{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:4BH7SXDBIW25VY253V4VAEN5TY","short_pith_number":"pith:4BH7SXDB","schema_version":"1.0","canonical_sha256":"e04ff95c6145b5dae35ddd795011bd9e35a80543b870ff6716898b52b422b239","source":{"kind":"arxiv","id":"2507.15739","version":1},"attestation_state":"computed","paper":{"title":"Superlinear gradient growth for 2D Euler equation without boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"In-Jee Jeong, Tao Zhou, Yao Yao","submitted_at":"2025-07-21T15:50:46Z","abstract_excerpt":"We consider the vorticity gradient growth of solutions to the two-dimensional Euler equations in domains without boundary, namely in the torus $\\mathbb{T}^{2}$ and the whole plane $\\mathbb{R}^{2}$. In the torus, whenever we have a steady state $\\omega^*$ that is orbitally stable up to a translation and has a saddle point, we construct ${\\tilde{\\omega}}_0 \\in C^\\infty(\\mathbb{T}^2)$ that is arbitrarily close to $\\omega^*$ in $L^2$, such that superlinear growth of the vorticity gradient occurs for an open set of smooth initial data around ${\\tilde{\\omega}}_0$. This seems to be the first superlin"},"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":"2507.15739","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-07-21T15:50:46Z","cross_cats_sorted":[],"title_canon_sha256":"62b897d1505e607b5613960a767096f892dd5c37437c8d4edeb435ee8364b643","abstract_canon_sha256":"ab0bb05c14d480945bee14519f365988ea7ed4911e90dc27cad89aa872884209"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:40:43.231884Z","signature_b64":"Nz8UwwgP1pzUEj70CGOXeLaHrJ0SxkMYIRAQPKSR2PJ4tCG0wQGczgFY18t0SwAVgaUcWvfDgaDY3bwJu9waDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e04ff95c6145b5dae35ddd795011bd9e35a80543b870ff6716898b52b422b239","last_reissued_at":"2026-07-05T11:40:43.231426Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:40:43.231426Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Superlinear gradient growth for 2D Euler equation without boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"In-Jee Jeong, Tao Zhou, Yao Yao","submitted_at":"2025-07-21T15:50:46Z","abstract_excerpt":"We consider the vorticity gradient growth of solutions to the two-dimensional Euler equations in domains without boundary, namely in the torus $\\mathbb{T}^{2}$ and the whole plane $\\mathbb{R}^{2}$. In the torus, whenever we have a steady state $\\omega^*$ that is orbitally stable up to a translation and has a saddle point, we construct ${\\tilde{\\omega}}_0 \\in C^\\infty(\\mathbb{T}^2)$ that is arbitrarily close to $\\omega^*$ in $L^2$, such that superlinear growth of the vorticity gradient occurs for an open set of smooth initial data around ${\\tilde{\\omega}}_0$. This seems to be the first superlin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.15739","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.15739/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":"2507.15739","created_at":"2026-07-05T11:40:43.231476+00:00"},{"alias_kind":"arxiv_version","alias_value":"2507.15739v1","created_at":"2026-07-05T11:40:43.231476+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.15739","created_at":"2026-07-05T11:40:43.231476+00:00"},{"alias_kind":"pith_short_12","alias_value":"4BH7SXDBIW25","created_at":"2026-07-05T11:40:43.231476+00:00"},{"alias_kind":"pith_short_16","alias_value":"4BH7SXDBIW25VY25","created_at":"2026-07-05T11:40:43.231476+00:00"},{"alias_kind":"pith_short_8","alias_value":"4BH7SXDB","created_at":"2026-07-05T11:40:43.231476+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":6,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.09775","citing_title":"Linear Stability of the Lamb-Chaplygin Dipole","ref_index":14,"is_internal_anchor":false},{"citing_arxiv_id":"2605.31541","citing_title":"Remarks on Linear Growth of Vorticity Gradients and Support Diameters for 2D Euler Flow in Half-Plane","ref_index":13,"is_internal_anchor":false},{"citing_arxiv_id":"2601.16110","citing_title":"Stability and Decay for the 2D Anisotropic Navier-Stokes Equations with Fractional Horizontal Dissipation on $\\mathbb{R}^2$","ref_index":12,"is_internal_anchor":false},{"citing_arxiv_id":"2605.01491","citing_title":"On the stability of Lamb-Chaplygin dipole for the 2D Euler equation","ref_index":36,"is_internal_anchor":false},{"citing_arxiv_id":"2604.19380","citing_title":"Small scale creation in 2D gravity-capillary water waves with vorticity","ref_index":16,"is_internal_anchor":false},{"citing_arxiv_id":"2604.19358","citing_title":"Growth of vorticity gradient for the Euler equation on the sphere","ref_index":17,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4BH7SXDBIW25VY253V4VAEN5TY","json":"https://pith.science/pith/4BH7SXDBIW25VY253V4VAEN5TY.json","graph_json":"https://pith.science/api/pith-number/4BH7SXDBIW25VY253V4VAEN5TY/graph.json","events_json":"https://pith.science/api/pith-number/4BH7SXDBIW25VY253V4VAEN5TY/events.json","paper":"https://pith.science/paper/4BH7SXDB"},"agent_actions":{"view_html":"https://pith.science/pith/4BH7SXDBIW25VY253V4VAEN5TY","download_json":"https://pith.science/pith/4BH7SXDBIW25VY253V4VAEN5TY.json","view_paper":"https://pith.science/paper/4BH7SXDB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2507.15739&json=true","fetch_graph":"https://pith.science/api/pith-number/4BH7SXDBIW25VY253V4VAEN5TY/graph.json","fetch_events":"https://pith.science/api/pith-number/4BH7SXDBIW25VY253V4VAEN5TY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4BH7SXDBIW25VY253V4VAEN5TY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4BH7SXDBIW25VY253V4VAEN5TY/action/storage_attestation","attest_author":"https://pith.science/pith/4BH7SXDBIW25VY253V4VAEN5TY/action/author_attestation","sign_citation":"https://pith.science/pith/4BH7SXDBIW25VY253V4VAEN5TY/action/citation_signature","submit_replication":"https://pith.science/pith/4BH7SXDBIW25VY253V4VAEN5TY/action/replication_record"}},"created_at":"2026-07-05T11:40:43.231476+00:00","updated_at":"2026-07-05T11:40:43.231476+00:00"}