{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:TG5FGVZSPILCYQYUAJUE4CQGAF","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":"e67e8697433f94180f9914015f4c1a2d4c3b190fac80a1212ac6fac906265937","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-04-29T08:16:56Z","title_canon_sha256":"be47540403bc6ed068374354a5725943a4ee65645dd6851910130e0ce59613bb"},"schema_version":"1.0","source":{"id":"1504.07757","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.07757","created_at":"2026-05-18T02:17:32Z"},{"alias_kind":"arxiv_version","alias_value":"1504.07757v1","created_at":"2026-05-18T02:17:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.07757","created_at":"2026-05-18T02:17:32Z"},{"alias_kind":"pith_short_12","alias_value":"TG5FGVZSPILC","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"TG5FGVZSPILCYQYU","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"TG5FGVZS","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:fad8370ef53de98942ebbc6c904d17f4a0df1c9af1fb815c315592a72acbd679","target":"graph","created_at":"2026-05-18T02:17:32Z","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"},"paper":{"abstract_excerpt":"In this paper, we study generalized constant ratio (GCR) hypersurfaces in Euclidean spaces. We mainly focus on the hypersurfaces in $\\mathbb E^4$. First, we deal with $\\delta(2)$-ideal GCR hypersurfaces. Then, we study on hypersurfaces with constant (first) mean curvature. Finally, we obtain the complete classification of GCR hypersurfaces with vanishing Gauss-Kronecker curvature. We also give some explicit examples.\n  Keywords: Generalized constant ratio submanifolds, $\\delta(r)$-invariant hypersurfaces, constant mean curvature, Gauss-Kronecker curvature","authors_text":"Nurettin Cenk Turgay","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-04-29T08:16:56Z","title":"Generalized constant ratio hypersurfaces in Euclidean spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.07757","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":"sha256:386e27c3be5afe994055997107530be90b196577999c6e6021f943a2cb109957","target":"record","created_at":"2026-05-18T02:17:32Z","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":"e67e8697433f94180f9914015f4c1a2d4c3b190fac80a1212ac6fac906265937","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-04-29T08:16:56Z","title_canon_sha256":"be47540403bc6ed068374354a5725943a4ee65645dd6851910130e0ce59613bb"},"schema_version":"1.0","source":{"id":"1504.07757","kind":"arxiv","version":1}},"canonical_sha256":"99ba5357327a162c431402684e0a0601491ecf1991ba1bf5e13aa480a504c7b9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"99ba5357327a162c431402684e0a0601491ecf1991ba1bf5e13aa480a504c7b9","first_computed_at":"2026-05-18T02:17:32.313987Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:17:32.313987Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"C6HmJLaVAIMfvVnP95+5D2HDKZyVYsfdsUgG+IbwtZP7MTAujvicln5UCTks6xWRQJ7tUo0i0aGsNwYLeob5Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:17:32.314723Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.07757","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:386e27c3be5afe994055997107530be90b196577999c6e6021f943a2cb109957","sha256:fad8370ef53de98942ebbc6c904d17f4a0df1c9af1fb815c315592a72acbd679"],"state_sha256":"0953ccf7142bc68953dd1f509c1e19193787b6c144e1d5d0aa7919655833ecb2"}