{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:AOX3TN6REXJPGME2JQ72T6GJWE","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"07a4079a3bf833a1c03e639aed4611f67275829757a671ad8b94198be21d5ecf","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-06-29T09:14:12Z","title_canon_sha256":"a94f48ab4fab9ad01f4728adef3d6b2ebf4d7d6e93dc4f744b946fe4e2ee8749"},"schema_version":"1.0","source":{"id":"2606.30008","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.30008","created_at":"2026-06-30T02:17:45Z"},{"alias_kind":"arxiv_version","alias_value":"2606.30008v1","created_at":"2026-06-30T02:17:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.30008","created_at":"2026-06-30T02:17:45Z"},{"alias_kind":"pith_short_12","alias_value":"AOX3TN6REXJP","created_at":"2026-06-30T02:17:45Z"},{"alias_kind":"pith_short_16","alias_value":"AOX3TN6REXJPGME2","created_at":"2026-06-30T02:17:45Z"},{"alias_kind":"pith_short_8","alias_value":"AOX3TN6R","created_at":"2026-06-30T02:17:45Z"}],"graph_snapshots":[{"event_id":"sha256:15139c4fe5510af94859b5c6f8430eaab94d213c80115e23afbd57d8a3d7a207","target":"graph","created_at":"2026-06-30T02:17:45Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.30008/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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]}. 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.","authors_text":"Hongbin Cui, Jiahuan Li, Xiaowei Xu","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-06-29T09:14:12Z","title":"Bernstein-type theorem for stationary hypersurfaces of the Euler-Dierkes-Huisken functional"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.30008","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:9f0d6eaed1d3948843f8636f479a43db522de618aab5cbea84ef704e743df51f","target":"record","created_at":"2026-06-30T02:17:45Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"07a4079a3bf833a1c03e639aed4611f67275829757a671ad8b94198be21d5ecf","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-06-29T09:14:12Z","title_canon_sha256":"a94f48ab4fab9ad01f4728adef3d6b2ebf4d7d6e93dc4f744b946fe4e2ee8749"},"schema_version":"1.0","source":{"id":"2606.30008","kind":"arxiv","version":1}},"canonical_sha256":"03afb9b7d125d2f3309a4c3fa9f8c9b108a55490de4f1aa440632ca34ec225bf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"03afb9b7d125d2f3309a4c3fa9f8c9b108a55490de4f1aa440632ca34ec225bf","first_computed_at":"2026-06-30T02:17:45.560642Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-30T02:17:45.560642Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vrcMM+ryN1zAx6tidAPwQ2y67U+Va3oF0x51Vit4IVRQomMSEPxjUNzlib5/rXdobTqd2iN06qcScGOnatozAQ==","signature_status":"signed_v1","signed_at":"2026-06-30T02:17:45.561177Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.30008","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9f0d6eaed1d3948843f8636f479a43db522de618aab5cbea84ef704e743df51f","sha256:15139c4fe5510af94859b5c6f8430eaab94d213c80115e23afbd57d8a3d7a207"],"state_sha256":"eee955504e6961b29d6921d12b055036f19f9f8343858cfd795948987cf6c18f"}