{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:2HZHAMACQ6D6LDAPVJPLKMNMTD","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":"fc45e7cc2e42e4b5a34627dcd52b07cbc604d82b69250992ccd4819a0e5327e4","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2009-04-24T19:39:22Z","title_canon_sha256":"c1b6bbe6497d01eba8e20a0a680c78a50278c40cc18095693884379737dc3fee"},"schema_version":"1.0","source":{"id":"0904.3928","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0904.3928","created_at":"2026-05-18T04:32:56Z"},{"alias_kind":"arxiv_version","alias_value":"0904.3928v2","created_at":"2026-05-18T04:32:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0904.3928","created_at":"2026-05-18T04:32:56Z"},{"alias_kind":"pith_short_12","alias_value":"2HZHAMACQ6D6","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"2HZHAMACQ6D6LDAP","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"2HZHAMAC","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:77bda5e9e0b89465a658b93044551ade96c3fbd970ab9e87972e383992678432","target":"graph","created_at":"2026-05-18T04:32:56Z","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 address the existence, the asymptotic behavior and stability in $L^p$ and $L^{p,\\infty}$, 3/2.","authors_text":"Clayton Bjorland, Dragos Iftimie (ICJ), Lorenzo Brandolese (ICJ), Maria Elena Schonbek","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2009-04-24T19:39:22Z","title":"L^p solutions of the steady-state Navier-Stokes equations with rough external forces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.3928","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:c5d9179417f1a53798524e4d85c919d98cc470280c46be5d48a025f546ac4a20","target":"record","created_at":"2026-05-18T04:32:56Z","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":"fc45e7cc2e42e4b5a34627dcd52b07cbc604d82b69250992ccd4819a0e5327e4","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2009-04-24T19:39:22Z","title_canon_sha256":"c1b6bbe6497d01eba8e20a0a680c78a50278c40cc18095693884379737dc3fee"},"schema_version":"1.0","source":{"id":"0904.3928","kind":"arxiv","version":2}},"canonical_sha256":"d1f27030028787e58c0faa5eb531ac98fd85ac4844e74a4549e84bf8d1a82e19","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d1f27030028787e58c0faa5eb531ac98fd85ac4844e74a4549e84bf8d1a82e19","first_computed_at":"2026-05-18T04:32:56.069822Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:32:56.069822Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZfneqTictdMb2OVS5FwxUNmaGhw7mWuI6dDFqdmQsOdaDT7ik38UNJ5KuzOIw6bosZ30AyaEvVyBxpB/wtgsDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:32:56.070740Z","signed_message":"canonical_sha256_bytes"},"source_id":"0904.3928","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c5d9179417f1a53798524e4d85c919d98cc470280c46be5d48a025f546ac4a20","sha256:77bda5e9e0b89465a658b93044551ade96c3fbd970ab9e87972e383992678432"],"state_sha256":"35a96108be2746a4b7f27acc8ceb575388984abcac554e190938fbb918d1a9ab"}