{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:D73MRMYRYKMHPKYPO4QJ4T5XUW","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":"3526306a3aa487e2256048aadcf065c6ea094df3c654b0a96a67840059d8763a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-09-30T04:38:13Z","title_canon_sha256":"67630339247379889eca19a27e473d2c803734027e61a44639e63f123a33e9d7"},"schema_version":"1.0","source":{"id":"1409.8382","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.8382","created_at":"2026-05-18T02:41:25Z"},{"alias_kind":"arxiv_version","alias_value":"1409.8382v1","created_at":"2026-05-18T02:41:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.8382","created_at":"2026-05-18T02:41:25Z"},{"alias_kind":"pith_short_12","alias_value":"D73MRMYRYKMH","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"D73MRMYRYKMHPKYP","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"D73MRMYR","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:7f753a908795ee3d378893b8a490658041b0eefe5f853471d9741967058f4289","target":"graph","created_at":"2026-05-18T02:41:25Z","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":"In this short note we address a problem raised in [21], concerning the uniqueness of solutions to Naiver Stokes equation with small initial data in $L^{3,\\infty}(R^3)$, the Lorentz space. We prove uniqueness for such initial data.","authors_text":"Hao Jia","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-09-30T04:38:13Z","title":"Uniqueness of solutions to to Navier Stokes equation with small initial data in $L^{3,\\infty}(R^3)$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.8382","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:b2a6b62dbaf333623388f0f6e7f156d63922e1f7a340ec62b4d79edb78ffa305","target":"record","created_at":"2026-05-18T02:41:25Z","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":"3526306a3aa487e2256048aadcf065c6ea094df3c654b0a96a67840059d8763a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-09-30T04:38:13Z","title_canon_sha256":"67630339247379889eca19a27e473d2c803734027e61a44639e63f123a33e9d7"},"schema_version":"1.0","source":{"id":"1409.8382","kind":"arxiv","version":1}},"canonical_sha256":"1ff6c8b311c29877ab0f77209e4fb7a5abe126c493ba971a34856b944a3b322d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1ff6c8b311c29877ab0f77209e4fb7a5abe126c493ba971a34856b944a3b322d","first_computed_at":"2026-05-18T02:41:25.440514Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:25.440514Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"81jFw1OOrz142eYAMr91FnhOIExkIDPVgFp5kZXgLm8WT3de/YJvNgJQTXFS58l99U4Bmk5XAf8GSB23LZPNBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:25.440892Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.8382","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b2a6b62dbaf333623388f0f6e7f156d63922e1f7a340ec62b4d79edb78ffa305","sha256:7f753a908795ee3d378893b8a490658041b0eefe5f853471d9741967058f4289"],"state_sha256":"e3b5d73fcafcd03384c1f51bf07a9cf2f54e155f34c8ae18a0631a15e3837a00"}