{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:JRFKJX76777GRHKB7WJFAYJRNV","short_pith_number":"pith:JRFKJX76","schema_version":"1.0","canonical_sha256":"4c4aa4dffefffe689d41fd925061316d46524889a29d894b1f31853cdc89f01e","source":{"kind":"arxiv","id":"1005.2698","version":3},"attestation_state":"computed","paper":{"title":"Discrete conformal maps and ideal hyperbolic polyhedra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.GT","authors_text":"Alexander Bobenko, Boris Springborn, Ulrich Pinkall","submitted_at":"2010-05-15T19:22:29Z","abstract_excerpt":"We establish a connection between two previously unrelated topics: a particular discrete version of conformal geometry for triangulated surfaces, and the geometry of ideal polyhedra in hyperbolic three-space. Two triangulated surfaces are considered discretely conformally equivalent if the edge lengths are related by scale factors associated with the vertices. This simple definition leads to a surprisingly rich theory featuring M\\\"obius invariance, the definition of discrete conformal maps as circumcircle preserving piecewise projective maps, and two variational principles. We show how literal"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1005.2698","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-05-15T19:22:29Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"ce0c6ecde6a9835ac119cf7d7e5b9b104f80337f8366d8f242a868336b2e42f4","abstract_canon_sha256":"0b34b1ab5cc1e2c191d28192800c198f5b70697ce75ccdd6882ffa6de280f4ba"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:30.367734Z","signature_b64":"NFYPvZ1/MhprLPX53fCpxGVyrRvmFdNUsvx+hLZY5FfxeAvKna99GCDoFdO9QfDp0zskvkuPYGwl3RwzZnftBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4c4aa4dffefffe689d41fd925061316d46524889a29d894b1f31853cdc89f01e","last_reissued_at":"2026-05-18T01:34:30.367306Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:30.367306Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Discrete conformal maps and ideal hyperbolic polyhedra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.GT","authors_text":"Alexander Bobenko, Boris Springborn, Ulrich Pinkall","submitted_at":"2010-05-15T19:22:29Z","abstract_excerpt":"We establish a connection between two previously unrelated topics: a particular discrete version of conformal geometry for triangulated surfaces, and the geometry of ideal polyhedra in hyperbolic three-space. Two triangulated surfaces are considered discretely conformally equivalent if the edge lengths are related by scale factors associated with the vertices. This simple definition leads to a surprisingly rich theory featuring M\\\"obius invariance, the definition of discrete conformal maps as circumcircle preserving piecewise projective maps, and two variational principles. We show how literal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.2698","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1005.2698","created_at":"2026-05-18T01:34:30.367372+00:00"},{"alias_kind":"arxiv_version","alias_value":"1005.2698v3","created_at":"2026-05-18T01:34:30.367372+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.2698","created_at":"2026-05-18T01:34:30.367372+00:00"},{"alias_kind":"pith_short_12","alias_value":"JRFKJX76777G","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_16","alias_value":"JRFKJX76777GRHKB","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_8","alias_value":"JRFKJX76","created_at":"2026-05-18T12:26:09.077623+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/JRFKJX76777GRHKB7WJFAYJRNV","json":"https://pith.science/pith/JRFKJX76777GRHKB7WJFAYJRNV.json","graph_json":"https://pith.science/api/pith-number/JRFKJX76777GRHKB7WJFAYJRNV/graph.json","events_json":"https://pith.science/api/pith-number/JRFKJX76777GRHKB7WJFAYJRNV/events.json","paper":"https://pith.science/paper/JRFKJX76"},"agent_actions":{"view_html":"https://pith.science/pith/JRFKJX76777GRHKB7WJFAYJRNV","download_json":"https://pith.science/pith/JRFKJX76777GRHKB7WJFAYJRNV.json","view_paper":"https://pith.science/paper/JRFKJX76","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1005.2698&json=true","fetch_graph":"https://pith.science/api/pith-number/JRFKJX76777GRHKB7WJFAYJRNV/graph.json","fetch_events":"https://pith.science/api/pith-number/JRFKJX76777GRHKB7WJFAYJRNV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JRFKJX76777GRHKB7WJFAYJRNV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JRFKJX76777GRHKB7WJFAYJRNV/action/storage_attestation","attest_author":"https://pith.science/pith/JRFKJX76777GRHKB7WJFAYJRNV/action/author_attestation","sign_citation":"https://pith.science/pith/JRFKJX76777GRHKB7WJFAYJRNV/action/citation_signature","submit_replication":"https://pith.science/pith/JRFKJX76777GRHKB7WJFAYJRNV/action/replication_record"}},"created_at":"2026-05-18T01:34:30.367372+00:00","updated_at":"2026-05-18T01:34:30.367372+00:00"}