{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:6K46GMTSMQPFQWSCXTO3GHDWJX","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":"f39072b8edacb4a0264a7acdb160fa0149f38837767155630a31036cbf298f75","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-03-01T19:32:48Z","title_canon_sha256":"2f36c68f62386d6afa92134f66ef5d088b83dc22fb5379e4c3391e87e5097124"},"schema_version":"1.0","source":{"id":"1303.0257","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.0257","created_at":"2026-05-18T01:51:18Z"},{"alias_kind":"arxiv_version","alias_value":"1303.0257v2","created_at":"2026-05-18T01:51:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.0257","created_at":"2026-05-18T01:51:18Z"},{"alias_kind":"pith_short_12","alias_value":"6K46GMTSMQPF","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"6K46GMTSMQPFQWSC","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"6K46GMTS","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:c04e1fbf7df17574bab06138ec02c3fff7f1c4c790a7b9c0fc930eba948dc3fa","target":"graph","created_at":"2026-05-18T01:51:18Z","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":"It is shown that, if the vorticity magnitude associated with a (presumed singular) three-dimensional incompressible Navier-Stokes flow blows-up in a manner exhibiting certain {\\em time dependent local structure}, then {\\em time independent} estimates on the $L^1$ norm of $|\\omega|\\log\\sqrt{1+ |\\omega|^2}$ follow. The implication is that the volume of the region of high vorticity decays at a rate of greater order than a rate connected to the critical scaling of one-dimensional local sparseness and, consequently, the solution becomes sub-critical.","authors_text":"Zachary Bradshaw, Zoran Grujic","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-03-01T19:32:48Z","title":"Blow-up scenarios for 3D NSE exhibiting sub-criticality with respect to the scaling of one-dimensional local sparseness"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.0257","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":"sha256:89365c9e2c7575291f176601ba0946edfb612e1fe741f954a52eb368af69cfbe","target":"record","created_at":"2026-05-18T01:51:18Z","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":"f39072b8edacb4a0264a7acdb160fa0149f38837767155630a31036cbf298f75","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-03-01T19:32:48Z","title_canon_sha256":"2f36c68f62386d6afa92134f66ef5d088b83dc22fb5379e4c3391e87e5097124"},"schema_version":"1.0","source":{"id":"1303.0257","kind":"arxiv","version":2}},"canonical_sha256":"f2b9e33272641e585a42bcddb31c764dfa6cb46e38226a8b3b916f3c333ed903","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f2b9e33272641e585a42bcddb31c764dfa6cb46e38226a8b3b916f3c333ed903","first_computed_at":"2026-05-18T01:51:18.081233Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:51:18.081233Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fzpadi6/k7OAAHkhFBJ/+qNVQjOprT/tZcreMkdiK2F1IQ9gKDlKccQs+jGBPez4jvTI0dWwayYfEv1xcmXBCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:51:18.081705Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.0257","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:89365c9e2c7575291f176601ba0946edfb612e1fe741f954a52eb368af69cfbe","sha256:c04e1fbf7df17574bab06138ec02c3fff7f1c4c790a7b9c0fc930eba948dc3fa"],"state_sha256":"ac4d4f6e983c1236ed916518a97241464ee0b3a6efbbcb4c5709d22c8253db82"}