{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:Z3LGXPXFNB5VBGPGGMBFBMKDFA","short_pith_number":"pith:Z3LGXPXF","schema_version":"1.0","canonical_sha256":"ced66bbee5687b5099e6330250b14328045d1304a217e6b50e9ded284f02da19","source":{"kind":"arxiv","id":"1608.06109","version":1},"attestation_state":"computed","paper":{"title":"Stability Results for Idealised Shear Flows on a Rectangular Periodic Domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Holger Dullin, Joachim Worthington","submitted_at":"2016-08-22T10:26:33Z","abstract_excerpt":"We present a new linearly stable solution of the Euler fluid flow on a torus. On a two-dimensional rectangular periodic domain $[0,2\\pi)\\times[0,2\\pi / \\kappa)$ for $\\kappa\\in\\mathbb{R}^+$, the Euler equations admit a family of stationary solutions given by the vorticity profiles $\\Omega^*(\\mathbf{x})= \\Gamma \\cos(p_1x_1+ \\kappa p_2x_2)$. We show linear stability for such flows when $p_2=0$ and $\\kappa \\geq |p_1|$ (equivalently $p_1=0$ and $\\kappa{|p_2|}\\leq{1}$). The classical result due to Arnold is that for $p_1 = 1, p_2 = 0$ and $\\kappa \\ge 1$ the stationary flow is {nonlinearly} stable vi"},"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":"1608.06109","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-08-22T10:26:33Z","cross_cats_sorted":[],"title_canon_sha256":"ce7a4d5368fdc4613a97c955f5506f95ed82acc811e91841f71d00fbc5ba32fd","abstract_canon_sha256":"876aac8c5db05d526f10c9de7a3454d3738412f680085e2f8f4d472386370fa6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:45.274466Z","signature_b64":"Ha292/Cheu5DpiWXjdalWjzUybmlgtj2/B5G/tnfijhn63Neu/sKCvx4s6l1TerwvkvAksN+8XeB1TGkObUEBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ced66bbee5687b5099e6330250b14328045d1304a217e6b50e9ded284f02da19","last_reissued_at":"2026-05-18T00:24:45.273798Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:45.273798Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stability Results for Idealised Shear Flows on a Rectangular Periodic Domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Holger Dullin, Joachim Worthington","submitted_at":"2016-08-22T10:26:33Z","abstract_excerpt":"We present a new linearly stable solution of the Euler fluid flow on a torus. On a two-dimensional rectangular periodic domain $[0,2\\pi)\\times[0,2\\pi / \\kappa)$ for $\\kappa\\in\\mathbb{R}^+$, the Euler equations admit a family of stationary solutions given by the vorticity profiles $\\Omega^*(\\mathbf{x})= \\Gamma \\cos(p_1x_1+ \\kappa p_2x_2)$. We show linear stability for such flows when $p_2=0$ and $\\kappa \\geq |p_1|$ (equivalently $p_1=0$ and $\\kappa{|p_2|}\\leq{1}$). The classical result due to Arnold is that for $p_1 = 1, p_2 = 0$ and $\\kappa \\ge 1$ the stationary flow is {nonlinearly} stable vi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.06109","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":"1608.06109","created_at":"2026-05-18T00:24:45.273912+00:00"},{"alias_kind":"arxiv_version","alias_value":"1608.06109v1","created_at":"2026-05-18T00:24:45.273912+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.06109","created_at":"2026-05-18T00:24:45.273912+00:00"},{"alias_kind":"pith_short_12","alias_value":"Z3LGXPXFNB5V","created_at":"2026-05-18T12:30:53.716459+00:00"},{"alias_kind":"pith_short_16","alias_value":"Z3LGXPXFNB5VBGPG","created_at":"2026-05-18T12:30:53.716459+00:00"},{"alias_kind":"pith_short_8","alias_value":"Z3LGXPXF","created_at":"2026-05-18T12:30:53.716459+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/Z3LGXPXFNB5VBGPGGMBFBMKDFA","json":"https://pith.science/pith/Z3LGXPXFNB5VBGPGGMBFBMKDFA.json","graph_json":"https://pith.science/api/pith-number/Z3LGXPXFNB5VBGPGGMBFBMKDFA/graph.json","events_json":"https://pith.science/api/pith-number/Z3LGXPXFNB5VBGPGGMBFBMKDFA/events.json","paper":"https://pith.science/paper/Z3LGXPXF"},"agent_actions":{"view_html":"https://pith.science/pith/Z3LGXPXFNB5VBGPGGMBFBMKDFA","download_json":"https://pith.science/pith/Z3LGXPXFNB5VBGPGGMBFBMKDFA.json","view_paper":"https://pith.science/paper/Z3LGXPXF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1608.06109&json=true","fetch_graph":"https://pith.science/api/pith-number/Z3LGXPXFNB5VBGPGGMBFBMKDFA/graph.json","fetch_events":"https://pith.science/api/pith-number/Z3LGXPXFNB5VBGPGGMBFBMKDFA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Z3LGXPXFNB5VBGPGGMBFBMKDFA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Z3LGXPXFNB5VBGPGGMBFBMKDFA/action/storage_attestation","attest_author":"https://pith.science/pith/Z3LGXPXFNB5VBGPGGMBFBMKDFA/action/author_attestation","sign_citation":"https://pith.science/pith/Z3LGXPXFNB5VBGPGGMBFBMKDFA/action/citation_signature","submit_replication":"https://pith.science/pith/Z3LGXPXFNB5VBGPGGMBFBMKDFA/action/replication_record"}},"created_at":"2026-05-18T00:24:45.273912+00:00","updated_at":"2026-05-18T00:24:45.273912+00:00"}