{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:WFHAILNIZWKNS3PXLSHN6BQGZP","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":"54d894a49d29b702a223bb439acfc23a4f5834bdbb6a7c0e293509b9fae5437e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-07-25T21:36:39Z","title_canon_sha256":"ca34b72f5c866b139b4e3bd3f0fb63c5b357cd62a9776225f93847db29f5262e"},"schema_version":"1.0","source":{"id":"1607.07492","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.07492","created_at":"2026-05-17T23:42:49Z"},{"alias_kind":"arxiv_version","alias_value":"1607.07492v3","created_at":"2026-05-17T23:42:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.07492","created_at":"2026-05-17T23:42:49Z"},{"alias_kind":"pith_short_12","alias_value":"WFHAILNIZWKN","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"WFHAILNIZWKNS3PX","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"WFHAILNI","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:ba1fb5c317563b2039aa24ab53aabe79b439545cbbfbc3eb4d9cf1aef6a057d8","target":"graph","created_at":"2026-05-17T23:42:49Z","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 [15] Robert Osserman proved that the image of the Gauss map of a complete, non flat minimal surface in R^3 with finite total curvature miss at most 3 points. In this paper we prove that the Gauss map of such a minimal immersions omit at most 2 points. This is a sharp result since the Gauss map of the catenoid omits exactly two points. In fact we prove this result for a wider class of isometric immersions, that share the basic differential topological properties of the complete minimal surfaces of finite total curvature.","authors_text":"Francesco Mercuri, Luquesio P. Jorge","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-07-25T21:36:39Z","title":"The Gauss map of a complete minimal surface with finite total curvature"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.07492","kind":"arxiv","version":3},"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":"sha256:058f9daca74cab6e6a01128a001cff61101339c5110f02f2b05f44d7e845a232","target":"record","created_at":"2026-05-17T23:42:49Z","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":"54d894a49d29b702a223bb439acfc23a4f5834bdbb6a7c0e293509b9fae5437e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-07-25T21:36:39Z","title_canon_sha256":"ca34b72f5c866b139b4e3bd3f0fb63c5b357cd62a9776225f93847db29f5262e"},"schema_version":"1.0","source":{"id":"1607.07492","kind":"arxiv","version":3}},"canonical_sha256":"b14e042da8cd94d96df75c8edf0606cbe0ec713d798ffe1656b1a60256cddaf0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b14e042da8cd94d96df75c8edf0606cbe0ec713d798ffe1656b1a60256cddaf0","first_computed_at":"2026-05-17T23:42:49.280851Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:49.280851Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hs9Va7gW6J07rFWkUdCMxAmzE3oHQuD79VTR9ovTZENF5xvQyHZL1Y2AOSCVmhOLNbAO3eteXA3/t11A9UlYBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:49.281348Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.07492","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:058f9daca74cab6e6a01128a001cff61101339c5110f02f2b05f44d7e845a232","sha256:ba1fb5c317563b2039aa24ab53aabe79b439545cbbfbc3eb4d9cf1aef6a057d8"],"state_sha256":"c9547eb437f7d8299093eeb4a26f9b03d4e6b88e77b60401d78f7ba410f0ef0a"}