{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:E4INSEIH42HEFN4VDY5CRFNIX4","short_pith_number":"pith:E4INSEIH","canonical_record":{"source":{"id":"1603.07820","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-03-25T04:52:48Z","cross_cats_sorted":[],"title_canon_sha256":"4f88441fc975bdb6b9fe942462e506ced81da6599695c192d2ca35a66469cbf1","abstract_canon_sha256":"3caa6ee38aca1de2927e6fd94b83c75f6c8e4b26deb1e473ee3fff5ce18155a4"},"schema_version":"1.0"},"canonical_sha256":"2710d91107e68e42b7951e3a2895a8bf29f88a66fac72f0bca0b9fa6fd6dffee","source":{"kind":"arxiv","id":"1603.07820","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:E4INSEIH42HEFN4VDY5CRFNIX4","target":"record","payload":{"canonical_record":{"source":{"id":"1603.07820","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-03-25T04:52:48Z","cross_cats_sorted":[],"title_canon_sha256":"4f88441fc975bdb6b9fe942462e506ced81da6599695c192d2ca35a66469cbf1","abstract_canon_sha256":"3caa6ee38aca1de2927e6fd94b83c75f6c8e4b26deb1e473ee3fff5ce18155a4"},"schema_version":"1.0"},"canonical_sha256":"2710d91107e68e42b7951e3a2895a8bf29f88a66fac72f0bca0b9fa6fd6dffee","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:55:34.283193Z","signature_b64":"6v45zZIErmOaPS29dPHhVeanHCDwVFghJVGpEEVEsQkeFpUwV+GRS/QJxTDmlHyjXcGXvaDyqnCCPksrEHHvAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2710d91107e68e42b7951e3a2895a8bf29f88a66fac72f0bca0b9fa6fd6dffee","last_reissued_at":"2026-05-18T00:55:34.282759Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:55:34.282759Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.07820","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:55:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WJ1jQnK+KVfr1xxKeelR39z3SqVn4ePPojrefzXc0I5Fcok232Di0rvYZkEonV8VqJicfaU5TlbCVEo+iWcPCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T12:06:31.361191Z"},"content_sha256":"179f10eb061add84da7edf62766e08ba42530f0bc878562572200689e64b3b0f","schema_version":"1.0","event_id":"sha256:179f10eb061add84da7edf62766e08ba42530f0bc878562572200689e64b3b0f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:E4INSEIH42HEFN4VDY5CRFNIX4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Ill-posedness for the incompressible Euler equations in critical Sobolev spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"In-Jee Jeong, Tarek Mohamed Elgindi","submitted_at":"2016-03-25T04:52:48Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.07820","kind":"arxiv","version":2},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:55:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zUDwYpy98yqIbaFZKy6HpoUjw7q0Ni200iuScqkkXSGIWkBopxNrPxqzgaB7ZelyFs/wDF4GsbdXf8YkahMxBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T12:06:31.361567Z"},"content_sha256":"c54fe4223af49d64c545cf34a0750204c5083214b9827a21daecdfbbe60d53d7","schema_version":"1.0","event_id":"sha256:c54fe4223af49d64c545cf34a0750204c5083214b9827a21daecdfbbe60d53d7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E4INSEIH42HEFN4VDY5CRFNIX4/bundle.json","state_url":"https://pith.science/pith/E4INSEIH42HEFN4VDY5CRFNIX4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E4INSEIH42HEFN4VDY5CRFNIX4/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":"2026-06-01T12:06:31Z","links":{"resolver":"https://pith.science/pith/E4INSEIH42HEFN4VDY5CRFNIX4","bundle":"https://pith.science/pith/E4INSEIH42HEFN4VDY5CRFNIX4/bundle.json","state":"https://pith.science/pith/E4INSEIH42HEFN4VDY5CRFNIX4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E4INSEIH42HEFN4VDY5CRFNIX4/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"StLvsT5BMxN1dzmP7eAWdkCV3SCGfSc5mPR37TlxON7w0aa2hLCiOZqxbtUjIJiKNTpyeHi6hpF8SOXh0vAzBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T12:06:31.363646Z","bundle_sha256":"86dd2823a5fbc215e8438e442af51698ff0c623d64663632ae1a80e425adfdbd"}}