{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:4GIGGDD4HPR77XVJYXNTV5J66N","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":"8c9e3ccd0a80c83cc960c7b131ed014ccdd789bebe083d67c9d760c488f0dae4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-26T19:02:53Z","title_canon_sha256":"7d2cab40e3fc53e684678503b5b246114510bd65469e68135c661da073a1b193"},"schema_version":"1.0","source":{"id":"1807.05425","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.05425","created_at":"2026-05-18T00:10:36Z"},{"alias_kind":"arxiv_version","alias_value":"1807.05425v2","created_at":"2026-05-18T00:10:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.05425","created_at":"2026-05-18T00:10:36Z"},{"alias_kind":"pith_short_12","alias_value":"4GIGGDD4HPR7","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"4GIGGDD4HPR77XVJ","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"4GIGGDD4","created_at":"2026-05-18T12:32:05Z"}],"graph_snapshots":[{"event_id":"sha256:8d9eaaa792fe1b1e8efe9ed14330708c26ed1a64575051ef606420bbbaaed0ce","target":"graph","created_at":"2026-05-18T00:10:36Z","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 paper, we give two family of explicit blowup solution for $3$D incompressible Navier-Stokes equations in $\\RR^3$. Here one family of solutions admit the smooth initial data, and the initial data of another family of solutions are not smooth. The energy of those solutions is infinite.","authors_text":"Weiping Yan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-26T19:02:53Z","title":"Two family of explicit blowup solutions for 3D incompressible Navier-Stokes equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.05425","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":"sha256:0abb0665df80c44b4ea10507423d2a9665b95f0177034bd6cdcb2d9c39aedc84","target":"record","created_at":"2026-05-18T00:10:36Z","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":"8c9e3ccd0a80c83cc960c7b131ed014ccdd789bebe083d67c9d760c488f0dae4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-26T19:02:53Z","title_canon_sha256":"7d2cab40e3fc53e684678503b5b246114510bd65469e68135c661da073a1b193"},"schema_version":"1.0","source":{"id":"1807.05425","kind":"arxiv","version":2}},"canonical_sha256":"e190630c7c3be3ffdea9c5db3af53ef352e87f4cae4af888df64d1447afd9623","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e190630c7c3be3ffdea9c5db3af53ef352e87f4cae4af888df64d1447afd9623","first_computed_at":"2026-05-18T00:10:36.511762Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:36.511762Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vrwyNdVUS7X95nuhr7PmwSTryzv360dV6wsuQkQZDjZWMDHD4V/LiwuFMt2oj4/qUfiHtR5681gosVzpjqQNCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:36.512248Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.05425","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0abb0665df80c44b4ea10507423d2a9665b95f0177034bd6cdcb2d9c39aedc84","sha256:8d9eaaa792fe1b1e8efe9ed14330708c26ed1a64575051ef606420bbbaaed0ce"],"state_sha256":"948dfe9caf595aea2f6655a870ae9a63d6e2c7aa8a463a6574ccdc89074b0a81"}