{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:BT4O23ZHSAJZBQDRZIDN45R7EU","short_pith_number":"pith:BT4O23ZH","schema_version":"1.0","canonical_sha256":"0cf8ed6f27901390c071ca06de763f253daa0f8ce586cd2efc88db2c649047eb","source":{"kind":"arxiv","id":"2608.09034","version":1},"attestation_state":"computed","paper":{"title":"Optimal Stability Bounds, Minimizers, and Critical Points for a Critical Nonlocal Sobolev Inequality on the Heisenberg Group","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Wenjing Chen, Zexi Wang","submitted_at":"2026-08-10T02:36:40Z","abstract_excerpt":"We investigate the optimal Bianchi-Egnell-type quantitative stability constant for the critical nonlocal Sobolev inequality on the Heisenberg group $\\mathbb{H}^{n}$, \\begin{equation}\\label{nS}\n  S_{HL}(Q,\\mu)\\left(\\int_{\\mathbb{H}^{n}}\\int_{\\mathbb{H}^{n}}\n  \\frac{|u(\\xi)|^{Q^{\\ast}_{\\mu}}|u(\\eta)|^{Q^{\\ast}_{\\mu}}}\n  {|\\eta^{-1}\\xi|^{\\mu}}\\,d\\xi d\\eta\\right)^{\\frac{1}{Q^{\\ast}_{\\mu}}}\n  \\leq \\int_{\\mathbb{H}^{n}}|\\nabla_{\\mathbb{H}}u|^{2}d\\xi,\n  \\qquad u\\in S^{1,2}(\\mathbb{H}^{n}), \\end{equation} where $Q=2n+2$, $n\\geq1$, $0<\\mu<Q$, and $Q^{\\ast}_{\\mu}=(2Q-\\mu)/(Q-2)$. Let $\\mathfrak{M}$ deno"},"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":"2608.09034","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-08-10T02:36:40Z","cross_cats_sorted":[],"title_canon_sha256":"198bca0c3a9d10f60d0e00f905ba694fc0b0fd8d382e76167e756492d47bba5a","abstract_canon_sha256":"bfbce52dca71e63ba68a66816f536aff2286d6cf12e03ab87ac6b3fc441897ab"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-11T02:21:38.923500Z","signature_b64":"5DRMN/UPFl1xZMO1UAEP88KQqTBvrIlV86HIf6SlVruoNIcJDJ7OA0EX2C851mcNh3B5qEtU9wd2VrckRE9VDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0cf8ed6f27901390c071ca06de763f253daa0f8ce586cd2efc88db2c649047eb","last_reissued_at":"2026-08-11T02:21:38.921040Z","signature_status":"signed_v1","first_computed_at":"2026-08-11T02:21:38.921040Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Optimal Stability Bounds, Minimizers, and Critical Points for a Critical Nonlocal Sobolev Inequality on the Heisenberg Group","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Wenjing Chen, Zexi Wang","submitted_at":"2026-08-10T02:36:40Z","abstract_excerpt":"We investigate the optimal Bianchi-Egnell-type quantitative stability constant for the critical nonlocal Sobolev inequality on the Heisenberg group $\\mathbb{H}^{n}$, \\begin{equation}\\label{nS}\n  S_{HL}(Q,\\mu)\\left(\\int_{\\mathbb{H}^{n}}\\int_{\\mathbb{H}^{n}}\n  \\frac{|u(\\xi)|^{Q^{\\ast}_{\\mu}}|u(\\eta)|^{Q^{\\ast}_{\\mu}}}\n  {|\\eta^{-1}\\xi|^{\\mu}}\\,d\\xi d\\eta\\right)^{\\frac{1}{Q^{\\ast}_{\\mu}}}\n  \\leq \\int_{\\mathbb{H}^{n}}|\\nabla_{\\mathbb{H}}u|^{2}d\\xi,\n  \\qquad u\\in S^{1,2}(\\mathbb{H}^{n}), \\end{equation} where $Q=2n+2$, $n\\geq1$, $0<\\mu<Q$, and $Q^{\\ast}_{\\mu}=(2Q-\\mu)/(Q-2)$. 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