{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:GX4WHKZOBMAAVF7XFWA2OZPSVS","short_pith_number":"pith:GX4WHKZO","schema_version":"1.0","canonical_sha256":"35f963ab2e0b000a97f72d81a765f2acaeb64a02d481c46d34617b2599ad53f3","source":{"kind":"arxiv","id":"1511.08890","version":3},"attestation_state":"computed","paper":{"title":"Stability properties of the regular set for the Navier--Stokes equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Piero D'Ancona, Renato Luc\\`a","submitted_at":"2015-11-28T11:03:51Z","abstract_excerpt":"We investigate the size of the regular set for small perturbations of some classes of strong large solutions to the Navier--Stokes equation. We consider perturbations of the data which are small in suitable weighted $L^{2}$ spaces but can be arbitrarily large in any translation invariant critical Banach space. We give similar results in the small data setting."},"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":"1511.08890","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-11-28T11:03:51Z","cross_cats_sorted":[],"title_canon_sha256":"fcbeff224fe0929a8bc84d371ba84dbf0c6c8a02720a8e3370a8c9ff1f389df0","abstract_canon_sha256":"1608c4c108bd83fdfa7bdde981085489799b0733c613385fe31fafd1399531fb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:18.975159Z","signature_b64":"Hqgu5RqsUjWSrtPEsPIQz9Nzcp1mW/zcs1lcoLSl7nVlsRAGtbSzNQGUFz9tO2hT8Zh1P9mIXcTFNJxMt9ejBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"35f963ab2e0b000a97f72d81a765f2acaeb64a02d481c46d34617b2599ad53f3","last_reissued_at":"2026-05-18T00:42:18.974463Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:18.974463Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stability properties of the regular set for the Navier--Stokes equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Piero D'Ancona, Renato Luc\\`a","submitted_at":"2015-11-28T11:03:51Z","abstract_excerpt":"We investigate the size of the regular set for small perturbations of some classes of strong large solutions to the Navier--Stokes equation. We consider perturbations of the data which are small in suitable weighted $L^{2}$ spaces but can be arbitrarily large in any translation invariant critical Banach space. We give similar results in the small data setting."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.08890","kind":"arxiv","version":3},"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":"1511.08890","created_at":"2026-05-18T00:42:18.974591+00:00"},{"alias_kind":"arxiv_version","alias_value":"1511.08890v3","created_at":"2026-05-18T00:42:18.974591+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.08890","created_at":"2026-05-18T00:42:18.974591+00:00"},{"alias_kind":"pith_short_12","alias_value":"GX4WHKZOBMAA","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_16","alias_value":"GX4WHKZOBMAAVF7X","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_8","alias_value":"GX4WHKZO","created_at":"2026-05-18T12:29:22.688609+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/GX4WHKZOBMAAVF7XFWA2OZPSVS","json":"https://pith.science/pith/GX4WHKZOBMAAVF7XFWA2OZPSVS.json","graph_json":"https://pith.science/api/pith-number/GX4WHKZOBMAAVF7XFWA2OZPSVS/graph.json","events_json":"https://pith.science/api/pith-number/GX4WHKZOBMAAVF7XFWA2OZPSVS/events.json","paper":"https://pith.science/paper/GX4WHKZO"},"agent_actions":{"view_html":"https://pith.science/pith/GX4WHKZOBMAAVF7XFWA2OZPSVS","download_json":"https://pith.science/pith/GX4WHKZOBMAAVF7XFWA2OZPSVS.json","view_paper":"https://pith.science/paper/GX4WHKZO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1511.08890&json=true","fetch_graph":"https://pith.science/api/pith-number/GX4WHKZOBMAAVF7XFWA2OZPSVS/graph.json","fetch_events":"https://pith.science/api/pith-number/GX4WHKZOBMAAVF7XFWA2OZPSVS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GX4WHKZOBMAAVF7XFWA2OZPSVS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GX4WHKZOBMAAVF7XFWA2OZPSVS/action/storage_attestation","attest_author":"https://pith.science/pith/GX4WHKZOBMAAVF7XFWA2OZPSVS/action/author_attestation","sign_citation":"https://pith.science/pith/GX4WHKZOBMAAVF7XFWA2OZPSVS/action/citation_signature","submit_replication":"https://pith.science/pith/GX4WHKZOBMAAVF7XFWA2OZPSVS/action/replication_record"}},"created_at":"2026-05-18T00:42:18.974591+00:00","updated_at":"2026-05-18T00:42:18.974591+00:00"}