{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:2WN5M65Z3J4P3KQ35I3Q4RTVCD","short_pith_number":"pith:2WN5M65Z","schema_version":"1.0","canonical_sha256":"d59bd67bb9da78fdaa1bea370e467510dcce597b4b14497f09a105f4f7e9a20e","source":{"kind":"arxiv","id":"1209.3738","version":1},"attestation_state":"computed","paper":{"title":"No steady water waves of small amplitude are supported by a shear flow with still free surface","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Nikolay Kuznetsov, Vladimir Kozlov","submitted_at":"2012-09-17T18:06:43Z","abstract_excerpt":"The two-dimensional free-boundary problem describing steady gravity waves with vorticity on water of finite depth is considered. It is proved that no small-amplitude waves are supported by a horizontal shear flow whose free surface is still in a coordinate frame such that the flow is time-independent in it. The class of vorticity distributions for which such flows exist includes all positive constant distributions, as well as linear and quadric ones with arbitrary positive coefficients."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1209.3738","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-09-17T18:06:43Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"a375270dd34fa6fee6aea3c574501808b992a02022e0c269ff3dacd924e0ddc7","abstract_canon_sha256":"dd5c1b31a2ea433d69613930d66d8015498a4b191b18383f9540670a432aacb4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:54:27.292376Z","signature_b64":"Ijs/6zUZgrHalPx0WaPzRj9opISYiC1kDbfbTU76kJ3LFCqdRQvbZOj3I7swis7iY2YsrclGMuaWCGcfWXK2Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d59bd67bb9da78fdaa1bea370e467510dcce597b4b14497f09a105f4f7e9a20e","last_reissued_at":"2026-05-18T01:54:27.291742Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:54:27.291742Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"No steady water waves of small amplitude are supported by a shear flow with still free surface","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Nikolay Kuznetsov, Vladimir Kozlov","submitted_at":"2012-09-17T18:06:43Z","abstract_excerpt":"The two-dimensional free-boundary problem describing steady gravity waves with vorticity on water of finite depth is considered. It is proved that no small-amplitude waves are supported by a horizontal shear flow whose free surface is still in a coordinate frame such that the flow is time-independent in it. The class of vorticity distributions for which such flows exist includes all positive constant distributions, as well as linear and quadric ones with arbitrary positive coefficients."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.3738","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1209.3738","created_at":"2026-05-18T01:54:27.291827+00:00"},{"alias_kind":"arxiv_version","alias_value":"1209.3738v1","created_at":"2026-05-18T01:54:27.291827+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.3738","created_at":"2026-05-18T01:54:27.291827+00:00"},{"alias_kind":"pith_short_12","alias_value":"2WN5M65Z3J4P","created_at":"2026-05-18T12:26:50.516681+00:00"},{"alias_kind":"pith_short_16","alias_value":"2WN5M65Z3J4P3KQ3","created_at":"2026-05-18T12:26:50.516681+00:00"},{"alias_kind":"pith_short_8","alias_value":"2WN5M65Z","created_at":"2026-05-18T12:26:50.516681+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2WN5M65Z3J4P3KQ35I3Q4RTVCD","json":"https://pith.science/pith/2WN5M65Z3J4P3KQ35I3Q4RTVCD.json","graph_json":"https://pith.science/api/pith-number/2WN5M65Z3J4P3KQ35I3Q4RTVCD/graph.json","events_json":"https://pith.science/api/pith-number/2WN5M65Z3J4P3KQ35I3Q4RTVCD/events.json","paper":"https://pith.science/paper/2WN5M65Z"},"agent_actions":{"view_html":"https://pith.science/pith/2WN5M65Z3J4P3KQ35I3Q4RTVCD","download_json":"https://pith.science/pith/2WN5M65Z3J4P3KQ35I3Q4RTVCD.json","view_paper":"https://pith.science/paper/2WN5M65Z","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1209.3738&json=true","fetch_graph":"https://pith.science/api/pith-number/2WN5M65Z3J4P3KQ35I3Q4RTVCD/graph.json","fetch_events":"https://pith.science/api/pith-number/2WN5M65Z3J4P3KQ35I3Q4RTVCD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2WN5M65Z3J4P3KQ35I3Q4RTVCD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2WN5M65Z3J4P3KQ35I3Q4RTVCD/action/storage_attestation","attest_author":"https://pith.science/pith/2WN5M65Z3J4P3KQ35I3Q4RTVCD/action/author_attestation","sign_citation":"https://pith.science/pith/2WN5M65Z3J4P3KQ35I3Q4RTVCD/action/citation_signature","submit_replication":"https://pith.science/pith/2WN5M65Z3J4P3KQ35I3Q4RTVCD/action/replication_record"}},"created_at":"2026-05-18T01:54:27.291827+00:00","updated_at":"2026-05-18T01:54:27.291827+00:00"}