{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:WRO7A6RTTPTO3ETLYL4X7RPJQB","short_pith_number":"pith:WRO7A6RT","schema_version":"1.0","canonical_sha256":"b45df07a339be6ed926bc2f97fc5e98061d6dd1993f5986b6d6e745f6351cb7c","source":{"kind":"arxiv","id":"1505.05673","version":1},"attestation_state":"computed","paper":{"title":"Discrete complex analysis on planar quad-graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.CV","authors_text":"Alexander I. Bobenko, Felix G\\\"unther","submitted_at":"2015-05-21T10:53:01Z","abstract_excerpt":"We develop a linear theory of discrete complex analysis on general quad-graphs, continuing and extending previous work of Duffin, Mercat, Kenyon, Chelkak and Smirnov on discrete complex analysis on rhombic quad-graphs. Our approach based on the medial graph yields more instructive proofs of discrete analogs of several classical theorems and even new results. We provide discrete counterparts of fundamental concepts in complex analysis such as holomorphic functions, derivatives, the Laplacian, and exterior calculus. Also, we discuss discrete versions of important basic theorems such as Green's i"},"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":"1505.05673","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-05-21T10:53:01Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"43bcacfc1e65588990390b35aec1d487c431068b0cf2e6bd1194a289eaa22c6f","abstract_canon_sha256":"9eb32c271cb056ffa36434c386bb7a5c82e9ce9f9e28bf32bd81bc3a12909095"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:55.068543Z","signature_b64":"kVdgXHiOc5DV0wmefk1icOY9L2GMKTV/78/qTCXuPHgeJRWNfc9u8j1aQZtHovU9KU02jX2j7Os3/+tI+MujDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b45df07a339be6ed926bc2f97fc5e98061d6dd1993f5986b6d6e745f6351cb7c","last_reissued_at":"2026-05-18T00:48:55.067811Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:55.067811Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Discrete complex analysis on planar quad-graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.CV","authors_text":"Alexander I. Bobenko, Felix G\\\"unther","submitted_at":"2015-05-21T10:53:01Z","abstract_excerpt":"We develop a linear theory of discrete complex analysis on general quad-graphs, continuing and extending previous work of Duffin, Mercat, Kenyon, Chelkak and Smirnov on discrete complex analysis on rhombic quad-graphs. Our approach based on the medial graph yields more instructive proofs of discrete analogs of several classical theorems and even new results. We provide discrete counterparts of fundamental concepts in complex analysis such as holomorphic functions, derivatives, the Laplacian, and exterior calculus. Also, we discuss discrete versions of important basic theorems such as Green's i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.05673","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":"1505.05673","created_at":"2026-05-18T00:48:55.067938+00:00"},{"alias_kind":"arxiv_version","alias_value":"1505.05673v1","created_at":"2026-05-18T00:48:55.067938+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.05673","created_at":"2026-05-18T00:48:55.067938+00:00"},{"alias_kind":"pith_short_12","alias_value":"WRO7A6RTTPTO","created_at":"2026-05-18T12:29:47.479230+00:00"},{"alias_kind":"pith_short_16","alias_value":"WRO7A6RTTPTO3ETL","created_at":"2026-05-18T12:29:47.479230+00:00"},{"alias_kind":"pith_short_8","alias_value":"WRO7A6RT","created_at":"2026-05-18T12:29:47.479230+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/WRO7A6RTTPTO3ETLYL4X7RPJQB","json":"https://pith.science/pith/WRO7A6RTTPTO3ETLYL4X7RPJQB.json","graph_json":"https://pith.science/api/pith-number/WRO7A6RTTPTO3ETLYL4X7RPJQB/graph.json","events_json":"https://pith.science/api/pith-number/WRO7A6RTTPTO3ETLYL4X7RPJQB/events.json","paper":"https://pith.science/paper/WRO7A6RT"},"agent_actions":{"view_html":"https://pith.science/pith/WRO7A6RTTPTO3ETLYL4X7RPJQB","download_json":"https://pith.science/pith/WRO7A6RTTPTO3ETLYL4X7RPJQB.json","view_paper":"https://pith.science/paper/WRO7A6RT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1505.05673&json=true","fetch_graph":"https://pith.science/api/pith-number/WRO7A6RTTPTO3ETLYL4X7RPJQB/graph.json","fetch_events":"https://pith.science/api/pith-number/WRO7A6RTTPTO3ETLYL4X7RPJQB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WRO7A6RTTPTO3ETLYL4X7RPJQB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WRO7A6RTTPTO3ETLYL4X7RPJQB/action/storage_attestation","attest_author":"https://pith.science/pith/WRO7A6RTTPTO3ETLYL4X7RPJQB/action/author_attestation","sign_citation":"https://pith.science/pith/WRO7A6RTTPTO3ETLYL4X7RPJQB/action/citation_signature","submit_replication":"https://pith.science/pith/WRO7A6RTTPTO3ETLYL4X7RPJQB/action/replication_record"}},"created_at":"2026-05-18T00:48:55.067938+00:00","updated_at":"2026-05-18T00:48:55.067938+00:00"}