{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:HMDED5JZC2YJUOC5G3GB4IAMUQ","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":"935f37a8c82b9dfb93dfcf4c41f7f0108a1753590a6342358e1c0f6b0e952dda","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-10-15T00:22:34Z","title_canon_sha256":"f3a65f34e5871a79852f3d86f1f9ce7f0474d77f969674059c225a7ddd347d2e"},"schema_version":"1.0","source":{"id":"1010.3049","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.3049","created_at":"2026-05-18T04:06:45Z"},{"alias_kind":"arxiv_version","alias_value":"1010.3049v4","created_at":"2026-05-18T04:06:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.3049","created_at":"2026-05-18T04:06:45Z"},{"alias_kind":"pith_short_12","alias_value":"HMDED5JZC2YJ","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"HMDED5JZC2YJUOC5","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"HMDED5JZ","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:cd8678ad8ff9ff3d7c0f3b8ada358811a78682a548c6babe687842719cded67b","target":"graph","created_at":"2026-05-18T04:06:45Z","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":"Schwartz's solution to the Bj\\\"orling problem leads to an equivalence class of spatial strips S(t)=(c(t),n(t)) which produce equivalent minimal surfaces. For the particular case when the generating strip S(t) belongs to some plane E and c(t) is symmetric with respect to some straight line in E, the symmetries of the minimal surface permit us to identify another planar curve ~c(t) that we call the CPG curve to c(t). A simple symmetric argument shows that self-CPG curves produce minimal surfaces whose adjoint surface contains another self-CPG curve. We ask for minimal surfaces generated by self-","authors_text":"Hugo Jim\\'enez-P\\'erez, Santiago L\\'opez de Medrano","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-10-15T00:22:34Z","title":"On the self-CPG curves and the Bj\\\"orling problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.3049","kind":"arxiv","version":4},"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":"sha256:93e0cbad3f3b6d22a601835f349d9afffc4fa205d218bfd7445d0fca1ac140c3","target":"record","created_at":"2026-05-18T04:06:45Z","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":"935f37a8c82b9dfb93dfcf4c41f7f0108a1753590a6342358e1c0f6b0e952dda","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-10-15T00:22:34Z","title_canon_sha256":"f3a65f34e5871a79852f3d86f1f9ce7f0474d77f969674059c225a7ddd347d2e"},"schema_version":"1.0","source":{"id":"1010.3049","kind":"arxiv","version":4}},"canonical_sha256":"3b0641f53916b09a385d36cc1e200ca401ceb772c7e5864fd791ac3a9179d9a9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3b0641f53916b09a385d36cc1e200ca401ceb772c7e5864fd791ac3a9179d9a9","first_computed_at":"2026-05-18T04:06:45.108446Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:06:45.108446Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9OgUva6YA31PLeWGQA6cFqS0uaheFAUZ5+6OLR50QvIBli2bwx8Z4HGrVy60aKneEu0PlaY0/lGbbBoWz/kLDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:06:45.109109Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.3049","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:93e0cbad3f3b6d22a601835f349d9afffc4fa205d218bfd7445d0fca1ac140c3","sha256:cd8678ad8ff9ff3d7c0f3b8ada358811a78682a548c6babe687842719cded67b"],"state_sha256":"94f2966a0234e492c397f2f79e3056314b742bf110976f2ce1d7c204feaf7ed5"}