{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:ZLXRGIAC6GMY4DBQFM3MG632PP","short_pith_number":"pith:ZLXRGIAC","schema_version":"1.0","canonical_sha256":"caef132002f1998e0c302b36c37b7a7beaa5498f8826c818d364ff909a0fdb28","source":{"kind":"arxiv","id":"0803.0716","version":1},"attestation_state":"computed","paper":{"title":"Discrete holomorphic geometry I. Darboux transformations and spectral curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Christoph Bohle, Franz Pedit, Ulrich Pinkall","submitted_at":"2008-03-05T17:46:26Z","abstract_excerpt":"Finding appropriate notions of discrete holomorphic maps and, more generally, conformal immersions of discrete Riemann surfaces into 3-space is an important problem of discrete differential geometry and computer visualization. We propose an approach to discrete conformality that is based on the concept of holomorphic line bundles over \"discrete surfaces\", by which we mean the vertex sets of triangulated surfaces with bi-colored set of faces. The resulting theory of discrete conformality is simultaneously Moebius invariant and based on linear equations. In the special case of maps into the 2-sp"},"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":"0803.0716","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-03-05T17:46:26Z","cross_cats_sorted":[],"title_canon_sha256":"390a68f31edc97db4eeaad373c302751c48b9126e70cdfd7984cfbe994ca5e17","abstract_canon_sha256":"f6360d4099f2ec63ea45e533a70e9b701b29a8fe4ae471b2ff60e328292f9d95"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:38:05.276201Z","signature_b64":"nwzkLVRPVU5ygafk4lDMIlbcofxQwXf3fC+DDnbjN+brhNgG47zkk8Ikb2QTf1+rYsSQ5TrdCuIu5JOlH/QbBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"caef132002f1998e0c302b36c37b7a7beaa5498f8826c818d364ff909a0fdb28","last_reissued_at":"2026-05-18T03:38:05.275753Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:38:05.275753Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Discrete holomorphic geometry I. Darboux transformations and spectral curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Christoph Bohle, Franz Pedit, Ulrich Pinkall","submitted_at":"2008-03-05T17:46:26Z","abstract_excerpt":"Finding appropriate notions of discrete holomorphic maps and, more generally, conformal immersions of discrete Riemann surfaces into 3-space is an important problem of discrete differential geometry and computer visualization. We propose an approach to discrete conformality that is based on the concept of holomorphic line bundles over \"discrete surfaces\", by which we mean the vertex sets of triangulated surfaces with bi-colored set of faces. The resulting theory of discrete conformality is simultaneously Moebius invariant and based on linear equations. In the special case of maps into the 2-sp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0803.0716","kind":"arxiv","version":1},"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":"0803.0716","created_at":"2026-05-18T03:38:05.275819+00:00"},{"alias_kind":"arxiv_version","alias_value":"0803.0716v1","created_at":"2026-05-18T03:38:05.275819+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0803.0716","created_at":"2026-05-18T03:38:05.275819+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZLXRGIAC6GMY","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZLXRGIAC6GMY4DBQ","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZLXRGIAC","created_at":"2026-05-18T12:25:58.018023+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/ZLXRGIAC6GMY4DBQFM3MG632PP","json":"https://pith.science/pith/ZLXRGIAC6GMY4DBQFM3MG632PP.json","graph_json":"https://pith.science/api/pith-number/ZLXRGIAC6GMY4DBQFM3MG632PP/graph.json","events_json":"https://pith.science/api/pith-number/ZLXRGIAC6GMY4DBQFM3MG632PP/events.json","paper":"https://pith.science/paper/ZLXRGIAC"},"agent_actions":{"view_html":"https://pith.science/pith/ZLXRGIAC6GMY4DBQFM3MG632PP","download_json":"https://pith.science/pith/ZLXRGIAC6GMY4DBQFM3MG632PP.json","view_paper":"https://pith.science/paper/ZLXRGIAC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0803.0716&json=true","fetch_graph":"https://pith.science/api/pith-number/ZLXRGIAC6GMY4DBQFM3MG632PP/graph.json","fetch_events":"https://pith.science/api/pith-number/ZLXRGIAC6GMY4DBQFM3MG632PP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZLXRGIAC6GMY4DBQFM3MG632PP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZLXRGIAC6GMY4DBQFM3MG632PP/action/storage_attestation","attest_author":"https://pith.science/pith/ZLXRGIAC6GMY4DBQFM3MG632PP/action/author_attestation","sign_citation":"https://pith.science/pith/ZLXRGIAC6GMY4DBQFM3MG632PP/action/citation_signature","submit_replication":"https://pith.science/pith/ZLXRGIAC6GMY4DBQFM3MG632PP/action/replication_record"}},"created_at":"2026-05-18T03:38:05.275819+00:00","updated_at":"2026-05-18T03:38:05.275819+00:00"}