{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:7W2CBK2M5F7VRECUF6AKXGLXFZ","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":"cb9d271a7c4680cc56f1e8c294346c019d28ad45356d0dc4243873eb83f9b99c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-04-24T17:08:36Z","title_canon_sha256":"90cc2ecec2440f32b091591f6e1e3da2fe126e9257a54b3af03e4cc2e5915fb6"},"schema_version":"1.0","source":{"id":"1904.10930","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.10930","created_at":"2026-05-17T23:47:49Z"},{"alias_kind":"arxiv_version","alias_value":"1904.10930v1","created_at":"2026-05-17T23:47:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.10930","created_at":"2026-05-17T23:47:49Z"},{"alias_kind":"pith_short_12","alias_value":"7W2CBK2M5F7V","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"7W2CBK2M5F7VRECU","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"7W2CBK2M","created_at":"2026-05-18T12:33:12Z"}],"graph_snapshots":[{"event_id":"sha256:531d783390517f0ecb97af6d09eb5856f4c92762f2749e84cece706b5075079a","target":"graph","created_at":"2026-05-17T23:47:49Z","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 this paper we study G-surfaces, a rather unknown surface class originally defined by Calapso, and show that the coordinate surfaces of a Guichard net are G-surfaces. Based on this observation, we present distinguished Combescure transformations that provide a duality for Guichard nets. Another class of special Combescure transformations is then used to construct a B\\\"acklund-type transformation for Guichard nets. In this realm a permutability theorem for the dual systems is proven.","authors_text":"Gudrun Szewieczek","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-04-24T17:08:36Z","title":"A duality for Guichard nets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.10930","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":"sha256:23e00e904e2f01d0f277bfb93649490c52b10bc46981bd7758d58fa3e625a8b8","target":"record","created_at":"2026-05-17T23:47:49Z","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":"cb9d271a7c4680cc56f1e8c294346c019d28ad45356d0dc4243873eb83f9b99c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-04-24T17:08:36Z","title_canon_sha256":"90cc2ecec2440f32b091591f6e1e3da2fe126e9257a54b3af03e4cc2e5915fb6"},"schema_version":"1.0","source":{"id":"1904.10930","kind":"arxiv","version":1}},"canonical_sha256":"fdb420ab4ce97f5890542f80ab99772e5c72fb01b4d82651fc7475a92290ca16","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fdb420ab4ce97f5890542f80ab99772e5c72fb01b4d82651fc7475a92290ca16","first_computed_at":"2026-05-17T23:47:49.652005Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:49.652005Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UcPIZv7Ks2UnMRqY1kAxo1uFrZWqP7LR4ic5+75aCFw6UR7P/5El3rvae9I2rQDGp0dLHghqty8+8ztzONdKDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:49.652498Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.10930","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:23e00e904e2f01d0f277bfb93649490c52b10bc46981bd7758d58fa3e625a8b8","sha256:531d783390517f0ecb97af6d09eb5856f4c92762f2749e84cece706b5075079a"],"state_sha256":"7dc326a9d5d03c4d0602a70d95fdd08c5e52dbc72bb5f8167085e33b69bd714b"}