{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:JM5AE7OCEM2JJTXRX2OPC646KQ","short_pith_number":"pith:JM5AE7OC","canonical_record":{"source":{"id":"2208.14898","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-08-31T14:42:28Z","cross_cats_sorted":["physics.flu-dyn"],"title_canon_sha256":"39f8f4934004006f317c806b00cd8c97763253e95a5c371309463d3360ece6d3","abstract_canon_sha256":"5424dbc13cd3ee8d4292a77384d92911eac979c9c65c84b5844b253b327955fd"},"schema_version":"1.0"},"canonical_sha256":"4b3a027dc2233494cef1be9cf17b9e54127dc13d7b93e9453faecf9757196aaf","source":{"kind":"arxiv","id":"2208.14898","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2208.14898","created_at":"2026-07-05T04:53:36Z"},{"alias_kind":"arxiv_version","alias_value":"2208.14898v1","created_at":"2026-07-05T04:53:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2208.14898","created_at":"2026-07-05T04:53:36Z"},{"alias_kind":"pith_short_12","alias_value":"JM5AE7OCEM2J","created_at":"2026-07-05T04:53:36Z"},{"alias_kind":"pith_short_16","alias_value":"JM5AE7OCEM2JJTXR","created_at":"2026-07-05T04:53:36Z"},{"alias_kind":"pith_short_8","alias_value":"JM5AE7OC","created_at":"2026-07-05T04:53:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:JM5AE7OCEM2JJTXRX2OPC646KQ","target":"record","payload":{"canonical_record":{"source":{"id":"2208.14898","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-08-31T14:42:28Z","cross_cats_sorted":["physics.flu-dyn"],"title_canon_sha256":"39f8f4934004006f317c806b00cd8c97763253e95a5c371309463d3360ece6d3","abstract_canon_sha256":"5424dbc13cd3ee8d4292a77384d92911eac979c9c65c84b5844b253b327955fd"},"schema_version":"1.0"},"canonical_sha256":"4b3a027dc2233494cef1be9cf17b9e54127dc13d7b93e9453faecf9757196aaf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:53:36.295451Z","signature_b64":"ZPG7ynbSwdvZOFzaS3BIXKFliFE2DSYx+RVLRYh5WF3ijIcJx6CGeuqYSYmULOl6DoaPPDNw4AodasFgRy22BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4b3a027dc2233494cef1be9cf17b9e54127dc13d7b93e9453faecf9757196aaf","last_reissued_at":"2026-07-05T04:53:36.295064Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:53:36.295064Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2208.14898","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:53:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XWJYFrMOB1OxeY3POvOE19k3abshuZQIx/2sWafIJFsDhzldW/7n23hxAJYOupNie39HNDH0J03xD+jl64zFDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T14:39:56.001723Z"},"content_sha256":"bf4f1e16ac62540de34afbee933a6a04fb0a42c8cd078e736f6138ebe66b0545","schema_version":"1.0","event_id":"sha256:bf4f1e16ac62540de34afbee933a6a04fb0a42c8cd078e736f6138ebe66b0545"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:JM5AE7OCEM2JJTXRX2OPC646KQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotic stability of two-dimensional Couette flow in a viscous fluid","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.flu-dyn"],"primary_cat":"math.AP","authors_text":"Hui Li, Nader Masmoudi, Weiren Zhao","submitted_at":"2022-08-31T14:42:28Z","abstract_excerpt":"In this paper, we study the nonlinear asymptotic stability of Couette flow for the two-dimensional Navier-Stokes equation with small viscosity $\\nu>0$ in $\\mathbb{T}\\times\\mathbb{R}$. It's generally known the nonlinear asymptotic stability of the Couette flow depends closely on the size and regularity of the initial perturbation, which yields the stability threshold problem. This work studies the relationship between the size and the regularity of the initial perturbation that makes the nonlinear asymptotic stability holds. More precisely, we proved that if the initial perturbation is in some "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.14898","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/2208.14898/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:53:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OqNeaML/V9jk7WTSIoZMMtljErMj3O7ERRlhmMsT0LDvHDIDF6cRSCg+X3QFyiiB6JI5mw6xgS3K2MalUuXCCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T14:39:56.002221Z"},"content_sha256":"908eed9954562be0fd41f9301f69a206ffb9f43c0c89ba6e26bfac95ceb131cd","schema_version":"1.0","event_id":"sha256:908eed9954562be0fd41f9301f69a206ffb9f43c0c89ba6e26bfac95ceb131cd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JM5AE7OCEM2JJTXRX2OPC646KQ/bundle.json","state_url":"https://pith.science/pith/JM5AE7OCEM2JJTXRX2OPC646KQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JM5AE7OCEM2JJTXRX2OPC646KQ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-08T14:39:56Z","links":{"resolver":"https://pith.science/pith/JM5AE7OCEM2JJTXRX2OPC646KQ","bundle":"https://pith.science/pith/JM5AE7OCEM2JJTXRX2OPC646KQ/bundle.json","state":"https://pith.science/pith/JM5AE7OCEM2JJTXRX2OPC646KQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JM5AE7OCEM2JJTXRX2OPC646KQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:JM5AE7OCEM2JJTXRX2OPC646KQ","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":"5424dbc13cd3ee8d4292a77384d92911eac979c9c65c84b5844b253b327955fd","cross_cats_sorted":["physics.flu-dyn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-08-31T14:42:28Z","title_canon_sha256":"39f8f4934004006f317c806b00cd8c97763253e95a5c371309463d3360ece6d3"},"schema_version":"1.0","source":{"id":"2208.14898","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2208.14898","created_at":"2026-07-05T04:53:36Z"},{"alias_kind":"arxiv_version","alias_value":"2208.14898v1","created_at":"2026-07-05T04:53:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2208.14898","created_at":"2026-07-05T04:53:36Z"},{"alias_kind":"pith_short_12","alias_value":"JM5AE7OCEM2J","created_at":"2026-07-05T04:53:36Z"},{"alias_kind":"pith_short_16","alias_value":"JM5AE7OCEM2JJTXR","created_at":"2026-07-05T04:53:36Z"},{"alias_kind":"pith_short_8","alias_value":"JM5AE7OC","created_at":"2026-07-05T04:53:36Z"}],"graph_snapshots":[{"event_id":"sha256:908eed9954562be0fd41f9301f69a206ffb9f43c0c89ba6e26bfac95ceb131cd","target":"graph","created_at":"2026-07-05T04:53:36Z","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/2208.14898/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we study the nonlinear asymptotic stability of Couette flow for the two-dimensional Navier-Stokes equation with small viscosity $\\nu>0$ in $\\mathbb{T}\\times\\mathbb{R}$. It's generally known the nonlinear asymptotic stability of the Couette flow depends closely on the size and regularity of the initial perturbation, which yields the stability threshold problem. This work studies the relationship between the size and the regularity of the initial perturbation that makes the nonlinear asymptotic stability holds. More precisely, we proved that if the initial perturbation is in some ","authors_text":"Hui Li, Nader Masmoudi, Weiren Zhao","cross_cats":["physics.flu-dyn"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-08-31T14:42:28Z","title":"Asymptotic stability of two-dimensional Couette flow in a viscous fluid"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.14898","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:bf4f1e16ac62540de34afbee933a6a04fb0a42c8cd078e736f6138ebe66b0545","target":"record","created_at":"2026-07-05T04:53:36Z","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":"5424dbc13cd3ee8d4292a77384d92911eac979c9c65c84b5844b253b327955fd","cross_cats_sorted":["physics.flu-dyn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-08-31T14:42:28Z","title_canon_sha256":"39f8f4934004006f317c806b00cd8c97763253e95a5c371309463d3360ece6d3"},"schema_version":"1.0","source":{"id":"2208.14898","kind":"arxiv","version":1}},"canonical_sha256":"4b3a027dc2233494cef1be9cf17b9e54127dc13d7b93e9453faecf9757196aaf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4b3a027dc2233494cef1be9cf17b9e54127dc13d7b93e9453faecf9757196aaf","first_computed_at":"2026-07-05T04:53:36.295064Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:53:36.295064Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZPG7ynbSwdvZOFzaS3BIXKFliFE2DSYx+RVLRYh5WF3ijIcJx6CGeuqYSYmULOl6DoaPPDNw4AodasFgRy22BQ==","signature_status":"signed_v1","signed_at":"2026-07-05T04:53:36.295451Z","signed_message":"canonical_sha256_bytes"},"source_id":"2208.14898","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bf4f1e16ac62540de34afbee933a6a04fb0a42c8cd078e736f6138ebe66b0545","sha256:908eed9954562be0fd41f9301f69a206ffb9f43c0c89ba6e26bfac95ceb131cd"],"state_sha256":"1dc2e741a2ca2b8a27b5e5068aea217f147cfa5e22d67c51105cbd3101772eb3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KWzrXXkep87l+PJ1rEp7Bsf89/P4KUU4XGb7QAq5IwxpqoubEH/gY7aZbO0GK8LyqgG67D9eIycEKpbR2nCSBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T14:39:56.006873Z","bundle_sha256":"c73f30cdc08dbbc2fd77f62851788b9ff2ac96ddb7eb114d22c8cfeeb2d1c891"}}