{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:EVHCXK7H6RCLNKTVZMNLBXSECC","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":"de354e357045e22c15634a7072873d7abe137119b83599752e47cf472e7af6a4","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-03-15T17:28:40Z","title_canon_sha256":"5ec2d1d2895c02b955ee1b982749b22bb65abe9acd3e810158b94759efffd680"},"schema_version":"1.0","source":{"id":"1703.05318","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.05318","created_at":"2026-05-18T00:48:34Z"},{"alias_kind":"arxiv_version","alias_value":"1703.05318v1","created_at":"2026-05-18T00:48:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.05318","created_at":"2026-05-18T00:48:34Z"},{"alias_kind":"pith_short_12","alias_value":"EVHCXK7H6RCL","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"EVHCXK7H6RCLNKTV","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"EVHCXK7H","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:b093fe914bd25a5c640cb90d6a93cc5f9d78213f76228eb9b0d9d9177389ac0b","target":"graph","created_at":"2026-05-18T00:48:34Z","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":"Polyhedral surfaces are fundamental objects in architectural geometry and industrial design. Whereas closeness of a given mesh to a smooth reference surface and its suitability for numerical simulations were already studied extensively, the aim of our work is to find and to discuss suitable assessments of smoothness of polyhedral surfaces that only take the geometry of the polyhedral surface itself into account. Motivated by analogies to classical differential geometry, we propose a theory of smoothness of polyhedral surfaces including suitable notions of normal vectors, tangent planes, asympt","authors_text":"Caigui Jiang, Felix G\\\"unther, Helmut Pottmann","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-03-15T17:28:40Z","title":"Smooth polyhedral surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.05318","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:a60279fa35d16006e3fc8bef94129ead186e3e0eb3425b565060312e393c87d2","target":"record","created_at":"2026-05-18T00:48:34Z","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":"de354e357045e22c15634a7072873d7abe137119b83599752e47cf472e7af6a4","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-03-15T17:28:40Z","title_canon_sha256":"5ec2d1d2895c02b955ee1b982749b22bb65abe9acd3e810158b94759efffd680"},"schema_version":"1.0","source":{"id":"1703.05318","kind":"arxiv","version":1}},"canonical_sha256":"254e2babe7f444b6aa75cb1ab0de4410a9d5205dbc6ff5dd7e5516da8e60c087","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"254e2babe7f444b6aa75cb1ab0de4410a9d5205dbc6ff5dd7e5516da8e60c087","first_computed_at":"2026-05-18T00:48:34.572124Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:34.572124Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yS2J5I6z+zU1K/wppdymDTi/prE6hZ8iDMR6Dabg+ndmw2qgifmwjLthywyOPLPdIdHKwG80gNMc5nCLZNZ1Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:34.572802Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.05318","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a60279fa35d16006e3fc8bef94129ead186e3e0eb3425b565060312e393c87d2","sha256:b093fe914bd25a5c640cb90d6a93cc5f9d78213f76228eb9b0d9d9177389ac0b"],"state_sha256":"cb42af5729fdd65c954a0cd99ee0b5304af6d8c7d16a551bd98e372766875a23"}