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If the Yamabe constant of the conformal class $[g]$ satisfies\n  $$ Y(S^4, [g]) >\\frac{1}{\\sqrt{3}} Y(S^4, [g_{\\mathbb S}]) - \\varepsilon_0 $$ where $g_{\\mathbb S}$ denotes the standard round metric on $S^4$, then, up to rescaling, $g$ is isometric to $g_{\\mathbb S}$.\n  This is an extension of Gursky's gap theorem for positive Einstein metrics on the four-sphere."},"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":"1801.10305","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-01-31T05:29:24Z","cross_cats_sorted":[],"title_canon_sha256":"402c9933981695475e17607c9fe088026a60463aff844e7deb60b1d41ed88b31","abstract_canon_sha256":"9810ef787d3aac4e42b2e6e8c51f7cf093ba4dd554010563bf00047593d5265d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:52.044929Z","signature_b64":"hK36qEgBpGP7gZPDRb1QDSmdljmrve3Y9/2xa0CAZSQa+sDFf9e6XWujBjKJJoxkNHYnsPMl60f2e95dzk4BBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4a21f5f1b75706c9a7617c0010f24d62b4039650dcd10e4705778e511054a083","last_reissued_at":"2026-05-18T00:23:52.044280Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:52.044280Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A gap theorem for positive Einstein metrics on the four-sphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Harish Seshadri, Hisaaki Endo, Kazuo Akutagawa","submitted_at":"2018-01-31T05:29:24Z","abstract_excerpt":"We show that there exists a universal positive constant $\\varepsilon_0 > 0$ with the following property: Let $g$ be a positive Einstein metric on $S^4$. 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