{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:B5E7ADXBTYD6M3MNHJS5ZDPJ2E","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":"9f4229d35708e7a05fcd59dfa5a41e56b5cc3d4d22a71c4d6b6c7f594da32512","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-10-30T17:56:19Z","title_canon_sha256":"4c8b01a78d9e06c1f1a173ddfa93b946ff6ad0e6aef23f8bdd7def2cfd310ce3"},"schema_version":"1.0","source":{"id":"1510.09178","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.09178","created_at":"2026-05-18T01:28:22Z"},{"alias_kind":"arxiv_version","alias_value":"1510.09178v1","created_at":"2026-05-18T01:28:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.09178","created_at":"2026-05-18T01:28:22Z"},{"alias_kind":"pith_short_12","alias_value":"B5E7ADXBTYD6","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"B5E7ADXBTYD6M3MN","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"B5E7ADXB","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:3839fe40ff6fe635e219b9f83d805638b48d7a8b91482df5f40adc4357ff8236","target":"graph","created_at":"2026-05-18T01:28:22Z","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":"Assuming $T$ is a potential blow up time for the Navier-Stokes system in $\\mathbb{R}^3$ or $\\mathbb{R}^3_+$, we show that the $L^{3,q}$ Lorentz norm, with $q$ finite, of the velocity field goes to infinity as time $t$ approaches $T$.","authors_text":"G. Seregin, T. Barker","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-10-30T17:56:19Z","title":"On blowup of nonendpoint borderline Lorentz norms for the Navier-Stokes equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.09178","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":"sha256:6ce23342781b10d1f9985c0f6f6faeb4883d0f94f5fb164e103f4bebf0bfe723","target":"record","created_at":"2026-05-18T01:28:22Z","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":"9f4229d35708e7a05fcd59dfa5a41e56b5cc3d4d22a71c4d6b6c7f594da32512","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-10-30T17:56:19Z","title_canon_sha256":"4c8b01a78d9e06c1f1a173ddfa93b946ff6ad0e6aef23f8bdd7def2cfd310ce3"},"schema_version":"1.0","source":{"id":"1510.09178","kind":"arxiv","version":1}},"canonical_sha256":"0f49f00ee19e07e66d8d3a65dc8de9d12593074f7a59af6deb523fc56e5b3ccc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0f49f00ee19e07e66d8d3a65dc8de9d12593074f7a59af6deb523fc56e5b3ccc","first_computed_at":"2026-05-18T01:28:22.453232Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:28:22.453232Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xg0gv6kvvghJpLr+q15Kk56OdwVO0O05OCrf99il1+wB6RVBi2fWu48Ewd+oXmKAF4hnVK69atyDYiFXR/mnBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:28:22.453867Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.09178","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6ce23342781b10d1f9985c0f6f6faeb4883d0f94f5fb164e103f4bebf0bfe723","sha256:3839fe40ff6fe635e219b9f83d805638b48d7a8b91482df5f40adc4357ff8236"],"state_sha256":"28563b8b37a71720fbc80a80975c446a19b5664e4b13dac77794fe754777eec1"}