{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:6T6DDIFSKCQAIIPLAFVDJTSEPW","short_pith_number":"pith:6T6DDIFS","schema_version":"1.0","canonical_sha256":"f4fc31a0b250a00421eb016a34ce447dbb6d495136b97f4e1c65bb9d888c2cfc","source":{"kind":"arxiv","id":"1609.02030","version":1},"attestation_state":"computed","paper":{"title":"Uniqueness of axisymmetric viscous flows originating from circular vortex filaments","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Thierry Gallay, Vladimir Sverak","submitted_at":"2016-09-07T15:45:28Z","abstract_excerpt":"The incompressible Navier-Stokes equations in R^3 are shown to admit a unique axisymmetric solution without swirl if the initial vorticity is a circular vortex filament with arbitrarily large circulation Reynolds number. The emphasis is on uniqueness, as existence has already been established in [10]. The main difficulty which has to be overcome is that the nonlinear regime for such flows is outside of applicability of standard perturbation theory, even for short times. The solutions we consider are archetypal examples of viscous vortex rings, and can be thought of as axisymmetric analogues of"},"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":"1609.02030","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-09-07T15:45:28Z","cross_cats_sorted":[],"title_canon_sha256":"89cf5a7a752c0d1da53edf4e2b7360500da1005c166316bb8898e611c7cdcadf","abstract_canon_sha256":"98738739ce2e1149a61729959af1f78fb1dc6709571ee4440619313357778ea3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:09.351755Z","signature_b64":"iT9ppBs8ZBVJxMkCxGCOEWXN3nUfF4BWXaSG5rPlYcOekL6q4CQEB6uLeHnpJFGSC0iPNuuLBuk80Xd0LgcVCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f4fc31a0b250a00421eb016a34ce447dbb6d495136b97f4e1c65bb9d888c2cfc","last_reissued_at":"2026-05-18T01:05:09.351092Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:09.351092Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Uniqueness of axisymmetric viscous flows originating from circular vortex filaments","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Thierry Gallay, Vladimir Sverak","submitted_at":"2016-09-07T15:45:28Z","abstract_excerpt":"The incompressible Navier-Stokes equations in R^3 are shown to admit a unique axisymmetric solution without swirl if the initial vorticity is a circular vortex filament with arbitrarily large circulation Reynolds number. The emphasis is on uniqueness, as existence has already been established in [10]. The main difficulty which has to be overcome is that the nonlinear regime for such flows is outside of applicability of standard perturbation theory, even for short times. The solutions we consider are archetypal examples of viscous vortex rings, and can be thought of as axisymmetric analogues of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.02030","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":"1609.02030","created_at":"2026-05-18T01:05:09.351188+00:00"},{"alias_kind":"arxiv_version","alias_value":"1609.02030v1","created_at":"2026-05-18T01:05:09.351188+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.02030","created_at":"2026-05-18T01:05:09.351188+00:00"},{"alias_kind":"pith_short_12","alias_value":"6T6DDIFSKCQA","created_at":"2026-05-18T12:30:04.600751+00:00"},{"alias_kind":"pith_short_16","alias_value":"6T6DDIFSKCQAIIPL","created_at":"2026-05-18T12:30:04.600751+00:00"},{"alias_kind":"pith_short_8","alias_value":"6T6DDIFS","created_at":"2026-05-18T12:30:04.600751+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/6T6DDIFSKCQAIIPLAFVDJTSEPW","json":"https://pith.science/pith/6T6DDIFSKCQAIIPLAFVDJTSEPW.json","graph_json":"https://pith.science/api/pith-number/6T6DDIFSKCQAIIPLAFVDJTSEPW/graph.json","events_json":"https://pith.science/api/pith-number/6T6DDIFSKCQAIIPLAFVDJTSEPW/events.json","paper":"https://pith.science/paper/6T6DDIFS"},"agent_actions":{"view_html":"https://pith.science/pith/6T6DDIFSKCQAIIPLAFVDJTSEPW","download_json":"https://pith.science/pith/6T6DDIFSKCQAIIPLAFVDJTSEPW.json","view_paper":"https://pith.science/paper/6T6DDIFS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1609.02030&json=true","fetch_graph":"https://pith.science/api/pith-number/6T6DDIFSKCQAIIPLAFVDJTSEPW/graph.json","fetch_events":"https://pith.science/api/pith-number/6T6DDIFSKCQAIIPLAFVDJTSEPW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6T6DDIFSKCQAIIPLAFVDJTSEPW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6T6DDIFSKCQAIIPLAFVDJTSEPW/action/storage_attestation","attest_author":"https://pith.science/pith/6T6DDIFSKCQAIIPLAFVDJTSEPW/action/author_attestation","sign_citation":"https://pith.science/pith/6T6DDIFSKCQAIIPLAFVDJTSEPW/action/citation_signature","submit_replication":"https://pith.science/pith/6T6DDIFSKCQAIIPLAFVDJTSEPW/action/replication_record"}},"created_at":"2026-05-18T01:05:09.351188+00:00","updated_at":"2026-05-18T01:05:09.351188+00:00"}