{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:WAYDO2SK5MYJVHO3YDKE63RMVH","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"bd013432198375694dee4969a3ffaf958dbdc511c8d9e9a89f85153bc55472ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-04-18T03:31:40Z","title_canon_sha256":"dd200b4b7c5db11ff2c0857ed8139417865a06d389fece51cc247b73e8591804"},"schema_version":"1.0","source":{"id":"2404.11878","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.11878","created_at":"2026-07-05T08:09:31Z"},{"alias_kind":"arxiv_version","alias_value":"2404.11878v1","created_at":"2026-07-05T08:09:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.11878","created_at":"2026-07-05T08:09:31Z"},{"alias_kind":"pith_short_12","alias_value":"WAYDO2SK5MYJ","created_at":"2026-07-05T08:09:31Z"},{"alias_kind":"pith_short_16","alias_value":"WAYDO2SK5MYJVHO3","created_at":"2026-07-05T08:09:31Z"},{"alias_kind":"pith_short_8","alias_value":"WAYDO2SK","created_at":"2026-07-05T08:09:31Z"}],"graph_snapshots":[{"event_id":"sha256:c340d2cd26974641c0a8e456f282ffa3aa58d8aa2e79d1fa8982b072f8a310fc","target":"graph","created_at":"2026-07-05T08:09:31Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2404.11878/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we investigate the transition threshold problem concerning the 2-D Navier-Stokes equations in the context of Couette flow $(y,0)$ at high Reynolds number $Re$ in whole space. By utilizing Green's function estimates for the linearized equations around Couette flow, we initially establish refined dissipation estimates for the linearized Navier-Stokes equations with a precise decay rate $(1+t)^{-1}.$ As an application, we prove that if the initial perturbation of vorticity satisfies$$\\|\\omega_{0}\\|_{H^{1}\\cap L^1}\\leq c_0\\nu^{\\frac{3}{4}}$$ for some small constant $c_0$ independent","authors_text":"Gaofeng Wang, Weike Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-04-18T03:31:40Z","title":"Transition threshold for the 2-D Couette flow in whole space via Green's function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.11878","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:de3f162b17cf26936c62537cc545a0fb0de2aecfd343935e5dd9c11e4b354e50","target":"record","created_at":"2026-07-05T08:09:31Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"bd013432198375694dee4969a3ffaf958dbdc511c8d9e9a89f85153bc55472ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-04-18T03:31:40Z","title_canon_sha256":"dd200b4b7c5db11ff2c0857ed8139417865a06d389fece51cc247b73e8591804"},"schema_version":"1.0","source":{"id":"2404.11878","kind":"arxiv","version":1}},"canonical_sha256":"b030376a4aeb309a9ddbc0d44f6e2ca9f23d8390e67e1c1132c473c1eaa152be","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b030376a4aeb309a9ddbc0d44f6e2ca9f23d8390e67e1c1132c473c1eaa152be","first_computed_at":"2026-07-05T08:09:31.854718Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:09:31.854718Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"djIZQQvL0TQdr7VBrLVdWbxTGbLiFZhIV3KCVfGPeXIdT9mslyqOMg4ZLB2jHJt6D2dXFjZEpKI915MKFDegBg==","signature_status":"signed_v1","signed_at":"2026-07-05T08:09:31.855118Z","signed_message":"canonical_sha256_bytes"},"source_id":"2404.11878","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:de3f162b17cf26936c62537cc545a0fb0de2aecfd343935e5dd9c11e4b354e50","sha256:c340d2cd26974641c0a8e456f282ffa3aa58d8aa2e79d1fa8982b072f8a310fc"],"state_sha256":"d1546b86c60203c88c562e5863ea65d26f7316d8a3d811535633d0f80ca9a0e8"}