{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:PSSZNDC3CTLOFEAOXOCOBTZXVR","short_pith_number":"pith:PSSZNDC3","schema_version":"1.0","canonical_sha256":"7ca5968c5b14d6e2900ebb84e0cf37ac50dd25ead8f4cd2f34dfc4bfe2e72486","source":{"kind":"arxiv","id":"2310.07083","version":1},"attestation_state":"computed","paper":{"title":"$L^{p}$-Caffarelli-Kohn-Nirenberg inequalities and their stabilities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Anh Xuan Do, Guozhen Lu, Joshua Flynn, Nguyen Lam","submitted_at":"2023-10-10T23:58:49Z","abstract_excerpt":"We establish a general identity (Theorem 1.2) that implies both the $L^{p}$-Hardy identities and the $L^{p}$-Caffarelli-Kohn-Nirenberg identities (Theorems 1.3 and 1.4) and $L^{p}$-Hardy inequalities and the $L^{p}$-Caffarelli-Kohn-Nirenberg inequalities (Theorems 1.5 and 1.6)). Weighted $L^{p}$-Caffarelli-Kohn-Nirenberg inequalities with nonradial weights are also obtained. (Theorem 1.7). Our results provide simple interpretations to the sharp constants, as well as the existence and non-existence of the optimizers, of several $L^{p}$-Hardy and $L^{p}% $-Caffarelli-Kohn-Nirenberg inequalities."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2310.07083","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-10-10T23:58:49Z","cross_cats_sorted":[],"title_canon_sha256":"a105d044fcce7089302fdc7d6f73dcc0516869f2c0370e0457cf5b4ffdaec25b","abstract_canon_sha256":"b43c87df791c8034069c77c8811f744e3005abb7b4dc8c74a37d1c00ebefeed3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:59:40.324491Z","signature_b64":"k0206zwqeIZxN7qJlt4GvRjYQ5Avf5iT9axNpOQI3tQ76+NCHchfB7i5JYO7y4TQe+nZ5pOfkRHwQBqQ96JPBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7ca5968c5b14d6e2900ebb84e0cf37ac50dd25ead8f4cd2f34dfc4bfe2e72486","last_reissued_at":"2026-07-05T06:59:40.324016Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:59:40.324016Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$L^{p}$-Caffarelli-Kohn-Nirenberg inequalities and their stabilities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Anh Xuan Do, Guozhen Lu, Joshua Flynn, Nguyen Lam","submitted_at":"2023-10-10T23:58:49Z","abstract_excerpt":"We establish a general identity (Theorem 1.2) that implies both the $L^{p}$-Hardy identities and the $L^{p}$-Caffarelli-Kohn-Nirenberg identities (Theorems 1.3 and 1.4) and $L^{p}$-Hardy inequalities and the $L^{p}$-Caffarelli-Kohn-Nirenberg inequalities (Theorems 1.5 and 1.6)). Weighted $L^{p}$-Caffarelli-Kohn-Nirenberg inequalities with nonradial weights are also obtained. (Theorem 1.7). Our results provide simple interpretations to the sharp constants, as well as the existence and non-existence of the optimizers, of several $L^{p}$-Hardy and $L^{p}% $-Caffarelli-Kohn-Nirenberg inequalities."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.07083","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/2310.07083/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":"2310.07083","created_at":"2026-07-05T06:59:40.324074+00:00"},{"alias_kind":"arxiv_version","alias_value":"2310.07083v1","created_at":"2026-07-05T06:59:40.324074+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2310.07083","created_at":"2026-07-05T06:59:40.324074+00:00"},{"alias_kind":"pith_short_12","alias_value":"PSSZNDC3CTLO","created_at":"2026-07-05T06:59:40.324074+00:00"},{"alias_kind":"pith_short_16","alias_value":"PSSZNDC3CTLOFEAO","created_at":"2026-07-05T06:59:40.324074+00:00"},{"alias_kind":"pith_short_8","alias_value":"PSSZNDC3","created_at":"2026-07-05T06:59:40.324074+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.08939","citing_title":"Caffarelli-Kohn-Nirenberg and Weighted Gaussian Poincar\\'e Inequalities: a complete characterization of sharp $L^2$ stability and $L^p$ extensions","ref_index":28,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PSSZNDC3CTLOFEAOXOCOBTZXVR","json":"https://pith.science/pith/PSSZNDC3CTLOFEAOXOCOBTZXVR.json","graph_json":"https://pith.science/api/pith-number/PSSZNDC3CTLOFEAOXOCOBTZXVR/graph.json","events_json":"https://pith.science/api/pith-number/PSSZNDC3CTLOFEAOXOCOBTZXVR/events.json","paper":"https://pith.science/paper/PSSZNDC3"},"agent_actions":{"view_html":"https://pith.science/pith/PSSZNDC3CTLOFEAOXOCOBTZXVR","download_json":"https://pith.science/pith/PSSZNDC3CTLOFEAOXOCOBTZXVR.json","view_paper":"https://pith.science/paper/PSSZNDC3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2310.07083&json=true","fetch_graph":"https://pith.science/api/pith-number/PSSZNDC3CTLOFEAOXOCOBTZXVR/graph.json","fetch_events":"https://pith.science/api/pith-number/PSSZNDC3CTLOFEAOXOCOBTZXVR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PSSZNDC3CTLOFEAOXOCOBTZXVR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PSSZNDC3CTLOFEAOXOCOBTZXVR/action/storage_attestation","attest_author":"https://pith.science/pith/PSSZNDC3CTLOFEAOXOCOBTZXVR/action/author_attestation","sign_citation":"https://pith.science/pith/PSSZNDC3CTLOFEAOXOCOBTZXVR/action/citation_signature","submit_replication":"https://pith.science/pith/PSSZNDC3CTLOFEAOXOCOBTZXVR/action/replication_record"}},"created_at":"2026-07-05T06:59:40.324074+00:00","updated_at":"2026-07-05T06:59:40.324074+00:00"}