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Then, we apply our general results to the particular case of the warped product model of the Euclidean sphere, and establish the unstability of $CM$, whenever $2\\leq n\\leq 14$ and $M^n$ is a closed, or"},"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":"1403.3451","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-03-13T22:30:29Z","cross_cats_sorted":[],"title_canon_sha256":"314f2a5042e72fbf0d0b7758a4c59e52e323f125c7c2cf4613aa66598fe3e9f9","abstract_canon_sha256":"c6c0cb1e85d5b8ea627cbba0e2b1646502cfe0214d6569bba628b5a2be92a648"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:56:20.405698Z","signature_b64":"Y7Oi9AqPhExLWygY5hDPC6WYplSM28++3WtEFrz2cwpj/PpQD+K8nO2csxLkXnEIlSgKzTR1V9kq7jtlrmBsAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e88a3a775b13e4e5fdf225505e831bbabca7851ed06d6508fb7dd644821099e4","last_reissued_at":"2026-05-18T02:56:20.404942Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:56:20.404942Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the stability of minimal cones in warped products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"A. 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