{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:2WXRQIO5ERBKC6QTA757QTFT5D","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":"fdc9d281226257e94fd6eb9734fbc64bdff17f50a9b6fd2b6845b57e65a93a21","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-15T09:34:18Z","title_canon_sha256":"45b92253f35cc06f1c1058a9880fab946d6069b17595a5fd3a7d86a31f817931"},"schema_version":"1.0","source":{"id":"1509.04463","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.04463","created_at":"2026-05-18T01:32:58Z"},{"alias_kind":"arxiv_version","alias_value":"1509.04463v1","created_at":"2026-05-18T01:32:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.04463","created_at":"2026-05-18T01:32:58Z"},{"alias_kind":"pith_short_12","alias_value":"2WXRQIO5ERBK","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"2WXRQIO5ERBKC6QT","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"2WXRQIO5","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:117039a64ccbb9dfe1ecfc717c7cf70f7a91132799fb9177e5bc02bb99112e74","target":"graph","created_at":"2026-05-18T01:32:58Z","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 that, in a two-dimensional strip, a steady flow of an ideal incompressible fluid with no stationary point and tangential boundary conditions is a shear flow. The same conclusion holds for a bounded steady flow in a half-plane. The proofs are based on the study of the geometric properties of the streamlines of the flow and on one-dimensional symmetry results for solutions of some semilinear elliptic equations. Some related rigidity results of independent interest are also shown in n-dimensional slabs in any dimension n.","authors_text":"Fran\\c{c}ois Hamel (I2M), Nikolai Nadirashvili (I2M)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-15T09:34:18Z","title":"Shear flows of an ideal fluid and elliptic equations in unbounded domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.04463","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":"sha256:8e12b28437f80e688019acc1d6234a73228f04a8f1929a9bb89756861b65d3d8","target":"record","created_at":"2026-05-18T01:32:58Z","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":"fdc9d281226257e94fd6eb9734fbc64bdff17f50a9b6fd2b6845b57e65a93a21","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-15T09:34:18Z","title_canon_sha256":"45b92253f35cc06f1c1058a9880fab946d6069b17595a5fd3a7d86a31f817931"},"schema_version":"1.0","source":{"id":"1509.04463","kind":"arxiv","version":1}},"canonical_sha256":"d5af1821dd2442a17a1307fbf84cb3e8f9de37f34de8552f0f5d1c5a27fe081d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d5af1821dd2442a17a1307fbf84cb3e8f9de37f34de8552f0f5d1c5a27fe081d","first_computed_at":"2026-05-18T01:32:58.862274Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:32:58.862274Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2bbMs/Vltf3xxCwryHF8vCwQZQU52ls6IRA31tmaOF3EDUF/k7U43VmRsu/Xz1sXNLJz7Swd6ywfTApDOa2IDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:32:58.862857Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.04463","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8e12b28437f80e688019acc1d6234a73228f04a8f1929a9bb89756861b65d3d8","sha256:117039a64ccbb9dfe1ecfc717c7cf70f7a91132799fb9177e5bc02bb99112e74"],"state_sha256":"a92a495ccda8dc01058f91f1eac1a45757f9c1af90e1d4e3967b1d56f7aebbcc"}