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If $K$ is a simplex, then the Ricci tensor of the Hessian metric $D^2 \\Phi$ is constant and equals $\\frac{n-1}{4(n+1)}$. We conjecture that the Ricci tensor of $D^2 \\Phi$ for arbitrary $K$ is uniformly bounded by $\\frac{n-1}{4(n+1)}$ and verify this conjecture in the two-dimensional case. The general case remains open."},"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":"1710.04618","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-10-12T17:07:29Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"1a9f6ab16427363efe1ccdb8d6484d092adae82556c9700f87fde9fa93e4c85c","abstract_canon_sha256":"e6aafc432da8a86320c8721d7cdaab89209496219cad0b164db1cc07baf82bf0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:00.546094Z","signature_b64":"u8ygO4mC+w7L3SRMyVNXGKl/PoiVqY9UPU2PvP5EM0eTDqKvKYVhwt1fPl6DVe/OC3J1CcGcqi9c1Mi+emvGDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e8e841b4556b949affbcd2bc987eb3964daa843e38b01b1cde62978f70b31e5e","last_reissued_at":"2026-05-18T00:33:00.545311Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:00.545311Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Extremal Kaehler-Einstein metric for two-dimensional convex bodies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.DG","authors_text":"Alexander V. 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