{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:E4INSEIH42HEFN4VDY5CRFNIX4","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":"3caa6ee38aca1de2927e6fd94b83c75f6c8e4b26deb1e473ee3fff5ce18155a4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-03-25T04:52:48Z","title_canon_sha256":"4f88441fc975bdb6b9fe942462e506ced81da6599695c192d2ca35a66469cbf1"},"schema_version":"1.0","source":{"id":"1603.07820","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.07820","created_at":"2026-05-18T00:55:34Z"},{"alias_kind":"arxiv_version","alias_value":"1603.07820v2","created_at":"2026-05-18T00:55:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.07820","created_at":"2026-05-18T00:55:34Z"},{"alias_kind":"pith_short_12","alias_value":"E4INSEIH42HE","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"E4INSEIH42HEFN4V","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"E4INSEIH","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:c54fe4223af49d64c545cf34a0750204c5083214b9827a21daecdfbbe60d53d7","target":"graph","created_at":"2026-05-18T00:55:34Z","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"},"paper":{"abstract_excerpt":"For the $2D$ Euler equation in vorticity formulation, we construct localized smooth solutions whose critical Sobolev norms become large in a short period of time, and solutions which initially belong to $L^\\infty \\cap H^1$ but escapes $H^1$ immediately for $t>0$. Our main observation is that a localized chunk of vorticity bounded in $L^\\infty \\cap H^1$ with odd-odd symmetry is able to generate a hyperbolic flow with large velocity gradient at least for a short period of time, which stretches the vorticity gradient.","authors_text":"In-Jee Jeong, Tarek Mohamed Elgindi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-03-25T04:52:48Z","title":"Ill-posedness for the incompressible Euler equations in critical Sobolev spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.07820","kind":"arxiv","version":2},"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":"sha256:179f10eb061add84da7edf62766e08ba42530f0bc878562572200689e64b3b0f","target":"record","created_at":"2026-05-18T00:55:34Z","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":"3caa6ee38aca1de2927e6fd94b83c75f6c8e4b26deb1e473ee3fff5ce18155a4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-03-25T04:52:48Z","title_canon_sha256":"4f88441fc975bdb6b9fe942462e506ced81da6599695c192d2ca35a66469cbf1"},"schema_version":"1.0","source":{"id":"1603.07820","kind":"arxiv","version":2}},"canonical_sha256":"2710d91107e68e42b7951e3a2895a8bf29f88a66fac72f0bca0b9fa6fd6dffee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2710d91107e68e42b7951e3a2895a8bf29f88a66fac72f0bca0b9fa6fd6dffee","first_computed_at":"2026-05-18T00:55:34.282759Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:55:34.282759Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6v45zZIErmOaPS29dPHhVeanHCDwVFghJVGpEEVEsQkeFpUwV+GRS/QJxTDmlHyjXcGXvaDyqnCCPksrEHHvAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:55:34.283193Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.07820","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:179f10eb061add84da7edf62766e08ba42530f0bc878562572200689e64b3b0f","sha256:c54fe4223af49d64c545cf34a0750204c5083214b9827a21daecdfbbe60d53d7"],"state_sha256":"512e58fbc6cef7569a18ce491e7e2b5fa27e4bebf036e28653edb00572e9f964"}