{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:FOEYIQOR766YE7TLHNJ34YLIGF","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":"a8877b53530e7d7af4c12e252c80391391a5695a71c8984a0df1bedd648eeaec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-28T02:41:28Z","title_canon_sha256":"30a035994a71562cca4ccb4c1cc087df3eef07660d7bbd706e1dbb3edb286a70"},"schema_version":"1.0","source":{"id":"1509.08177","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.08177","created_at":"2026-05-18T00:51:34Z"},{"alias_kind":"arxiv_version","alias_value":"1509.08177v2","created_at":"2026-05-18T00:51:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.08177","created_at":"2026-05-18T00:51:34Z"},{"alias_kind":"pith_short_12","alias_value":"FOEYIQOR766Y","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"FOEYIQOR766YE7TL","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"FOEYIQOR","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:d075a99b8444a09ae7746a970612fa77bf093066aa8a710c08c1d64b2b4afad4","target":"graph","created_at":"2026-05-18T00:51:34Z","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":"We rule out the existence of Leray's backward self-similar solutions to the Navier--Stokes equations with profiles in $L^{12/5}(\\R^3)$ or in the Marcinkiewicz space $L^{q,\\infty}(\\R^3)$ for $q\\in(12/5, 6)$. This follows from a more general result formulated in terms of Morrey spaces and the first order Riesz's potential.","authors_text":"Cristi Guevara, Nguyen Cong Phuc","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-28T02:41:28Z","title":"Leray's self-similar solutions to the Navier--Stokes equations with profiles in Marcinkiewicz and Morrey spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.08177","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:d0825f2820d079b71a69b9a251b6341733b1de9780bbb183ef9870f29b1ca8bd","target":"record","created_at":"2026-05-18T00:51:34Z","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":"a8877b53530e7d7af4c12e252c80391391a5695a71c8984a0df1bedd648eeaec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-28T02:41:28Z","title_canon_sha256":"30a035994a71562cca4ccb4c1cc087df3eef07660d7bbd706e1dbb3edb286a70"},"schema_version":"1.0","source":{"id":"1509.08177","kind":"arxiv","version":2}},"canonical_sha256":"2b898441d1ffbd827e6b3b53be61683162c233fd87b45849ec758e13099a5baf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2b898441d1ffbd827e6b3b53be61683162c233fd87b45849ec758e13099a5baf","first_computed_at":"2026-05-18T00:51:34.256697Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:34.256697Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7h+K3lJsJ7OCfvOLrJwOrdpP/dRl5WXfZqAK1GRdeKslcjU/2rdHlLLkQAPApXgM47CMjzoUNKgb1oZRqAnkCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:34.257215Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.08177","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d0825f2820d079b71a69b9a251b6341733b1de9780bbb183ef9870f29b1ca8bd","sha256:d075a99b8444a09ae7746a970612fa77bf093066aa8a710c08c1d64b2b4afad4"],"state_sha256":"3ccb99fc462e60741e8bdd4a3a982c4382477c6f0cdbd2a12e5cd0c4dd13d6b3"}