{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:M5LBBWL2MLAAYK7HDW22PQIIIP","short_pith_number":"pith:M5LBBWL2","schema_version":"1.0","canonical_sha256":"675610d97a62c00c2be71db5a7c10843de61ca43fe8829b5577c3b43f28be1f0","source":{"kind":"arxiv","id":"1908.02655","version":2},"attestation_state":"computed","paper":{"title":"An existence theory for small-amplitude doubly periodic water waves with vorticity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["physics.flu-dyn"],"primary_cat":"math.AP","authors_text":"Douglas Svensson Seth, Erik Wahl\\'en, Evgeniy Lokharu","submitted_at":"2019-08-07T14:23:30Z","abstract_excerpt":"We prove the existence of three-dimensional steady gravity-capillary waves with vorticity on water of finite depth. The waves are periodic with respect to a given two-dimensional lattice and the relative velocity field is a Beltrami field, meaning that the vorticity is collinear to the velocity. The existence theory is based on multi-parameter bifurcation theory."},"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":"1908.02655","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2019-08-07T14:23:30Z","cross_cats_sorted":["physics.flu-dyn"],"title_canon_sha256":"b2258b095ac05e131cfd162053e3a4a8f9e1d48dba98ca13d0c36a0bef291ce8","abstract_canon_sha256":"efd6a12307ce2b69c49cbb8859382bb1044edc6c28fb79b5a416311167647d3a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:22:14.292344Z","signature_b64":"wWWxKcvYBzk6nlsZdeTV2TlIz7L4YyoCQB/l7G/ZRxWZVXl4W34/TKNNtLgVNI3PUTAjO0vzZZjdEj+2CC/fBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"675610d97a62c00c2be71db5a7c10843de61ca43fe8829b5577c3b43f28be1f0","last_reissued_at":"2026-07-05T01:22:14.291844Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:22:14.291844Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An existence theory for small-amplitude doubly periodic water waves with vorticity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["physics.flu-dyn"],"primary_cat":"math.AP","authors_text":"Douglas Svensson Seth, Erik Wahl\\'en, Evgeniy Lokharu","submitted_at":"2019-08-07T14:23:30Z","abstract_excerpt":"We prove the existence of three-dimensional steady gravity-capillary waves with vorticity on water of finite depth. The waves are periodic with respect to a given two-dimensional lattice and the relative velocity field is a Beltrami field, meaning that the vorticity is collinear to the velocity. The existence theory is based on multi-parameter bifurcation theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.02655","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.02655/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1908.02655","created_at":"2026-07-05T01:22:14.291915+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.02655v2","created_at":"2026-07-05T01:22:14.291915+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.02655","created_at":"2026-07-05T01:22:14.291915+00:00"},{"alias_kind":"pith_short_12","alias_value":"M5LBBWL2MLAA","created_at":"2026-07-05T01:22:14.291915+00:00"},{"alias_kind":"pith_short_16","alias_value":"M5LBBWL2MLAAYK7H","created_at":"2026-07-05T01:22:14.291915+00:00"},{"alias_kind":"pith_short_8","alias_value":"M5LBBWL2","created_at":"2026-07-05T01:22:14.291915+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/M5LBBWL2MLAAYK7HDW22PQIIIP","json":"https://pith.science/pith/M5LBBWL2MLAAYK7HDW22PQIIIP.json","graph_json":"https://pith.science/api/pith-number/M5LBBWL2MLAAYK7HDW22PQIIIP/graph.json","events_json":"https://pith.science/api/pith-number/M5LBBWL2MLAAYK7HDW22PQIIIP/events.json","paper":"https://pith.science/paper/M5LBBWL2"},"agent_actions":{"view_html":"https://pith.science/pith/M5LBBWL2MLAAYK7HDW22PQIIIP","download_json":"https://pith.science/pith/M5LBBWL2MLAAYK7HDW22PQIIIP.json","view_paper":"https://pith.science/paper/M5LBBWL2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.02655&json=true","fetch_graph":"https://pith.science/api/pith-number/M5LBBWL2MLAAYK7HDW22PQIIIP/graph.json","fetch_events":"https://pith.science/api/pith-number/M5LBBWL2MLAAYK7HDW22PQIIIP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/M5LBBWL2MLAAYK7HDW22PQIIIP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/M5LBBWL2MLAAYK7HDW22PQIIIP/action/storage_attestation","attest_author":"https://pith.science/pith/M5LBBWL2MLAAYK7HDW22PQIIIP/action/author_attestation","sign_citation":"https://pith.science/pith/M5LBBWL2MLAAYK7HDW22PQIIIP/action/citation_signature","submit_replication":"https://pith.science/pith/M5LBBWL2MLAAYK7HDW22PQIIIP/action/replication_record"}},"created_at":"2026-07-05T01:22:14.291915+00:00","updated_at":"2026-07-05T01:22:14.291915+00:00"}