{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:WENW643H3G3H6OOZX4CXLLAV4G","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":"90ed12338a1abe485454707ebc4e81c0182924714b814f9a68c2863cdd04957b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-03-18T12:04:07Z","title_canon_sha256":"fba4c907253c3ab63b90b8c4249f4919897cad199e474fd8691ff39603bda195"},"schema_version":"1.0","source":{"id":"1303.4221","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.4221","created_at":"2026-05-18T03:25:58Z"},{"alias_kind":"arxiv_version","alias_value":"1303.4221v2","created_at":"2026-05-18T03:25:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.4221","created_at":"2026-05-18T03:25:58Z"},{"alias_kind":"pith_short_12","alias_value":"WENW643H3G3H","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"WENW643H3G3H6OOZ","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"WENW643H","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:913ff6a7549c068dde1f03ab1bb91acf144e49812433787bff5440d66e22e3bc","target":"graph","created_at":"2026-05-18T03:25:58Z","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":"Inspired by an argument of Ros [15] -- we use the L\\'{o}pez-Ros deformation to give another proof of the fact -- due to Meeks and Wolf [13] -- that the only smooth, connected, singly-periodic minimal surfaces in $\\Real^3$ with the area growth of two planes are the singly-periodic Scherk surfaces.","authors_text":"Jacob Bernstein","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-03-18T12:04:07Z","title":"Regarding a uniqueness property of singly-periodic Scherk surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.4221","kind":"arxiv","version":2},"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":"sha256:26b070092fc48e1c50f2fb037eb4f162451424d397f11b120927c7255741fb12","target":"record","created_at":"2026-05-18T03:25:58Z","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":"90ed12338a1abe485454707ebc4e81c0182924714b814f9a68c2863cdd04957b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-03-18T12:04:07Z","title_canon_sha256":"fba4c907253c3ab63b90b8c4249f4919897cad199e474fd8691ff39603bda195"},"schema_version":"1.0","source":{"id":"1303.4221","kind":"arxiv","version":2}},"canonical_sha256":"b11b6f7367d9b67f39d9bf0575ac15e18bb78a8bb8806a2931115792c00e24bc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b11b6f7367d9b67f39d9bf0575ac15e18bb78a8bb8806a2931115792c00e24bc","first_computed_at":"2026-05-18T03:25:58.333585Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:25:58.333585Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xMMLmIRQYziug0BM0lxl5cr/oYbsKNvoCCzsJjKgvDDFyQ0A3zZoSWfavEBAakGkCR6L5Lwd1ukuBTfUkIFNBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:25:58.334134Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.4221","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:26b070092fc48e1c50f2fb037eb4f162451424d397f11b120927c7255741fb12","sha256:913ff6a7549c068dde1f03ab1bb91acf144e49812433787bff5440d66e22e3bc"],"state_sha256":"9852828970174320bb1fed555165b92dab53f69704179f0f17ec43593ea42fff"}