{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:MMT6WNXK4SPEGZYCCY2WINMMNY","short_pith_number":"pith:MMT6WNXK","schema_version":"1.0","canonical_sha256":"6327eb36eae49e436702163564358c6e06514f80f0238115e7e38d5e1d93f17a","source":{"kind":"arxiv","id":"2407.19366","version":1},"attestation_state":"computed","paper":{"title":"Stability of the Caffarelli-Kohn-Nirenberg inequality along Felli-Schneider curve: critical points at infinity","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Juncheng Wei, Yunze Wu","submitted_at":"2024-07-28T02:24:44Z","abstract_excerpt":"In this paper, we consider the following Caffarelli-Kohn-Nirenberg (CKN for short) inequality \\begin{eqnarray*} \\bigg(\\int_{{\\mathbb R}^d}|x|^{-b(p+1)}|u|^{p+1}dx\\bigg)^{\\frac{2}{p+1}}\\leq S_{a,b}\\int_{{\\mathbb R}^d}|x|^{-2a}|\\nabla u|^2dx, \\end{eqnarray*} where $u\\in D^{1,2}_{a}({\\mathbb R}^d)$, $d\\geq2$, $p=\\frac{d+2(1+a-b)}{d-2(1+a-b)}$ and \\begin{eqnarray}\\label{eq0003} \\left\\{\\aligned &a<b<a+1,\\quad d=2,\\\\ &a\\leq b<a+1,\\quad d\\geq3. \\endaligned \\right. \\end{eqnarray} Based on the ideas of \\cite{DSW2024,FP2024}, we develop a suitable strategy to derive the following sharp stability of the "},"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":"2407.19366","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.AP","submitted_at":"2024-07-28T02:24:44Z","cross_cats_sorted":[],"title_canon_sha256":"ca229d410ade7b54a4384390ecec627f71fe2ebeb401e6025f90ef039f0623b7","abstract_canon_sha256":"0a8a0187a13c137b1ade154b1fc607d08f962246d3452b4b52aeca80cc7643e5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:49:38.901221Z","signature_b64":"RvRiL+72ZXYVXTCIdhDfISHrbxoKEerMcMlw9mFwKG1imGURxrVsurF66394qZMU+UoxndgNJlLIiPw+tK9XCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6327eb36eae49e436702163564358c6e06514f80f0238115e7e38d5e1d93f17a","last_reissued_at":"2026-07-05T08:49:38.900872Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:49:38.900872Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stability of the Caffarelli-Kohn-Nirenberg inequality along Felli-Schneider curve: critical points at infinity","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Juncheng Wei, Yunze Wu","submitted_at":"2024-07-28T02:24:44Z","abstract_excerpt":"In this paper, we consider the following Caffarelli-Kohn-Nirenberg (CKN for short) inequality \\begin{eqnarray*} \\bigg(\\int_{{\\mathbb R}^d}|x|^{-b(p+1)}|u|^{p+1}dx\\bigg)^{\\frac{2}{p+1}}\\leq S_{a,b}\\int_{{\\mathbb R}^d}|x|^{-2a}|\\nabla u|^2dx, \\end{eqnarray*} where $u\\in D^{1,2}_{a}({\\mathbb R}^d)$, $d\\geq2$, $p=\\frac{d+2(1+a-b)}{d-2(1+a-b)}$ and \\begin{eqnarray}\\label{eq0003} \\left\\{\\aligned &a<b<a+1,\\quad d=2,\\\\ &a\\leq b<a+1,\\quad d\\geq3. \\endaligned \\right. \\end{eqnarray} Based on the ideas of \\cite{DSW2024,FP2024}, we develop a suitable strategy to derive the following sharp stability of the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.19366","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/2407.19366/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":"2407.19366","created_at":"2026-07-05T08:49:38.900935+00:00"},{"alias_kind":"arxiv_version","alias_value":"2407.19366v1","created_at":"2026-07-05T08:49:38.900935+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.19366","created_at":"2026-07-05T08:49:38.900935+00:00"},{"alias_kind":"pith_short_12","alias_value":"MMT6WNXK4SPE","created_at":"2026-07-05T08:49:38.900935+00:00"},{"alias_kind":"pith_short_16","alias_value":"MMT6WNXK4SPEGZYC","created_at":"2026-07-05T08:49:38.900935+00:00"},{"alias_kind":"pith_short_8","alias_value":"MMT6WNXK","created_at":"2026-07-05T08:49:38.900935+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2506.07602","citing_title":"Sharp quantitative stability estimates for the Brezis-Nirenberg problem","ref_index":58,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MMT6WNXK4SPEGZYCCY2WINMMNY","json":"https://pith.science/pith/MMT6WNXK4SPEGZYCCY2WINMMNY.json","graph_json":"https://pith.science/api/pith-number/MMT6WNXK4SPEGZYCCY2WINMMNY/graph.json","events_json":"https://pith.science/api/pith-number/MMT6WNXK4SPEGZYCCY2WINMMNY/events.json","paper":"https://pith.science/paper/MMT6WNXK"},"agent_actions":{"view_html":"https://pith.science/pith/MMT6WNXK4SPEGZYCCY2WINMMNY","download_json":"https://pith.science/pith/MMT6WNXK4SPEGZYCCY2WINMMNY.json","view_paper":"https://pith.science/paper/MMT6WNXK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2407.19366&json=true","fetch_graph":"https://pith.science/api/pith-number/MMT6WNXK4SPEGZYCCY2WINMMNY/graph.json","fetch_events":"https://pith.science/api/pith-number/MMT6WNXK4SPEGZYCCY2WINMMNY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MMT6WNXK4SPEGZYCCY2WINMMNY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MMT6WNXK4SPEGZYCCY2WINMMNY/action/storage_attestation","attest_author":"https://pith.science/pith/MMT6WNXK4SPEGZYCCY2WINMMNY/action/author_attestation","sign_citation":"https://pith.science/pith/MMT6WNXK4SPEGZYCCY2WINMMNY/action/citation_signature","submit_replication":"https://pith.science/pith/MMT6WNXK4SPEGZYCCY2WINMMNY/action/replication_record"}},"created_at":"2026-07-05T08:49:38.900935+00:00","updated_at":"2026-07-05T08:49:38.900935+00:00"}