{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:INAYV2M33GK42YQ3DSPDA5PYDL","short_pith_number":"pith:INAYV2M3","schema_version":"1.0","canonical_sha256":"43418ae99bd995cd621b1c9e3075f81ac5f7b7058ab1848af2264aa63b7490af","source":{"kind":"arxiv","id":"2411.10823","version":1},"attestation_state":"computed","paper":{"title":"A note on the development of singularities on solutions to the Navier-Stokes equations under super critical forcing terms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hugo Beir\\~ao da Veiga, Jiaqi Yang","submitted_at":"2024-11-16T15:25:36Z","abstract_excerpt":"Recently Qi S. Zhang provides examples of solutions to the Navier-Stokes equations which, under suitable hypothesis, blow up in finite time. He considers axially symmetric solutions in a cylinder $D\\,$ under appropriate boundary conditions and under the effect of super critical external forces $f\\,.$ The loss of boundedness for the velocity field, as $t\\rightarrow T\\,,$ is the basic case of blow up. However a more general situation is considered below, as explained in the preamble.\\par In his main result Zhang exhibits, for each $q<\\infty\\,,$ a blow up solution with an external force $f\\in L^q"},"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":"2411.10823","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-11-16T15:25:36Z","cross_cats_sorted":[],"title_canon_sha256":"254a657580b52c2e8cf87382d37e7fa1cb5c2a2d395a2506c857e3cf28edb1cc","abstract_canon_sha256":"8f0d0baa53e14a2b35a4f5a6f0c0bf4d2dae6fc7effa3d84af5a3f42b48ceb31"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:36:22.820464Z","signature_b64":"NDldgA3GS4t8k+7l6vLvKJ0xYyCIAnqAC1T7YEzYeiHA59Bfn+xja/VzAqf8+Qr+W9BD19PeKaMGU/d53r6vCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"43418ae99bd995cd621b1c9e3075f81ac5f7b7058ab1848af2264aa63b7490af","last_reissued_at":"2026-07-05T09:36:22.820055Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:36:22.820055Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A note on the development of singularities on solutions to the Navier-Stokes equations under super critical forcing terms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hugo Beir\\~ao da Veiga, Jiaqi Yang","submitted_at":"2024-11-16T15:25:36Z","abstract_excerpt":"Recently Qi S. Zhang provides examples of solutions to the Navier-Stokes equations which, under suitable hypothesis, blow up in finite time. He considers axially symmetric solutions in a cylinder $D\\,$ under appropriate boundary conditions and under the effect of super critical external forces $f\\,.$ The loss of boundedness for the velocity field, as $t\\rightarrow T\\,,$ is the basic case of blow up. However a more general situation is considered below, as explained in the preamble.\\par In his main result Zhang exhibits, for each $q<\\infty\\,,$ a blow up solution with an external force $f\\in L^q"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.10823","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.10823/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2411.10823","created_at":"2026-07-05T09:36:22.820112+00:00"},{"alias_kind":"arxiv_version","alias_value":"2411.10823v1","created_at":"2026-07-05T09:36:22.820112+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.10823","created_at":"2026-07-05T09:36:22.820112+00:00"},{"alias_kind":"pith_short_12","alias_value":"INAYV2M33GK4","created_at":"2026-07-05T09:36:22.820112+00:00"},{"alias_kind":"pith_short_16","alias_value":"INAYV2M33GK42YQ3","created_at":"2026-07-05T09:36:22.820112+00:00"},{"alias_kind":"pith_short_8","alias_value":"INAYV2M3","created_at":"2026-07-05T09:36:22.820112+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/INAYV2M33GK42YQ3DSPDA5PYDL","json":"https://pith.science/pith/INAYV2M33GK42YQ3DSPDA5PYDL.json","graph_json":"https://pith.science/api/pith-number/INAYV2M33GK42YQ3DSPDA5PYDL/graph.json","events_json":"https://pith.science/api/pith-number/INAYV2M33GK42YQ3DSPDA5PYDL/events.json","paper":"https://pith.science/paper/INAYV2M3"},"agent_actions":{"view_html":"https://pith.science/pith/INAYV2M33GK42YQ3DSPDA5PYDL","download_json":"https://pith.science/pith/INAYV2M33GK42YQ3DSPDA5PYDL.json","view_paper":"https://pith.science/paper/INAYV2M3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2411.10823&json=true","fetch_graph":"https://pith.science/api/pith-number/INAYV2M33GK42YQ3DSPDA5PYDL/graph.json","fetch_events":"https://pith.science/api/pith-number/INAYV2M33GK42YQ3DSPDA5PYDL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/INAYV2M33GK42YQ3DSPDA5PYDL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/INAYV2M33GK42YQ3DSPDA5PYDL/action/storage_attestation","attest_author":"https://pith.science/pith/INAYV2M33GK42YQ3DSPDA5PYDL/action/author_attestation","sign_citation":"https://pith.science/pith/INAYV2M33GK42YQ3DSPDA5PYDL/action/citation_signature","submit_replication":"https://pith.science/pith/INAYV2M33GK42YQ3DSPDA5PYDL/action/replication_record"}},"created_at":"2026-07-05T09:36:22.820112+00:00","updated_at":"2026-07-05T09:36:22.820112+00:00"}