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To implement the classical proof of Bianchi and Egnell, we overcome the main difficulty that the underlying operator $A_{2s}$ is not positive definite.\n  As a consequence of our analysis and recent results from Gong et al. (arXiv:2503.20350 [math.AP]), the case $s - \\frac{n}{2} \\in (1,2)$ remarkably constitutes the first example of a Sobolev-type stability inequality (i) whose best constant is explicit and (ii)"},"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":"2504.19939","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-04-28T16:09:42Z","cross_cats_sorted":[],"title_canon_sha256":"f1e97fdd63538e11078a3d171f6b57fd2733807e5f100e873f5c49da9b0f2930","abstract_canon_sha256":"8d4ae3657e5f84d538d94d8f6e25f6d46a9c6a306ab5f9b1b04e00a51c728b17"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:00:06.897766Z","signature_b64":"Fm4GlOaaw2PbDmBdOPJS85BMo8Fsafy1kNh5hg/OQUcVWq91preMmQZQEkz3mabvBKcvFfwDoJn/o7EIqXKYAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f81cf5fbc96ac9f266388ee1e6cd89f2a3e4cc716e7483661e4a4a0dc0677924","last_reissued_at":"2026-07-05T11:00:06.897299Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:00:06.897299Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stability inequalities with explicit constants for a family of reverse Sobolev inequalities on the sphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Tobias K\\\"onig","submitted_at":"2025-04-28T16:09:42Z","abstract_excerpt":"We prove a stability inequality associated to the reverse Sobolev inequality on the sphere $\\mathbb S^n$, for the full admissible parameter range $s - \\frac{n}{2} \\in (0,1) \\cup (1,2)$. 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