{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:GARXAVGFABTRFNYQ66GO3EVFBP","short_pith_number":"pith:GARXAVGF","schema_version":"1.0","canonical_sha256":"30237054c5006712b710f78ced92a50bed892ba355e64072345d858048379506","source":{"kind":"arxiv","id":"2502.06357","version":2},"attestation_state":"computed","paper":{"title":"Strong ill-posedness and non-existence in Sobolev spaces for generalized-SQG","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Diego C\\'ordoba, Jos\\'e Lucas-Manch\\'on, Luis Mart\\'inez-Zoroa","submitted_at":"2025-02-10T11:17:56Z","abstract_excerpt":"The general surface quasi-geostrophic equation is the scalar transport equation defined by \\begin{equation*}\n  \\frac{\\partial \\theta}{\\partial t}+v^\\gamma_1 \\frac{\\partial \\theta}{\\partial x_1}+v^\\gamma_2 \\frac{\\partial \\theta}{\\partial x_2} =0 ,\n  \\end{equation*} where the velocity comes defined by\n  \\begin{equation*}\n  v^\\gamma=\\nabla^{\\perp} \\psi_\\gamma=\\left(\\partial_{2} \\psi_\\gamma,-\\partial_{1} \\psi_\\gamma \\right), \\quad \\psi_\\gamma=-\\Lambda^{-1+\\gamma} \\theta,\n  \\end{equation*} and $\\theta(\\cdot,0)=\\theta_0(\\cdot)$ is the initial condition. We consider the parameter $\\gamma \\in (-1,1)$ "},"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":"2502.06357","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-02-10T11:17:56Z","cross_cats_sorted":[],"title_canon_sha256":"60850a71bb642ca90993578871816b3551f11610a65daa2618d90ab33b2658ed","abstract_canon_sha256":"7f2e505bc8f284ab08ce5e47a1c7ec38a1e45570b01f62026e11db9b553e12f7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:36:27.912129Z","signature_b64":"AmAczPoKaaF7Kk+u8xJ7yurHL7k/tvICk8qTntOU/x7vDz6VxXIGabaJ/mAabL1sIl6weOkzYh0qD7ZqROSqDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"30237054c5006712b710f78ced92a50bed892ba355e64072345d858048379506","last_reissued_at":"2026-07-05T11:36:27.911638Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:36:27.911638Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Strong ill-posedness and non-existence in Sobolev spaces for generalized-SQG","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Diego C\\'ordoba, Jos\\'e Lucas-Manch\\'on, Luis Mart\\'inez-Zoroa","submitted_at":"2025-02-10T11:17:56Z","abstract_excerpt":"The general surface quasi-geostrophic equation is the scalar transport equation defined by \\begin{equation*}\n  \\frac{\\partial \\theta}{\\partial t}+v^\\gamma_1 \\frac{\\partial \\theta}{\\partial x_1}+v^\\gamma_2 \\frac{\\partial \\theta}{\\partial x_2} =0 ,\n  \\end{equation*} where the velocity comes defined by\n  \\begin{equation*}\n  v^\\gamma=\\nabla^{\\perp} \\psi_\\gamma=\\left(\\partial_{2} \\psi_\\gamma,-\\partial_{1} \\psi_\\gamma \\right), \\quad \\psi_\\gamma=-\\Lambda^{-1+\\gamma} \\theta,\n  \\end{equation*} and $\\theta(\\cdot,0)=\\theta_0(\\cdot)$ is the initial condition. We consider the parameter $\\gamma \\in (-1,1)$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.06357","kind":"arxiv","version":2},"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/2502.06357/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":"2502.06357","created_at":"2026-07-05T11:36:27.911694+00:00"},{"alias_kind":"arxiv_version","alias_value":"2502.06357v2","created_at":"2026-07-05T11:36:27.911694+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.06357","created_at":"2026-07-05T11:36:27.911694+00:00"},{"alias_kind":"pith_short_12","alias_value":"GARXAVGFABTR","created_at":"2026-07-05T11:36:27.911694+00:00"},{"alias_kind":"pith_short_16","alias_value":"GARXAVGFABTRFNYQ","created_at":"2026-07-05T11:36:27.911694+00:00"},{"alias_kind":"pith_short_8","alias_value":"GARXAVGF","created_at":"2026-07-05T11:36:27.911694+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2502.10274","citing_title":"Unstable vortices, sharp non-uniqueness with forcing, and global smooth solutions for the SQG equation","ref_index":44,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GARXAVGFABTRFNYQ66GO3EVFBP","json":"https://pith.science/pith/GARXAVGFABTRFNYQ66GO3EVFBP.json","graph_json":"https://pith.science/api/pith-number/GARXAVGFABTRFNYQ66GO3EVFBP/graph.json","events_json":"https://pith.science/api/pith-number/GARXAVGFABTRFNYQ66GO3EVFBP/events.json","paper":"https://pith.science/paper/GARXAVGF"},"agent_actions":{"view_html":"https://pith.science/pith/GARXAVGFABTRFNYQ66GO3EVFBP","download_json":"https://pith.science/pith/GARXAVGFABTRFNYQ66GO3EVFBP.json","view_paper":"https://pith.science/paper/GARXAVGF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2502.06357&json=true","fetch_graph":"https://pith.science/api/pith-number/GARXAVGFABTRFNYQ66GO3EVFBP/graph.json","fetch_events":"https://pith.science/api/pith-number/GARXAVGFABTRFNYQ66GO3EVFBP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GARXAVGFABTRFNYQ66GO3EVFBP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GARXAVGFABTRFNYQ66GO3EVFBP/action/storage_attestation","attest_author":"https://pith.science/pith/GARXAVGFABTRFNYQ66GO3EVFBP/action/author_attestation","sign_citation":"https://pith.science/pith/GARXAVGFABTRFNYQ66GO3EVFBP/action/citation_signature","submit_replication":"https://pith.science/pith/GARXAVGFABTRFNYQ66GO3EVFBP/action/replication_record"}},"created_at":"2026-07-05T11:36:27.911694+00:00","updated_at":"2026-07-05T11:36:27.911694+00:00"}