{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:BLCIZ7YQJO4HZQOE5ACHRAIPZB","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":"d93f5c0b8d1edb9c37c9f8a237a6b0dde89b45943a7ff956c7076146662d5bb5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-08-13T18:16:50Z","title_canon_sha256":"60f801c63569e16cc3dbb0cf944e7bb14b4cfa8753fdc3a73c888a5f93148b17"},"schema_version":"1.0","source":{"id":"1408.3075","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.3075","created_at":"2026-05-18T02:45:15Z"},{"alias_kind":"arxiv_version","alias_value":"1408.3075v1","created_at":"2026-05-18T02:45:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.3075","created_at":"2026-05-18T02:45:15Z"},{"alias_kind":"pith_short_12","alias_value":"BLCIZ7YQJO4H","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"BLCIZ7YQJO4HZQOE","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"BLCIZ7YQ","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:62fba05f036103a146300ddef634907ac08fda0c6c8637d5604ab31dfd5d834e","target":"graph","created_at":"2026-05-18T02:45:15Z","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 article, we study the modified defect relations of the Gauss map of complete minimal surfaces in $\\mathbb R^3$ and $ \\mathbb R^4$ on annular ends. We obtain results which are similar to the ones obtained by Fujimoto~[J. Differential Geometry \\textbf{29} (1989), 245-262] for (the whole) complete minimal surfaces. We thus give some improvements of the previous results for the Gauss maps of complete minimal surfaces restricted on annular ends.","authors_text":"Nguyen Hoang Trang, Pham Hoang Ha","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-08-13T18:16:50Z","title":"Modified defect relations of the Gauss map of complete minimal surfaces on annular ends"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.3075","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:f69714eacc7978f6628f80fd06b2c6e4aa067f1d07416bbe4483a814781c284a","target":"record","created_at":"2026-05-18T02:45:15Z","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":"d93f5c0b8d1edb9c37c9f8a237a6b0dde89b45943a7ff956c7076146662d5bb5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-08-13T18:16:50Z","title_canon_sha256":"60f801c63569e16cc3dbb0cf944e7bb14b4cfa8753fdc3a73c888a5f93148b17"},"schema_version":"1.0","source":{"id":"1408.3075","kind":"arxiv","version":1}},"canonical_sha256":"0ac48cff104bb87cc1c4e80478810fc869c4584abf2a77f1fcd0c6bbb6cc3cfa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0ac48cff104bb87cc1c4e80478810fc869c4584abf2a77f1fcd0c6bbb6cc3cfa","first_computed_at":"2026-05-18T02:45:15.094491Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:45:15.094491Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6B8oMnaWJSyepjTXo/yR1Z/NtLdjMCac+QOM/7WQGXqqREB4g8R5XCn4jdLc55hARGjpjwW5vfxnKZGz23+iBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:45:15.095016Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.3075","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f69714eacc7978f6628f80fd06b2c6e4aa067f1d07416bbe4483a814781c284a","sha256:62fba05f036103a146300ddef634907ac08fda0c6c8637d5604ab31dfd5d834e"],"state_sha256":"f879c0dc3d936b541a058cfb1564981d1328b418a71b98587fc44e38a3ecce35"}