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Zhang \\cite{CMZ} have proved that weak Leray solutions of the Navier-Stokes are unique in the class $L^{\\frac{2}{1+r}% }([0,T].B_{\\infty}^{r,\\infty}(\\mathbb{R}^{3})$ with $r\\in]-\\frac{1}{2},1].$ In this paper, we establish that this criterion remains true for $r\\in ]-1,-\\frac{1}{2}].$"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1804.02853","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-04-09T07:38:25Z","cross_cats_sorted":[],"title_canon_sha256":"70b269f310f5cf5c90eb6f1d2bd2ad9764ae42efb6102b5a2b291ff38a94f040","abstract_canon_sha256":"b6fb170d64f8dec27a216a1334ee58db64a49f07fd17da5c4471aa6d6429c4be"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:58.162847Z","signature_b64":"rpEizX+Msr6/NM7IPv3yRcxWRP88+Kza/CZoCsj+LkJJ2bNm9UT73XM9JvKu3mLdY4leXd0dA2dP1rBgUI95Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2b49ab79048a0e408f2098679c24d7eb5c16a12321acaeed9fa49ee1043e57ce","last_reissued_at":"2026-05-18T00:18:58.160674Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:58.160674Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An extension of an unicity class for Navier-Stokes equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ramzi May","submitted_at":"2018-04-09T07:38:25Z","abstract_excerpt":"This is a translation from French of my paper [R. 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Zhang \\cite{CMZ} have proved that weak Leray solutions of the Navier-Stokes are unique in the class $L^{\\frac{2}{1+r}% }([0,T].B_{\\infty}^{r,\\infty}(\\mathbb{R}^{3})$ with $r\\in]-\\frac{1}{2},1].$ In this paper, we establish that this criterion remains true for $r\\in ]-1,-\\frac{1}{2}].$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.02853","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1804.02853","created_at":"2026-05-18T00:18:58.162305+00:00"},{"alias_kind":"arxiv_version","alias_value":"1804.02853v1","created_at":"2026-05-18T00:18:58.162305+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.02853","created_at":"2026-05-18T00:18:58.162305+00:00"},{"alias_kind":"pith_short_12","alias_value":"FNE2W6IERIHE","created_at":"2026-05-18T12:32:25.280505+00:00"},{"alias_kind":"pith_short_16","alias_value":"FNE2W6IERIHEBDZA","created_at":"2026-05-18T12:32:25.280505+00:00"},{"alias_kind":"pith_short_8","alias_value":"FNE2W6IE","created_at":"2026-05-18T12:32:25.280505+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FNE2W6IERIHEBDZATBTZYJGX5N","json":"https://pith.science/pith/FNE2W6IERIHEBDZATBTZYJGX5N.json","graph_json":"https://pith.science/api/pith-number/FNE2W6IERIHEBDZATBTZYJGX5N/graph.json","events_json":"https://pith.science/api/pith-number/FNE2W6IERIHEBDZATBTZYJGX5N/events.json","paper":"https://pith.science/paper/FNE2W6IE"},"agent_actions":{"view_html":"https://pith.science/pith/FNE2W6IERIHEBDZATBTZYJGX5N","download_json":"https://pith.science/pith/FNE2W6IERIHEBDZATBTZYJGX5N.json","view_paper":"https://pith.science/paper/FNE2W6IE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1804.02853&json=true","fetch_graph":"https://pith.science/api/pith-number/FNE2W6IERIHEBDZATBTZYJGX5N/graph.json","fetch_events":"https://pith.science/api/pith-number/FNE2W6IERIHEBDZATBTZYJGX5N/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FNE2W6IERIHEBDZATBTZYJGX5N/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FNE2W6IERIHEBDZATBTZYJGX5N/action/storage_attestation","attest_author":"https://pith.science/pith/FNE2W6IERIHEBDZATBTZYJGX5N/action/author_attestation","sign_citation":"https://pith.science/pith/FNE2W6IERIHEBDZATBTZYJGX5N/action/citation_signature","submit_replication":"https://pith.science/pith/FNE2W6IERIHEBDZATBTZYJGX5N/action/replication_record"}},"created_at":"2026-05-18T00:18:58.162305+00:00","updated_at":"2026-05-18T00:18:58.162305+00:00"}