{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:NMJ53TDJCBQAFXNRTLLJ75TH3L","short_pith_number":"pith:NMJ53TDJ","schema_version":"1.0","canonical_sha256":"6b13ddcc69106002ddb19ad69ff667daf9ac3f6fefd12280612863879d93f338","source":{"kind":"arxiv","id":"0903.3161","version":1},"attestation_state":"computed","paper":{"title":"On complex singularities of the 2D Euler equation at short times","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.CD","authors_text":"W. Pauls","submitted_at":"2009-03-18T13:40:38Z","abstract_excerpt":"We present a study of complex singularities of a two-parameter family of solutions for the two-dimensional Euler equation with periodic boundary conditions and initial conditions F(p) cos p z + F(q) cos q z in the short-time asymptotic regime. As has been shown numerically in W. Pauls et al., Physica D 219, 40-59 (2006), the type of the singularities depends on the angle between the modes p and q. Here we show for the two particular cases of the angle going to zero and to pi that the type of the singularities can be determined very accurately, being characterised by the values 5/2 and 3 respec"},"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":"0903.3161","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2009-03-18T13:40:38Z","cross_cats_sorted":[],"title_canon_sha256":"63b5b434aade581d0374f9e2c9ca4b4d42b38df8d6b59e9745a65d08a8d0cb5b","abstract_canon_sha256":"ff3bc82c9b08b5fcb7cc0e9e39758dd7ce911922ee50a407ec9f7cbcd72e2208"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:14:27.538823Z","signature_b64":"prvM/MC28n6vDGQpQcpyFrVJ/VmWVOeaCwzhPw7zd02fUSh+opb3z7b3sNXv+gVUBSJnOWjA4dVqtOTui1h3Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6b13ddcc69106002ddb19ad69ff667daf9ac3f6fefd12280612863879d93f338","last_reissued_at":"2026-05-18T02:14:27.538418Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:14:27.538418Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On complex singularities of the 2D Euler equation at short times","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.CD","authors_text":"W. Pauls","submitted_at":"2009-03-18T13:40:38Z","abstract_excerpt":"We present a study of complex singularities of a two-parameter family of solutions for the two-dimensional Euler equation with periodic boundary conditions and initial conditions F(p) cos p z + F(q) cos q z in the short-time asymptotic regime. As has been shown numerically in W. Pauls et al., Physica D 219, 40-59 (2006), the type of the singularities depends on the angle between the modes p and q. Here we show for the two particular cases of the angle going to zero and to pi that the type of the singularities can be determined very accurately, being characterised by the values 5/2 and 3 respec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.3161","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":"0903.3161","created_at":"2026-05-18T02:14:27.538478+00:00"},{"alias_kind":"arxiv_version","alias_value":"0903.3161v1","created_at":"2026-05-18T02:14:27.538478+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0903.3161","created_at":"2026-05-18T02:14:27.538478+00:00"},{"alias_kind":"pith_short_12","alias_value":"NMJ53TDJCBQA","created_at":"2026-05-18T12:26:00.592388+00:00"},{"alias_kind":"pith_short_16","alias_value":"NMJ53TDJCBQAFXNR","created_at":"2026-05-18T12:26:00.592388+00:00"},{"alias_kind":"pith_short_8","alias_value":"NMJ53TDJ","created_at":"2026-05-18T12:26:00.592388+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/NMJ53TDJCBQAFXNRTLLJ75TH3L","json":"https://pith.science/pith/NMJ53TDJCBQAFXNRTLLJ75TH3L.json","graph_json":"https://pith.science/api/pith-number/NMJ53TDJCBQAFXNRTLLJ75TH3L/graph.json","events_json":"https://pith.science/api/pith-number/NMJ53TDJCBQAFXNRTLLJ75TH3L/events.json","paper":"https://pith.science/paper/NMJ53TDJ"},"agent_actions":{"view_html":"https://pith.science/pith/NMJ53TDJCBQAFXNRTLLJ75TH3L","download_json":"https://pith.science/pith/NMJ53TDJCBQAFXNRTLLJ75TH3L.json","view_paper":"https://pith.science/paper/NMJ53TDJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0903.3161&json=true","fetch_graph":"https://pith.science/api/pith-number/NMJ53TDJCBQAFXNRTLLJ75TH3L/graph.json","fetch_events":"https://pith.science/api/pith-number/NMJ53TDJCBQAFXNRTLLJ75TH3L/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NMJ53TDJCBQAFXNRTLLJ75TH3L/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NMJ53TDJCBQAFXNRTLLJ75TH3L/action/storage_attestation","attest_author":"https://pith.science/pith/NMJ53TDJCBQAFXNRTLLJ75TH3L/action/author_attestation","sign_citation":"https://pith.science/pith/NMJ53TDJCBQAFXNRTLLJ75TH3L/action/citation_signature","submit_replication":"https://pith.science/pith/NMJ53TDJCBQAFXNRTLLJ75TH3L/action/replication_record"}},"created_at":"2026-05-18T02:14:27.538478+00:00","updated_at":"2026-05-18T02:14:27.538478+00:00"}