{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:MADNSENY2FKD6O5WLX6MEGXFPB","short_pith_number":"pith:MADNSENY","schema_version":"1.0","canonical_sha256":"6006d911b8d1543f3bb65dfcc21ae578417f4898f12c594ac59b9bf4bcee1baf","source":{"kind":"arxiv","id":"1410.3186","version":1},"attestation_state":"computed","paper":{"title":"On the global regularity for the supercritical SQG equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Michele Coti Zelati, Vlad Vicol","submitted_at":"2014-10-13T04:21:48Z","abstract_excerpt":"We consider the initial value problem for the fractionally dissipative quasi-geostrophic equation \\[ \\partial_t \\theta + \\mathcal{R}^\\perp \\theta \\cdot \\nabla \\theta + \\Lambda^\\gamma \\theta = 0, \\qquad \\theta(\\cdot,0) =\\theta_0 \\] on $\\mathbb{T}^2 = [0,1]^2$, with $\\gamma \\in (0,1)$. The coefficient in front of the dissipative term $\\Lambda^\\gamma = (-\\Delta)^{\\gamma/2}$ is normalized to $1$. We show that given a smooth initial datum with $\\|\\theta_0\\|_{L^2}^{\\gamma/2} \\|\\theta_0\\|_{\\dot{H}^2}^{1-\\gamma/2}\\leq R$, where {\\em $R$ is arbitrarily large}, there exists $\\gamma_1 = \\gamma_1(R) \\in ("},"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":"1410.3186","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-10-13T04:21:48Z","cross_cats_sorted":[],"title_canon_sha256":"9e381c2675ace5fd34099f07df3d52df49e3e42539eb82bca82d820d354d358f","abstract_canon_sha256":"b9e36f8bd58dc144cf764e122045b2e45092b3278533f6494779e35f0c0125b0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:40:11.929104Z","signature_b64":"Glz4Pvn+DUCIFkd0w+CAubxGEQm+Pp4qNW+sPBNs1Lfnvx198sp+HWLa2OhBlUM8fZ8cZGMdtnBMjmhR8OEMCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6006d911b8d1543f3bb65dfcc21ae578417f4898f12c594ac59b9bf4bcee1baf","last_reissued_at":"2026-05-18T02:40:11.928661Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:40:11.928661Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the global regularity for the supercritical SQG equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Michele Coti Zelati, Vlad Vicol","submitted_at":"2014-10-13T04:21:48Z","abstract_excerpt":"We consider the initial value problem for the fractionally dissipative quasi-geostrophic equation \\[ \\partial_t \\theta + \\mathcal{R}^\\perp \\theta \\cdot \\nabla \\theta + \\Lambda^\\gamma \\theta = 0, \\qquad \\theta(\\cdot,0) =\\theta_0 \\] on $\\mathbb{T}^2 = [0,1]^2$, with $\\gamma \\in (0,1)$. The coefficient in front of the dissipative term $\\Lambda^\\gamma = (-\\Delta)^{\\gamma/2}$ is normalized to $1$. We show that given a smooth initial datum with $\\|\\theta_0\\|_{L^2}^{\\gamma/2} \\|\\theta_0\\|_{\\dot{H}^2}^{1-\\gamma/2}\\leq R$, where {\\em $R$ is arbitrarily large}, there exists $\\gamma_1 = \\gamma_1(R) \\in ("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.3186","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":"1410.3186","created_at":"2026-05-18T02:40:11.928712+00:00"},{"alias_kind":"arxiv_version","alias_value":"1410.3186v1","created_at":"2026-05-18T02:40:11.928712+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.3186","created_at":"2026-05-18T02:40:11.928712+00:00"},{"alias_kind":"pith_short_12","alias_value":"MADNSENY2FKD","created_at":"2026-05-18T12:28:38.356838+00:00"},{"alias_kind":"pith_short_16","alias_value":"MADNSENY2FKD6O5W","created_at":"2026-05-18T12:28:38.356838+00:00"},{"alias_kind":"pith_short_8","alias_value":"MADNSENY","created_at":"2026-05-18T12:28:38.356838+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/MADNSENY2FKD6O5WLX6MEGXFPB","json":"https://pith.science/pith/MADNSENY2FKD6O5WLX6MEGXFPB.json","graph_json":"https://pith.science/api/pith-number/MADNSENY2FKD6O5WLX6MEGXFPB/graph.json","events_json":"https://pith.science/api/pith-number/MADNSENY2FKD6O5WLX6MEGXFPB/events.json","paper":"https://pith.science/paper/MADNSENY"},"agent_actions":{"view_html":"https://pith.science/pith/MADNSENY2FKD6O5WLX6MEGXFPB","download_json":"https://pith.science/pith/MADNSENY2FKD6O5WLX6MEGXFPB.json","view_paper":"https://pith.science/paper/MADNSENY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1410.3186&json=true","fetch_graph":"https://pith.science/api/pith-number/MADNSENY2FKD6O5WLX6MEGXFPB/graph.json","fetch_events":"https://pith.science/api/pith-number/MADNSENY2FKD6O5WLX6MEGXFPB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MADNSENY2FKD6O5WLX6MEGXFPB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MADNSENY2FKD6O5WLX6MEGXFPB/action/storage_attestation","attest_author":"https://pith.science/pith/MADNSENY2FKD6O5WLX6MEGXFPB/action/author_attestation","sign_citation":"https://pith.science/pith/MADNSENY2FKD6O5WLX6MEGXFPB/action/citation_signature","submit_replication":"https://pith.science/pith/MADNSENY2FKD6O5WLX6MEGXFPB/action/replication_record"}},"created_at":"2026-05-18T02:40:11.928712+00:00","updated_at":"2026-05-18T02:40:11.928712+00:00"}