{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:Y3RUATVRDFB27SD2WDBKNIFNSB","short_pith_number":"pith:Y3RUATVR","schema_version":"1.0","canonical_sha256":"c6e3404eb11943afc87ab0c2a6a0ad9064fcfd324021a069f7b78854504ac217","source":{"kind":"arxiv","id":"1902.06313","version":2},"attestation_state":"computed","paper":{"title":"On the universality of the incompressible Euler equation on compact manifolds, II. Non-rigidity of Euler flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Terence Tao","submitted_at":"2019-02-17T19:52:33Z","abstract_excerpt":"The incompressible Euler equations on a compact Riemannian manifold $(M,g)$ take the form \\begin{align*} \\partial_t u + \\nabla_u u &= - \\mathrm{grad}_g p \\\\ \\mathrm{div}_g u &= 0, \\end{align*} where $u: [0,T] \\to \\Gamma(T M)$ is the velocity field and $p: [0,T] \\to C^\\infty(M)$ is the pressure field. In this paper we show that if one is permitted to extend the base manifold $M$ by taking an arbitrary warped product with a torus, then the space of solutions to this equation becomes \"non-rigid'\"in the sense that a non-empty open set of smooth incompressible flows $u: [0,T] \\to \\Gamma(T M)$ can b"},"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":"1902.06313","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-02-17T19:52:33Z","cross_cats_sorted":[],"title_canon_sha256":"1848a3e1fee3be19908f2926770fbb1c236d054c1520b5ffa424761f71324d0e","abstract_canon_sha256":"b6affc81f65e14776fc5a7f5fd89924acb0f2e03b66bd8a9823da4092f76b5b8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:50.047362Z","signature_b64":"Czlf9DgoObmfOLuHg4fU5f/4XLPS2SegenBBjGEnmmdSe9Hsrat3qko3p5I9H4yMLuLczEGs2tMGAgd2I5hHBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c6e3404eb11943afc87ab0c2a6a0ad9064fcfd324021a069f7b78854504ac217","last_reissued_at":"2026-05-17T23:49:50.046860Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:50.046860Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the universality of the incompressible Euler equation on compact manifolds, II. Non-rigidity of Euler flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Terence Tao","submitted_at":"2019-02-17T19:52:33Z","abstract_excerpt":"The incompressible Euler equations on a compact Riemannian manifold $(M,g)$ take the form \\begin{align*} \\partial_t u + \\nabla_u u &= - \\mathrm{grad}_g p \\\\ \\mathrm{div}_g u &= 0, \\end{align*} where $u: [0,T] \\to \\Gamma(T M)$ is the velocity field and $p: [0,T] \\to C^\\infty(M)$ is the pressure field. In this paper we show that if one is permitted to extend the base manifold $M$ by taking an arbitrary warped product with a torus, then the space of solutions to this equation becomes \"non-rigid'\"in the sense that a non-empty open set of smooth incompressible flows $u: [0,T] \\to \\Gamma(T M)$ can b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.06313","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":""},"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":"1902.06313","created_at":"2026-05-17T23:49:50.046947+00:00"},{"alias_kind":"arxiv_version","alias_value":"1902.06313v2","created_at":"2026-05-17T23:49:50.046947+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.06313","created_at":"2026-05-17T23:49:50.046947+00:00"},{"alias_kind":"pith_short_12","alias_value":"Y3RUATVRDFB2","created_at":"2026-05-18T12:33:33.725879+00:00"},{"alias_kind":"pith_short_16","alias_value":"Y3RUATVRDFB27SD2","created_at":"2026-05-18T12:33:33.725879+00:00"},{"alias_kind":"pith_short_8","alias_value":"Y3RUATVR","created_at":"2026-05-18T12:33:33.725879+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/Y3RUATVRDFB27SD2WDBKNIFNSB","json":"https://pith.science/pith/Y3RUATVRDFB27SD2WDBKNIFNSB.json","graph_json":"https://pith.science/api/pith-number/Y3RUATVRDFB27SD2WDBKNIFNSB/graph.json","events_json":"https://pith.science/api/pith-number/Y3RUATVRDFB27SD2WDBKNIFNSB/events.json","paper":"https://pith.science/paper/Y3RUATVR"},"agent_actions":{"view_html":"https://pith.science/pith/Y3RUATVRDFB27SD2WDBKNIFNSB","download_json":"https://pith.science/pith/Y3RUATVRDFB27SD2WDBKNIFNSB.json","view_paper":"https://pith.science/paper/Y3RUATVR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1902.06313&json=true","fetch_graph":"https://pith.science/api/pith-number/Y3RUATVRDFB27SD2WDBKNIFNSB/graph.json","fetch_events":"https://pith.science/api/pith-number/Y3RUATVRDFB27SD2WDBKNIFNSB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Y3RUATVRDFB27SD2WDBKNIFNSB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Y3RUATVRDFB27SD2WDBKNIFNSB/action/storage_attestation","attest_author":"https://pith.science/pith/Y3RUATVRDFB27SD2WDBKNIFNSB/action/author_attestation","sign_citation":"https://pith.science/pith/Y3RUATVRDFB27SD2WDBKNIFNSB/action/citation_signature","submit_replication":"https://pith.science/pith/Y3RUATVRDFB27SD2WDBKNIFNSB/action/replication_record"}},"created_at":"2026-05-17T23:49:50.046947+00:00","updated_at":"2026-05-17T23:49:50.046947+00:00"}