{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:JTVZ533PGDL676HCHA7L2CFVGE","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":"1f24977ca3f5bdca7879cac7e2fd463a768bdf0c1f8aef2af0007b4c0dcc4aed","cross_cats_sorted":[],"license":"","primary_cat":"math.AP","submitted_at":"2006-09-28T05:44:35Z","title_canon_sha256":"8745726a50bda53fd31eeebb31b88897966d377ddb204636bc1086457feeba71"},"schema_version":"1.0","source":{"id":"math/0609781","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0609781","created_at":"2026-05-18T01:08:49Z"},{"alias_kind":"arxiv_version","alias_value":"math/0609781v2","created_at":"2026-05-18T01:08:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0609781","created_at":"2026-05-18T01:08:49Z"},{"alias_kind":"pith_short_12","alias_value":"JTVZ533PGDL6","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"JTVZ533PGDL676HC","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"JTVZ533P","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:6e56568bda1a3443449a9c06227265953a11ec5af5c88063ea04351ef2abd8f8","target":"graph","created_at":"2026-05-18T01:08:49Z","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 2001, H. Koch and D. Tataru proved the existence of global in time solutions to the incompressible Navier-Stokes equations in ${\\mathbb{R}}^d$ for initial data small enough in $BMO^{-1}$. We show in this article that the Koch and Tataru solution has higher regularity. As a consequence, we get a decay estimate in time for any space derivative, and space analyticity of the solution. Also as an application of our regularity theorem, we prove a regularity result for self-similar solutions.","authors_text":"Gigliola Staffilani, Nata\\v{s}a Pavlovi\\'c, Pierre Germain","cross_cats":[],"headline":"","license":"","primary_cat":"math.AP","submitted_at":"2006-09-28T05:44:35Z","title":"Regularity of solutions to the Navier-Stokes equations evolving from small data in BMO^{-1}"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0609781","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:fae3374df279fc32ce507f53a0f9ad1396ec476d4c5ee8ea9599ce661bc31eb1","target":"record","created_at":"2026-05-18T01:08:49Z","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":"1f24977ca3f5bdca7879cac7e2fd463a768bdf0c1f8aef2af0007b4c0dcc4aed","cross_cats_sorted":[],"license":"","primary_cat":"math.AP","submitted_at":"2006-09-28T05:44:35Z","title_canon_sha256":"8745726a50bda53fd31eeebb31b88897966d377ddb204636bc1086457feeba71"},"schema_version":"1.0","source":{"id":"math/0609781","kind":"arxiv","version":2}},"canonical_sha256":"4ceb9eef6f30d7eff8e2383ebd08b5310fb786fc1119e3dd73312392c459070e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4ceb9eef6f30d7eff8e2383ebd08b5310fb786fc1119e3dd73312392c459070e","first_computed_at":"2026-05-18T01:08:49.672356Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:08:49.672356Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uLK1vzazFOHHv02CA34ImR5aYit+XCq3DE4kR7KtVc3L4Tu2Ojbrae4m3FkWIA7f/6Rcx3HwybFcL3oRECxDDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:08:49.672943Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0609781","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fae3374df279fc32ce507f53a0f9ad1396ec476d4c5ee8ea9599ce661bc31eb1","sha256:6e56568bda1a3443449a9c06227265953a11ec5af5c88063ea04351ef2abd8f8"],"state_sha256":"7f4c16d4a39e0a6788d0703a21acb07a44508d15392f21ff3ae3939891852101"}