{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:2EP2E34GYIOIEL2DPH54MVWVF4","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":"065650b2a72fcb167d3be8378381765a8a6c8b69cb6527d38a86d25e47ef7056","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-07-09T11:03:27Z","title_canon_sha256":"ab780a90a9d925e35f5b15e4fd74230eed7acefc40239b97468b6a2f1dd2439c"},"schema_version":"1.0","source":{"id":"1307.2399","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.2399","created_at":"2026-05-18T02:03:38Z"},{"alias_kind":"arxiv_version","alias_value":"1307.2399v1","created_at":"2026-05-18T02:03:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.2399","created_at":"2026-05-18T02:03:38Z"},{"alias_kind":"pith_short_12","alias_value":"2EP2E34GYIOI","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"2EP2E34GYIOIEL2D","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"2EP2E34G","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:fa22938bc2dab027a3ce10e8c43896c5907501ae564a1e3b1d544f2205018af9","target":"graph","created_at":"2026-05-18T02:03:38Z","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":"We prove a version of the classical Runge and Mergelyan uniform approximation theorems for non-orientable minimal surfaces in Euclidean 3-space R3. Then, we obtain some geometric applications. Among them, we emphasize the following ones:\n  1. A Gunning-Narasimhan type theorem for non-orientable conformal surfaces.\n  2. An existence theorem for non-orientable minimal surfaces in R3, with arbitrary conformal structure, properly projecting into a plane.\n  3. An existence result for non-orientable minimal surfaces in R3 with arbitrary conformal structure and Gauss map omitting one projective direc","authors_text":"Antonio Alarcon, Francisco J. Lopez","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-07-09T11:03:27Z","title":"Approximation theory for non-orientable minimal surfaces and applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.2399","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:dedc2af9773663643082802e51396bf07dcbba0a3ca589a2e0f50782ba92e8e2","target":"record","created_at":"2026-05-18T02:03:38Z","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":"065650b2a72fcb167d3be8378381765a8a6c8b69cb6527d38a86d25e47ef7056","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-07-09T11:03:27Z","title_canon_sha256":"ab780a90a9d925e35f5b15e4fd74230eed7acefc40239b97468b6a2f1dd2439c"},"schema_version":"1.0","source":{"id":"1307.2399","kind":"arxiv","version":1}},"canonical_sha256":"d11fa26f86c21c822f4379fbc656d52f25e97c15ea82764a6d64b45840f842f3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d11fa26f86c21c822f4379fbc656d52f25e97c15ea82764a6d64b45840f842f3","first_computed_at":"2026-05-18T02:03:38.220418Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:03:38.220418Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mkTU4QwtW93wSD8I13aYwdgwt7N/uGY2into6S1LDXWGhCa6++XCM3xWQBVwYGaxQx8afx/WYsCS/Lp+lMQhAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:03:38.221217Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.2399","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dedc2af9773663643082802e51396bf07dcbba0a3ca589a2e0f50782ba92e8e2","sha256:fa22938bc2dab027a3ce10e8c43896c5907501ae564a1e3b1d544f2205018af9"],"state_sha256":"0d61af21cae31b0e567ffd7387efb68bf2295c314d653fb6d451682734aef271"}