{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:H4MWXQXXU7PYXPPNBEITOLSMDB","short_pith_number":"pith:H4MWXQXX","schema_version":"1.0","canonical_sha256":"3f196bc2f7a7df8bbded0911372e4c18783f9473282ba7e9f64464ad7d219115","source":{"kind":"arxiv","id":"1805.08987","version":1},"attestation_state":"computed","paper":{"title":"Local bifurcation of steady almost periodic water waves with constant vorticity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Wei Luo, Zhaoyang Yin","submitted_at":"2018-05-23T07:36:51Z","abstract_excerpt":"In this paper we mainly investigate the traveling wave solution of the two dimensional Euler equations with gravity at the free surface over a flat bed. We assume that the free surface is almost periodic in the horizontal direction. Using conformal mappings, one can change the free boundary problem into a fixed boundary problem with some unknown functions in the boundary condition. By virtue of the Hilbert transform, the problem is equivalent to a quasilinear pseudodifferential equation for a almost periodic function of one variable. The bifurcation theory ensures us to obtain a existence resu"},"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":"1805.08987","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-05-23T07:36:51Z","cross_cats_sorted":[],"title_canon_sha256":"8f10e209183ca7a87f3bb61b7f8218b9f7bc0de7ca810e026946d65622ffa913","abstract_canon_sha256":"d01c91fb547014f359778f54dfade46e49c912189235d5b6def66de4f510a38a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:15:08.860988Z","signature_b64":"MgyxikBrCJ/WqUBzS4Pc8ry5As5jzTciPOWfR/ro1WKI021dt4+IfJZLb2CeCdBp+C75pG08Ey6HRmv0EkZCBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3f196bc2f7a7df8bbded0911372e4c18783f9473282ba7e9f64464ad7d219115","last_reissued_at":"2026-05-18T00:15:08.860388Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:15:08.860388Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Local bifurcation of steady almost periodic water waves with constant vorticity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Wei Luo, Zhaoyang Yin","submitted_at":"2018-05-23T07:36:51Z","abstract_excerpt":"In this paper we mainly investigate the traveling wave solution of the two dimensional Euler equations with gravity at the free surface over a flat bed. We assume that the free surface is almost periodic in the horizontal direction. Using conformal mappings, one can change the free boundary problem into a fixed boundary problem with some unknown functions in the boundary condition. By virtue of the Hilbert transform, the problem is equivalent to a quasilinear pseudodifferential equation for a almost periodic function of one variable. The bifurcation theory ensures us to obtain a existence resu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.08987","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":"1805.08987","created_at":"2026-05-18T00:15:08.860495+00:00"},{"alias_kind":"arxiv_version","alias_value":"1805.08987v1","created_at":"2026-05-18T00:15:08.860495+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.08987","created_at":"2026-05-18T00:15:08.860495+00:00"},{"alias_kind":"pith_short_12","alias_value":"H4MWXQXXU7PY","created_at":"2026-05-18T12:32:28.185984+00:00"},{"alias_kind":"pith_short_16","alias_value":"H4MWXQXXU7PYXPPN","created_at":"2026-05-18T12:32:28.185984+00:00"},{"alias_kind":"pith_short_8","alias_value":"H4MWXQXX","created_at":"2026-05-18T12:32:28.185984+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/H4MWXQXXU7PYXPPNBEITOLSMDB","json":"https://pith.science/pith/H4MWXQXXU7PYXPPNBEITOLSMDB.json","graph_json":"https://pith.science/api/pith-number/H4MWXQXXU7PYXPPNBEITOLSMDB/graph.json","events_json":"https://pith.science/api/pith-number/H4MWXQXXU7PYXPPNBEITOLSMDB/events.json","paper":"https://pith.science/paper/H4MWXQXX"},"agent_actions":{"view_html":"https://pith.science/pith/H4MWXQXXU7PYXPPNBEITOLSMDB","download_json":"https://pith.science/pith/H4MWXQXXU7PYXPPNBEITOLSMDB.json","view_paper":"https://pith.science/paper/H4MWXQXX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1805.08987&json=true","fetch_graph":"https://pith.science/api/pith-number/H4MWXQXXU7PYXPPNBEITOLSMDB/graph.json","fetch_events":"https://pith.science/api/pith-number/H4MWXQXXU7PYXPPNBEITOLSMDB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/H4MWXQXXU7PYXPPNBEITOLSMDB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/H4MWXQXXU7PYXPPNBEITOLSMDB/action/storage_attestation","attest_author":"https://pith.science/pith/H4MWXQXXU7PYXPPNBEITOLSMDB/action/author_attestation","sign_citation":"https://pith.science/pith/H4MWXQXXU7PYXPPNBEITOLSMDB/action/citation_signature","submit_replication":"https://pith.science/pith/H4MWXQXXU7PYXPPNBEITOLSMDB/action/replication_record"}},"created_at":"2026-05-18T00:15:08.860495+00:00","updated_at":"2026-05-18T00:15:08.860495+00:00"}