{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:U7ZJHESXPGHF44BJNGTGCJOJRU","short_pith_number":"pith:U7ZJHESX","schema_version":"1.0","canonical_sha256":"a7f2939257798e5e702969a66125c98d135a1b48b50d94571fc314ed1cd6a297","source":{"kind":"arxiv","id":"2404.02412","version":3},"attestation_state":"computed","paper":{"title":"Quantitative Hydrodynamic Stability for Couette Flow on Unbounded Domains with Navier Boundary Conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jacob Bedrossian, Ryan Arbon","submitted_at":"2024-04-03T02:27:03Z","abstract_excerpt":"We prove a stability threshold theorem for 2D Navier-Stokes on three unbounded domains: the whole plane $\\mathbb{R} \\times \\mathbb{R}$, the half plane $\\mathbb{R} \\times [0,\\infty)$ with Navier boundary conditions, and the infinite channel $\\mathbb{R} \\times [-1, 1]$ with Navier boundary conditions. Starting with the Couette shear flow, we consider initial perturbations $\\omega_{in}$ which are of size $\\nu^{1/2}(1+\\ln(1/\\nu)^{1/2})^{-1}$ in an anisotropic Sobolev space with an additional low frequency control condition for the planar cases. We then demonstrate that such perturbations exhibit i"},"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":"2404.02412","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-04-03T02:27:03Z","cross_cats_sorted":[],"title_canon_sha256":"abde5df61202df6df25f8650e43c0e42285a393a12f856231e7e7ba9105d39e4","abstract_canon_sha256":"312c0313f0c990c838da7746a134d9b562d9f7088465549b6f556347766d7d53"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:28:04.661731Z","signature_b64":"qaiGWDeS0/4DMrSdJe5C8tIuQy7qaaViki6KF3krBYlDx93M3LV8ZEycvQe2ajbOIB7Jyp/MPM3U9mQ+n4s0Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a7f2939257798e5e702969a66125c98d135a1b48b50d94571fc314ed1cd6a297","last_reissued_at":"2026-07-05T10:28:04.661241Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:28:04.661241Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quantitative Hydrodynamic Stability for Couette Flow on Unbounded Domains with Navier Boundary Conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jacob Bedrossian, Ryan Arbon","submitted_at":"2024-04-03T02:27:03Z","abstract_excerpt":"We prove a stability threshold theorem for 2D Navier-Stokes on three unbounded domains: the whole plane $\\mathbb{R} \\times \\mathbb{R}$, the half plane $\\mathbb{R} \\times [0,\\infty)$ with Navier boundary conditions, and the infinite channel $\\mathbb{R} \\times [-1, 1]$ with Navier boundary conditions. Starting with the Couette shear flow, we consider initial perturbations $\\omega_{in}$ which are of size $\\nu^{1/2}(1+\\ln(1/\\nu)^{1/2})^{-1}$ in an anisotropic Sobolev space with an additional low frequency control condition for the planar cases. We then demonstrate that such perturbations exhibit i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.02412","kind":"arxiv","version":3},"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/2404.02412/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":"2404.02412","created_at":"2026-07-05T10:28:04.661297+00:00"},{"alias_kind":"arxiv_version","alias_value":"2404.02412v3","created_at":"2026-07-05T10:28:04.661297+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.02412","created_at":"2026-07-05T10:28:04.661297+00:00"},{"alias_kind":"pith_short_12","alias_value":"U7ZJHESXPGHF","created_at":"2026-07-05T10:28:04.661297+00:00"},{"alias_kind":"pith_short_16","alias_value":"U7ZJHESXPGHF44BJ","created_at":"2026-07-05T10:28:04.661297+00:00"},{"alias_kind":"pith_short_8","alias_value":"U7ZJHESX","created_at":"2026-07-05T10:28:04.661297+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2505.19822","citing_title":"The stability threshold for 3D MHD equations around Couette with rationally aligned magnetic field","ref_index":2,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/U7ZJHESXPGHF44BJNGTGCJOJRU","json":"https://pith.science/pith/U7ZJHESXPGHF44BJNGTGCJOJRU.json","graph_json":"https://pith.science/api/pith-number/U7ZJHESXPGHF44BJNGTGCJOJRU/graph.json","events_json":"https://pith.science/api/pith-number/U7ZJHESXPGHF44BJNGTGCJOJRU/events.json","paper":"https://pith.science/paper/U7ZJHESX"},"agent_actions":{"view_html":"https://pith.science/pith/U7ZJHESXPGHF44BJNGTGCJOJRU","download_json":"https://pith.science/pith/U7ZJHESXPGHF44BJNGTGCJOJRU.json","view_paper":"https://pith.science/paper/U7ZJHESX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2404.02412&json=true","fetch_graph":"https://pith.science/api/pith-number/U7ZJHESXPGHF44BJNGTGCJOJRU/graph.json","fetch_events":"https://pith.science/api/pith-number/U7ZJHESXPGHF44BJNGTGCJOJRU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/U7ZJHESXPGHF44BJNGTGCJOJRU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/U7ZJHESXPGHF44BJNGTGCJOJRU/action/storage_attestation","attest_author":"https://pith.science/pith/U7ZJHESXPGHF44BJNGTGCJOJRU/action/author_attestation","sign_citation":"https://pith.science/pith/U7ZJHESXPGHF44BJNGTGCJOJRU/action/citation_signature","submit_replication":"https://pith.science/pith/U7ZJHESXPGHF44BJNGTGCJOJRU/action/replication_record"}},"created_at":"2026-07-05T10:28:04.661297+00:00","updated_at":"2026-07-05T10:28:04.661297+00:00"}