{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:GEAEY46AKBGJVIYL73DUSIWH2K","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":"3b3be15106722b43bf98b0f4532ca3ef374107854c4325c4dd7a92133edddb7c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-05-19T15:36:32Z","title_canon_sha256":"34978d06348479da0819ca39cba238b820e5b247cb0bf06a5d6302c2b50d3505"},"schema_version":"1.0","source":{"id":"1305.4373","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.4373","created_at":"2026-05-18T03:25:23Z"},{"alias_kind":"arxiv_version","alias_value":"1305.4373v1","created_at":"2026-05-18T03:25:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.4373","created_at":"2026-05-18T03:25:23Z"},{"alias_kind":"pith_short_12","alias_value":"GEAEY46AKBGJ","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"GEAEY46AKBGJVIYL","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"GEAEY46A","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:2b207e79bbaf689aa9609f6a2c41a915e9e535b687c1bbd42b180cd9b5b5c1c0","target":"graph","created_at":"2026-05-18T03:25:23Z","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":"A depth surface of E^3 is a range image observed from a single view can be represented by a digital graph (Monge patch) surface . That is, a depth or range value at a point (u,v) is given by a single valued function z=f(u,v). In the present study we consider the surfaces in Euclidean 4-space E^4 given with a Monge patch z=f(u,v),w=g(u,v). We investigated the curvature properties of these surfaces. We also give some special examples of these surfaces which are first defined by Yu. Aminov. Finally, we proved that every Aminov surface is a non-trivial Chen surface.","authors_text":"Betul Bulca, Kadri Arslan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-05-19T15:36:32Z","title":"Surfaces given with the Monge patch in E^4"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.4373","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":"sha256:6532c2f30bc4eb7184c1853e06206979e0585f6a1cda25fa282a719c367b28d7","target":"record","created_at":"2026-05-18T03:25:23Z","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":"3b3be15106722b43bf98b0f4532ca3ef374107854c4325c4dd7a92133edddb7c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-05-19T15:36:32Z","title_canon_sha256":"34978d06348479da0819ca39cba238b820e5b247cb0bf06a5d6302c2b50d3505"},"schema_version":"1.0","source":{"id":"1305.4373","kind":"arxiv","version":1}},"canonical_sha256":"31004c73c0504c9aa30bfec74922c7d2a3f18dc38242e28abd381cb216d5f84b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"31004c73c0504c9aa30bfec74922c7d2a3f18dc38242e28abd381cb216d5f84b","first_computed_at":"2026-05-18T03:25:23.946888Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:25:23.946888Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bELhZxUJnZbzboECfXnZ+ilTk4rzxqKGnelauxOBI+A9+PTTHeAHTliBZNtFXmLS7uId080JzHiC/yGU6j7SCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:25:23.947495Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.4373","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6532c2f30bc4eb7184c1853e06206979e0585f6a1cda25fa282a719c367b28d7","sha256:2b207e79bbaf689aa9609f6a2c41a915e9e535b687c1bbd42b180cd9b5b5c1c0"],"state_sha256":"01d08056f5ad5f46fb34808ea19715edd807501cb0fc02560fd53126578bf94c"}