{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:GBWFI7W5WRB4X6EWGLICS7LPYN","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":"9d160cc639655d7662fce611ab63ff8885c3b53c36a2a3f7d6a689717aa26419","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-04-11T14:56:17Z","title_canon_sha256":"fdd3a91c07f98f576501b4649c627db9445d3c32062784a045176458a640ca66"},"schema_version":"1.0","source":{"id":"2404.07813","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.07813","created_at":"2026-07-05T08:23:21Z"},{"alias_kind":"arxiv_version","alias_value":"2404.07813v2","created_at":"2026-07-05T08:23:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.07813","created_at":"2026-07-05T08:23:21Z"},{"alias_kind":"pith_short_12","alias_value":"GBWFI7W5WRB4","created_at":"2026-07-05T08:23:21Z"},{"alias_kind":"pith_short_16","alias_value":"GBWFI7W5WRB4X6EW","created_at":"2026-07-05T08:23:21Z"},{"alias_kind":"pith_short_8","alias_value":"GBWFI7W5","created_at":"2026-07-05T08:23:21Z"}],"graph_snapshots":[{"event_id":"sha256:3c5a83574e60b4d6bb8027f33fafd0b2db415d77f1afa021c7ced2fae4d628d6","target":"graph","created_at":"2026-07-05T08:23:21Z","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/2404.07813/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that the 3D Euler and Navier-Stokes equations are strongly illposed in supercritical Sobolev spaces. In the inviscid case, for any $0 < s < \\frac{5}{2} $, we construct a $C^\\infty_c$ initial velocity field with arbitrarily small $H^{s}$ norm for which the unique local-in-time smooth solution of the 3D Euler equation develops large $\\dot{H}^{s}$ norm inflation almost instantaneously. In the viscous case, the same $\\dot{H}^{s}$ norm inflation occurs in the 3D Navier-Stokes equation for $0< s < \\frac{1}{2} $, where $s = \\frac{1}{2}$ is scaling critical for this equation.","authors_text":"Xiaoyutao Luo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-04-11T14:56:17Z","title":"Illposedness of incompressible fluids in supercritical Sobolev spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.07813","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:e29270b1ea131f11804a980a503614dcbd437c4a1c5646684e73cdabc9c3ab24","target":"record","created_at":"2026-07-05T08:23:21Z","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":"9d160cc639655d7662fce611ab63ff8885c3b53c36a2a3f7d6a689717aa26419","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-04-11T14:56:17Z","title_canon_sha256":"fdd3a91c07f98f576501b4649c627db9445d3c32062784a045176458a640ca66"},"schema_version":"1.0","source":{"id":"2404.07813","kind":"arxiv","version":2}},"canonical_sha256":"306c547eddb443cbf89632d0297d6fc35f298914c64d0afe51365dc8d3207897","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"306c547eddb443cbf89632d0297d6fc35f298914c64d0afe51365dc8d3207897","first_computed_at":"2026-07-05T08:23:21.135731Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:23:21.135731Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BeBE0RUP/RmNpPyOG1VE7DEPtKq05H1LezFOMU80dffroZCYf582B89UkKji0PgNXNp0qK13J8vzxwLVNBxhCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T08:23:21.136217Z","signed_message":"canonical_sha256_bytes"},"source_id":"2404.07813","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e29270b1ea131f11804a980a503614dcbd437c4a1c5646684e73cdabc9c3ab24","sha256:3c5a83574e60b4d6bb8027f33fafd0b2db415d77f1afa021c7ced2fae4d628d6"],"state_sha256":"6c99313c969665e42ad068d2a808cc011768569079041ac879cdc8d2ec357250"}