+N2mFmo38tX4bYFf9KWCuCUhyFDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:23.820234Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.0957","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c88c0a43d5c2a4e0edbdf3d982a94696df01498d6a6adcc9ebfba32902de6cb6","sha256:0dc46a781ad37bfd5d403a1aa2e76f227eb0e67111bffed891bfdefd816b22ed"],"state_sha256":"364ceea5179034ff4a411f0f254e3bf11fef1e5d90e15e1f47b2b278ea5abaff"}