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In this paper, we prove that every smooth, complete, connected, embedded $\\alpha$-stationary hypersurface in $\\mathbb{R}^{n+1}$ passing through the origin with $\\alpha>0$ is a linear hyperplane."},"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":"2606.30008","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-06-29T09:14:12Z","cross_cats_sorted":[],"title_canon_sha256":"a94f48ab4fab9ad01f4728adef3d6b2ebf4d7d6e93dc4f744b946fe4e2ee8749","abstract_canon_sha256":"07a4079a3bf833a1c03e639aed4611f67275829757a671ad8b94198be21d5ecf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-30T02:17:45.561177Z","signature_b64":"vrcMM+ryN1zAx6tidAPwQ2y67U+Va3oF0x51Vit4IVRQomMSEPxjUNzlib5/rXdobTqd2iN06qcScGOnatozAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"03afb9b7d125d2f3309a4c3fa9f8c9b108a55490de4f1aa440632ca34ec225bf","last_reissued_at":"2026-06-30T02:17:45.560642Z","signature_status":"signed_v1","first_computed_at":"2026-06-30T02:17:45.560642Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bernstein-type theorem for stationary hypersurfaces of the Euler-Dierkes-Huisken functional","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Hongbin Cui, Jiahuan Li, Xiaowei Xu","submitted_at":"2026-06-29T09:14:12Z","abstract_excerpt":"We say that a hypersurface $\\Sigma \\subset\\mathbb{R}^{n+1}$ is $\\alpha$-stationary if it is a critical point of the Euler-Dierkes-Huisken functional $\\mathcal{E}_\\alpha(\\Sigma)=\\int_\\Sigma|X|^\\alpha\\, d\\mathcal{H}^n$, introduced by Dierkes and Huisken in \\cite{[DH-24]}. 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