{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2001:YNL4W34JPNBTRDP63DKI6HX6UR","short_pith_number":"pith:YNL4W34J","schema_version":"1.0","canonical_sha256":"c357cb6f897b43388dfed8d48f1efea45d557c9020a155b358d6783d46f29444","source":{"kind":"arxiv","id":"math/0104199","version":1},"attestation_state":"computed","paper":{"title":"A cheap Caffarelli-Kohn-Nirenberg inequality for Navier-Stokes equations with hyper-dissipation","license":"","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"Nata\\v{s}a Pavlovi\\'c, Nets Hawk Katz","submitted_at":"2001-04-19T18:37:33Z","abstract_excerpt":"We prove that for the Navier Stokes equation with dissipation $(-\\Delta)^{\\alpha}$, where $1<\\alpha<{5/4}$, and smooth initial data, the Hausdorff dimension of the singular set at time of first blow up is at most $5-4\\alpha$. This unifies two directions from which one might approach the Clay prize problem."},"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":"math/0104199","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AP","submitted_at":"2001-04-19T18:37:33Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"ec94abab9c55b6258aed30b9b89e2b13bc7f554baac6f79ebf282fe132a35228","abstract_canon_sha256":"325a8ff81d10914896e718f0c1fcabfa2498229218f06c53184337fd4855a50e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:07.851725Z","signature_b64":"ufV4Zg4bkj7tHmo55NlLzaUM0hMbVcrungghrbMoLGhHrDaob9W9upRFPSfCiLfO0WJeHvAb/rglP0LVNi1xBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c357cb6f897b43388dfed8d48f1efea45d557c9020a155b358d6783d46f29444","last_reissued_at":"2026-05-18T01:09:07.851265Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:07.851265Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A cheap Caffarelli-Kohn-Nirenberg inequality for Navier-Stokes equations with hyper-dissipation","license":"","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"Nata\\v{s}a Pavlovi\\'c, Nets Hawk Katz","submitted_at":"2001-04-19T18:37:33Z","abstract_excerpt":"We prove that for the Navier Stokes equation with dissipation $(-\\Delta)^{\\alpha}$, where $1<\\alpha<{5/4}$, and smooth initial data, the Hausdorff dimension of the singular set at time of first blow up is at most $5-4\\alpha$. This unifies two directions from which one might approach the Clay prize problem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0104199","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":""},"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":"math/0104199","created_at":"2026-05-18T01:09:07.851336+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0104199v1","created_at":"2026-05-18T01:09:07.851336+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0104199","created_at":"2026-05-18T01:09:07.851336+00:00"},{"alias_kind":"pith_short_12","alias_value":"YNL4W34JPNBT","created_at":"2026-05-18T12:25:50.845339+00:00"},{"alias_kind":"pith_short_16","alias_value":"YNL4W34JPNBTRDP6","created_at":"2026-05-18T12:25:50.845339+00:00"},{"alias_kind":"pith_short_8","alias_value":"YNL4W34J","created_at":"2026-05-18T12:25:50.845339+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/YNL4W34JPNBTRDP63DKI6HX6UR","json":"https://pith.science/pith/YNL4W34JPNBTRDP63DKI6HX6UR.json","graph_json":"https://pith.science/api/pith-number/YNL4W34JPNBTRDP63DKI6HX6UR/graph.json","events_json":"https://pith.science/api/pith-number/YNL4W34JPNBTRDP63DKI6HX6UR/events.json","paper":"https://pith.science/paper/YNL4W34J"},"agent_actions":{"view_html":"https://pith.science/pith/YNL4W34JPNBTRDP63DKI6HX6UR","download_json":"https://pith.science/pith/YNL4W34JPNBTRDP63DKI6HX6UR.json","view_paper":"https://pith.science/paper/YNL4W34J","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0104199&json=true","fetch_graph":"https://pith.science/api/pith-number/YNL4W34JPNBTRDP63DKI6HX6UR/graph.json","fetch_events":"https://pith.science/api/pith-number/YNL4W34JPNBTRDP63DKI6HX6UR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YNL4W34JPNBTRDP63DKI6HX6UR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YNL4W34JPNBTRDP63DKI6HX6UR/action/storage_attestation","attest_author":"https://pith.science/pith/YNL4W34JPNBTRDP63DKI6HX6UR/action/author_attestation","sign_citation":"https://pith.science/pith/YNL4W34JPNBTRDP63DKI6HX6UR/action/citation_signature","submit_replication":"https://pith.science/pith/YNL4W34JPNBTRDP63DKI6HX6UR/action/replication_record"}},"created_at":"2026-05-18T01:09:07.851336+00:00","updated_at":"2026-05-18T01:09:07.851336+00:00"}