{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:XUGJCW2OPLP4CBSJF6TA47FV7L","short_pith_number":"pith:XUGJCW2O","schema_version":"1.0","canonical_sha256":"bd0c915b4e7adfc106492fa60e7cb5faf160c36cd4cc1249614f1eec372c3601","source":{"kind":"arxiv","id":"2305.05182","version":4},"attestation_state":"computed","paper":{"title":"Self-similar algebraic spiral solution of 2-D incompressible Euler equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Dongyi Wei, Feng Shao, Zhifei Zhang","submitted_at":"2023-05-09T05:31:25Z","abstract_excerpt":"In this paper, we prove the existence of self-similar algebraic spiral solutions for 2-D incompressible Euler equations for the initial vorticity of the form $|y|^{-\\frac1\\mu}\\ \\mathring{\\omega}(\\theta)$ with $\\mu>\\frac12$ and $\\mathring{\\omega}\\in L^1(\\mathbb T)$ satisfying $m$-fold symmetry ($m\\geq 2$) and a dominant condition. As an important application, we prove the existence of weak solution when $\\mathring{\\omega}$ is a Radon measure on $\\mathbb T$ with $m$-fold symmetry, which is related to the vortex sheet solution."},"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":"2305.05182","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-05-09T05:31:25Z","cross_cats_sorted":[],"title_canon_sha256":"aa7c9a852f00b89420827c977ec38cc38eff927cbca89b41067314f9dee94488","abstract_canon_sha256":"bf5e3501c43eb892c2cf7b00bdfc5b105a8779ae5d8b212e103d3afcad036446"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:54:29.966523Z","signature_b64":"FH9PGa9lSviXG2doDKVyZ3eK2ZAcdtOAA+v0L4JCAwjPm3ykURJVZd2BUzc/l2/MwpQehpKhjbnLa/DBFmrsAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bd0c915b4e7adfc106492fa60e7cb5faf160c36cd4cc1249614f1eec372c3601","last_reissued_at":"2026-07-05T10:54:29.966010Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:54:29.966010Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Self-similar algebraic spiral solution of 2-D incompressible Euler equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Dongyi Wei, Feng Shao, Zhifei Zhang","submitted_at":"2023-05-09T05:31:25Z","abstract_excerpt":"In this paper, we prove the existence of self-similar algebraic spiral solutions for 2-D incompressible Euler equations for the initial vorticity of the form $|y|^{-\\frac1\\mu}\\ \\mathring{\\omega}(\\theta)$ with $\\mu>\\frac12$ and $\\mathring{\\omega}\\in L^1(\\mathbb T)$ satisfying $m$-fold symmetry ($m\\geq 2$) and a dominant condition. As an important application, we prove the existence of weak solution when $\\mathring{\\omega}$ is a Radon measure on $\\mathbb T$ with $m$-fold symmetry, which is related to the vortex sheet solution."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.05182","kind":"arxiv","version":4},"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/2305.05182/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":"2305.05182","created_at":"2026-07-05T10:54:29.966070+00:00"},{"alias_kind":"arxiv_version","alias_value":"2305.05182v4","created_at":"2026-07-05T10:54:29.966070+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2305.05182","created_at":"2026-07-05T10:54:29.966070+00:00"},{"alias_kind":"pith_short_12","alias_value":"XUGJCW2OPLP4","created_at":"2026-07-05T10:54:29.966070+00:00"},{"alias_kind":"pith_short_16","alias_value":"XUGJCW2OPLP4CBSJ","created_at":"2026-07-05T10:54:29.966070+00:00"},{"alias_kind":"pith_short_8","alias_value":"XUGJCW2O","created_at":"2026-07-05T10:54:29.966070+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2404.15995","citing_title":"A proof of Vishik's nonuniqueness Theorem for the forced 2D Euler equation","ref_index":50,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XUGJCW2OPLP4CBSJF6TA47FV7L","json":"https://pith.science/pith/XUGJCW2OPLP4CBSJF6TA47FV7L.json","graph_json":"https://pith.science/api/pith-number/XUGJCW2OPLP4CBSJF6TA47FV7L/graph.json","events_json":"https://pith.science/api/pith-number/XUGJCW2OPLP4CBSJF6TA47FV7L/events.json","paper":"https://pith.science/paper/XUGJCW2O"},"agent_actions":{"view_html":"https://pith.science/pith/XUGJCW2OPLP4CBSJF6TA47FV7L","download_json":"https://pith.science/pith/XUGJCW2OPLP4CBSJF6TA47FV7L.json","view_paper":"https://pith.science/paper/XUGJCW2O","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2305.05182&json=true","fetch_graph":"https://pith.science/api/pith-number/XUGJCW2OPLP4CBSJF6TA47FV7L/graph.json","fetch_events":"https://pith.science/api/pith-number/XUGJCW2OPLP4CBSJF6TA47FV7L/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XUGJCW2OPLP4CBSJF6TA47FV7L/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XUGJCW2OPLP4CBSJF6TA47FV7L/action/storage_attestation","attest_author":"https://pith.science/pith/XUGJCW2OPLP4CBSJF6TA47FV7L/action/author_attestation","sign_citation":"https://pith.science/pith/XUGJCW2OPLP4CBSJF6TA47FV7L/action/citation_signature","submit_replication":"https://pith.science/pith/XUGJCW2OPLP4CBSJF6TA47FV7L/action/replication_record"}},"created_at":"2026-07-05T10:54:29.966070+00:00","updated_at":"2026-07-05T10:54:29.966070+00:00"}