{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:DHOLIW4AQ7JICU2TQBCXSB7FWM","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":"d5756192bd1cee95a8f065a2ff13e987981dfd88e3433ced4735db140afde23b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-12-23T16:03:10Z","title_canon_sha256":"8414b6419cf1e83b9e5d18d678f38ceb4d5a3d31c762375cd9fb77d64fc8fde2"},"schema_version":"1.0","source":{"id":"1412.7422","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.7422","created_at":"2026-05-18T00:35:52Z"},{"alias_kind":"arxiv_version","alias_value":"1412.7422v1","created_at":"2026-05-18T00:35:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.7422","created_at":"2026-05-18T00:35:52Z"},{"alias_kind":"pith_short_12","alias_value":"DHOLIW4AQ7JI","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"DHOLIW4AQ7JICU2T","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"DHOLIW4A","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:fa6f1ca710b8f809a9e57516db00545e6adb58079e4b1ae7211949ab99a3c7b6","target":"graph","created_at":"2026-05-18T00:35:52Z","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":"Supercyclides are surfaces with a characteristic conjugate parametrization consisting of two families of conics. Patches of supercyclides can be adapted to a Q-net (a discrete quadrilateral net with planar faces) such that neighboring surface patches share tangent planes along common boundary curves. We call the resulting patchworks 'supercyclidic nets' and show that every Q-net in $\\mathbb{R}P^3$ can be extended to a supercyclidic net. The construction is governed by a multidimensionally consistent 3D system. One essential aspect of the theory is the extension of a given Q-net in $\\mathbb{R}P","authors_text":"Alexander I. Bobenko, Emanuel Huhnen-Venedey, Thilo R\\\"orig","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-12-23T16:03:10Z","title":"Supercyclidic nets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.7422","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:ce338f0fb9ce52521f36bb3ee0e26a95c8514a2c8f09719d9be160001b6512c3","target":"record","created_at":"2026-05-18T00:35:52Z","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":"d5756192bd1cee95a8f065a2ff13e987981dfd88e3433ced4735db140afde23b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-12-23T16:03:10Z","title_canon_sha256":"8414b6419cf1e83b9e5d18d678f38ceb4d5a3d31c762375cd9fb77d64fc8fde2"},"schema_version":"1.0","source":{"id":"1412.7422","kind":"arxiv","version":1}},"canonical_sha256":"19dcb45b8087d281535380457907e5b329b309bcdcd78ea594c1c58690073b4d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"19dcb45b8087d281535380457907e5b329b309bcdcd78ea594c1c58690073b4d","first_computed_at":"2026-05-18T00:35:52.011785Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:35:52.011785Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6T8Ly4TeKUjK7kOifTymoKZ2RrVLaouNZmRAsoyMD4d/9nHdubAgfBVBdsx4cHaq3C81Rkt3R3veQIcjd28FCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:35:52.012144Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.7422","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ce338f0fb9ce52521f36bb3ee0e26a95c8514a2c8f09719d9be160001b6512c3","sha256:fa6f1ca710b8f809a9e57516db00545e6adb58079e4b1ae7211949ab99a3c7b6"],"state_sha256":"262f756af92e126e2e15e404ddd602144f0a99bce21ccb31463477e0dfb5b78c"}