{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:ZV2ZLLF64ZUZOOC3UV6JAXZWRB","short_pith_number":"pith:ZV2ZLLF6","schema_version":"1.0","canonical_sha256":"cd7595acbee66997385ba57c905f368848cd850802195b0787077f0bc7c82ef6","source":{"kind":"arxiv","id":"1212.0766","version":6},"attestation_state":"computed","paper":{"title":"Global Mild Solutions of Fractional Naiver-Stokes Equations with Small Initial Data in Critical Besov-Q Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jie Xiao, Pengtao Li, Qixiang Yang","submitted_at":"2012-12-04T15:33:34Z","abstract_excerpt":"In this paper, we establish the global existence and uniqueness of a mild solution of the so-called fractional Navier-Stokes equations with a small initial data in the critical Besov-Q space covering many already known function spaces."},"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":"1212.0766","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-12-04T15:33:34Z","cross_cats_sorted":[],"title_canon_sha256":"c877d00666a04d48b134f60a773a9bc90cb4eaa39ad072476f0dcbe25526c565","abstract_canon_sha256":"8670a2767422bf70a19c81a0a62b27920b3cad08fd5dc038d66de08bdc082589"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:47:05.879132Z","signature_b64":"+c6CKDJVIClb+zjiWbeFCZaeoz9IZ2eQojU9SKQbZgF89oMeO/vmCUdIdnUc97BLQnLGvxS/cxfiq+DiwTPcCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cd7595acbee66997385ba57c905f368848cd850802195b0787077f0bc7c82ef6","last_reissued_at":"2026-05-18T02:47:05.878485Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:47:05.878485Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Global Mild Solutions of Fractional Naiver-Stokes Equations with Small Initial Data in Critical Besov-Q Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jie Xiao, Pengtao Li, Qixiang Yang","submitted_at":"2012-12-04T15:33:34Z","abstract_excerpt":"In this paper, we establish the global existence and uniqueness of a mild solution of the so-called fractional Navier-Stokes equations with a small initial data in the critical Besov-Q space covering many already known function spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.0766","kind":"arxiv","version":6},"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":"1212.0766","created_at":"2026-05-18T02:47:05.878585+00:00"},{"alias_kind":"arxiv_version","alias_value":"1212.0766v6","created_at":"2026-05-18T02:47:05.878585+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.0766","created_at":"2026-05-18T02:47:05.878585+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZV2ZLLF64ZUZ","created_at":"2026-05-18T12:27:30.460161+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZV2ZLLF64ZUZOOC3","created_at":"2026-05-18T12:27:30.460161+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZV2ZLLF6","created_at":"2026-05-18T12:27:30.460161+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/ZV2ZLLF64ZUZOOC3UV6JAXZWRB","json":"https://pith.science/pith/ZV2ZLLF64ZUZOOC3UV6JAXZWRB.json","graph_json":"https://pith.science/api/pith-number/ZV2ZLLF64ZUZOOC3UV6JAXZWRB/graph.json","events_json":"https://pith.science/api/pith-number/ZV2ZLLF64ZUZOOC3UV6JAXZWRB/events.json","paper":"https://pith.science/paper/ZV2ZLLF6"},"agent_actions":{"view_html":"https://pith.science/pith/ZV2ZLLF64ZUZOOC3UV6JAXZWRB","download_json":"https://pith.science/pith/ZV2ZLLF64ZUZOOC3UV6JAXZWRB.json","view_paper":"https://pith.science/paper/ZV2ZLLF6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1212.0766&json=true","fetch_graph":"https://pith.science/api/pith-number/ZV2ZLLF64ZUZOOC3UV6JAXZWRB/graph.json","fetch_events":"https://pith.science/api/pith-number/ZV2ZLLF64ZUZOOC3UV6JAXZWRB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZV2ZLLF64ZUZOOC3UV6JAXZWRB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZV2ZLLF64ZUZOOC3UV6JAXZWRB/action/storage_attestation","attest_author":"https://pith.science/pith/ZV2ZLLF64ZUZOOC3UV6JAXZWRB/action/author_attestation","sign_citation":"https://pith.science/pith/ZV2ZLLF64ZUZOOC3UV6JAXZWRB/action/citation_signature","submit_replication":"https://pith.science/pith/ZV2ZLLF64ZUZOOC3UV6JAXZWRB/action/replication_record"}},"created_at":"2026-05-18T02:47:05.878585+00:00","updated_at":"2026-05-18T02:47:05.878585+00:00"}