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The result is sharp, i.e. we show that (1), (2) and (3) are necessary"},"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":"2506.10809","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-06-12T15:24:18Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"9207a3d2456dc0f5fb8a71cd3efe008defa78805f5b3567a1bf5b87edd2cf66f","abstract_canon_sha256":"92c0143d9b534707b846a0f342105e4a99090347b94b9dc53dc40183bac0faba"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:44:07.195370Z","signature_b64":"pglTSN6Btgw98xk0BNjciqGXFfk+KLScRY0uGXV5gdi8Tl3AsvoHwfTEgpaLAjfH0JNjAufoFXSw3/HijIU8Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6911e9175bc83b5bb2580ccfbd253d048af1704cf171f6ae23c1f35dc27c760d","last_reissued_at":"2026-07-05T11:44:07.194835Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:44:07.194835Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Warped products over one-dimensional base spaces and the RCD condition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.DG","authors_text":"Christian Ketterer","submitted_at":"2025-06-12T15:24:18Z","abstract_excerpt":"We prove the Riemannian curvature-dimension condition $\\mathsf{RCD}(KN,N+1)$ for an $N$-warped product $B\\times_f^N F$ over a one-dimensional base space $B$ with a Lipschitz function $f: B\\rightarrow \\mathbb R_{\\geq 0}$, provided (1) $f$ is a $Kf$-concave function, (2) $f$ satisfies a sub-Neumann boundary condition $\\frac{\\partial f}{\\partial n}\\geq 0$ on $\\partial B\\backslash f^{-1}(0)$ and $F$ is a compact metric measure space satisfying (3) the condition $\\mathsf{RCD}(K_F (N-1), N)$ with $K_F:= \\sup_B \\{ (Df)^2 + Kf^2\\}$. 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