{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:BTZYNUFWD5QUNTI76CZJT7R464","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":"22d5d3ff178159dba51ee47166f61f9d4797c7649acaeebc2b03385a6c866c17","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-12-15T13:44:37Z","title_canon_sha256":"c5d556e1e6b889b8e7b5af051b3378133e38eb9c15d268eea11b09f07be32651"},"schema_version":"1.0","source":{"id":"1112.3508","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.3508","created_at":"2026-05-18T03:01:11Z"},{"alias_kind":"arxiv_version","alias_value":"1112.3508v1","created_at":"2026-05-18T03:01:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.3508","created_at":"2026-05-18T03:01:11Z"},{"alias_kind":"pith_short_12","alias_value":"BTZYNUFWD5QU","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"BTZYNUFWD5QUNTI7","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"BTZYNUFW","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:3480672a3b47324ebe4a8b003e7e1807afed60c47cce0ab6d8a4d3b066d59238","target":"graph","created_at":"2026-05-18T03:01:11Z","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":"Two-dimensional affine A-nets in 3-space are quadrilateral meshes that discretize surfaces parametrized along asymptotic lines. The characterizing property of A-nets is planarity of vertex stars, so for generic A-nets the elementary quadrilaterals are skew. We classify the simply connected affine A-nets that can be extended to continuously differentiable surfaces by gluing hyperboloid surface patches into the skew quadrilaterals. The resulting surfaces are called \"hyperbolic nets\" and are a novel piecewise smooth discretization of surfaces parametrized along asymptotic lines. It turns out that","authors_text":"Emanuel Huhnen-Venedey, Thilo R\\\"orig","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-12-15T13:44:37Z","title":"Discretization of asymptotic line parametrizations using hyperboloid patches"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.3508","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":"sha256:31395f77983001651be8f2db8effdf1c246e2d07845b154c5c5f5d642ef32572","target":"record","created_at":"2026-05-18T03:01:11Z","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":"22d5d3ff178159dba51ee47166f61f9d4797c7649acaeebc2b03385a6c866c17","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-12-15T13:44:37Z","title_canon_sha256":"c5d556e1e6b889b8e7b5af051b3378133e38eb9c15d268eea11b09f07be32651"},"schema_version":"1.0","source":{"id":"1112.3508","kind":"arxiv","version":1}},"canonical_sha256":"0cf386d0b61f6146cd1ff0b299fe3cf72279cc4d9c63cce996cedcf36270874b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0cf386d0b61f6146cd1ff0b299fe3cf72279cc4d9c63cce996cedcf36270874b","first_computed_at":"2026-05-18T03:01:11.391113Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:01:11.391113Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n3DP/w3cTUURqWCsPHwoaXF7kNqil1YD5SN4YEA4adfM5TMDuQ3fZauuJK4Xl6gSfAo3Lrc6ykpfEHs7XWoTBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:01:11.391904Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.3508","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:31395f77983001651be8f2db8effdf1c246e2d07845b154c5c5f5d642ef32572","sha256:3480672a3b47324ebe4a8b003e7e1807afed60c47cce0ab6d8a4d3b066d59238"],"state_sha256":"82800e8f376c3f233989a47b9dedd4b84d43c00fb4d9a2faca880af012b2bbbe"}