{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:Y3NSTE7XNGUVQBXBZJ5VP3SGFO","short_pith_number":"pith:Y3NSTE7X","schema_version":"1.0","canonical_sha256":"c6db2993f769a95806e1ca7b57ee462b9425e3a9f55ecb3ec758b7dd64eb97f5","source":{"kind":"arxiv","id":"1806.07024","version":1},"attestation_state":"computed","paper":{"title":"Complete regular dessins and skew-morphisms of cyclic groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.CO","authors_text":"Kan Hu, Martin Skoviera, Na-Er Wang, Roman Nedela, Yan-Quan Feng","submitted_at":"2018-06-19T02:47:31Z","abstract_excerpt":"A dessin is a 2-cell embedding of a connected $2$-coloured bipartite graph into an orientable closed surface. A dessin is regular if its group of orientation- and colour-preserving automorphisms acts regularly on the edges. In this paper we study regular dessins whose underlying graph is a complete bipartite graph $K_{m,n}$, called $(m,n)$-complete regular dessins. The purpose is to establish a rather surprising correspondence between $(m,n)$-complete regular dessins and pairs of skew-morphisms of cyclic groups. A skew-morphism of a finite group $A$ is a bijection $\\varphi\\colon A\\to A$ that s"},"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":"1806.07024","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-06-19T02:47:31Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"1d32f9f432b2d5939426e42d1b5ec09a49eeacbafda34e9aa6551af9f49c1480","abstract_canon_sha256":"fbdb3dc8ba29fc3e124d5d5d827f324762a9812929f549562ba10e6cb1d09128"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:57.676876Z","signature_b64":"0vvO8u6h6r/uEjRd7yw4z5fTly9/16llIfwLNN6s87Q848dAbquLQpRQp0WB5lDbTbdvKsAhQI8ivpmQc9VBCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c6db2993f769a95806e1ca7b57ee462b9425e3a9f55ecb3ec758b7dd64eb97f5","last_reissued_at":"2026-05-18T00:12:57.676234Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:57.676234Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Complete regular dessins and skew-morphisms of cyclic groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.CO","authors_text":"Kan Hu, Martin Skoviera, Na-Er Wang, Roman Nedela, Yan-Quan Feng","submitted_at":"2018-06-19T02:47:31Z","abstract_excerpt":"A dessin is a 2-cell embedding of a connected $2$-coloured bipartite graph into an orientable closed surface. A dessin is regular if its group of orientation- and colour-preserving automorphisms acts regularly on the edges. In this paper we study regular dessins whose underlying graph is a complete bipartite graph $K_{m,n}$, called $(m,n)$-complete regular dessins. The purpose is to establish a rather surprising correspondence between $(m,n)$-complete regular dessins and pairs of skew-morphisms of cyclic groups. A skew-morphism of a finite group $A$ is a bijection $\\varphi\\colon A\\to A$ that s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.07024","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":"1806.07024","created_at":"2026-05-18T00:12:57.676342+00:00"},{"alias_kind":"arxiv_version","alias_value":"1806.07024v1","created_at":"2026-05-18T00:12:57.676342+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.07024","created_at":"2026-05-18T00:12:57.676342+00:00"},{"alias_kind":"pith_short_12","alias_value":"Y3NSTE7XNGUV","created_at":"2026-05-18T12:33:04.347982+00:00"},{"alias_kind":"pith_short_16","alias_value":"Y3NSTE7XNGUVQBXB","created_at":"2026-05-18T12:33:04.347982+00:00"},{"alias_kind":"pith_short_8","alias_value":"Y3NSTE7X","created_at":"2026-05-18T12:33:04.347982+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/Y3NSTE7XNGUVQBXBZJ5VP3SGFO","json":"https://pith.science/pith/Y3NSTE7XNGUVQBXBZJ5VP3SGFO.json","graph_json":"https://pith.science/api/pith-number/Y3NSTE7XNGUVQBXBZJ5VP3SGFO/graph.json","events_json":"https://pith.science/api/pith-number/Y3NSTE7XNGUVQBXBZJ5VP3SGFO/events.json","paper":"https://pith.science/paper/Y3NSTE7X"},"agent_actions":{"view_html":"https://pith.science/pith/Y3NSTE7XNGUVQBXBZJ5VP3SGFO","download_json":"https://pith.science/pith/Y3NSTE7XNGUVQBXBZJ5VP3SGFO.json","view_paper":"https://pith.science/paper/Y3NSTE7X","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1806.07024&json=true","fetch_graph":"https://pith.science/api/pith-number/Y3NSTE7XNGUVQBXBZJ5VP3SGFO/graph.json","fetch_events":"https://pith.science/api/pith-number/Y3NSTE7XNGUVQBXBZJ5VP3SGFO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Y3NSTE7XNGUVQBXBZJ5VP3SGFO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Y3NSTE7XNGUVQBXBZJ5VP3SGFO/action/storage_attestation","attest_author":"https://pith.science/pith/Y3NSTE7XNGUVQBXBZJ5VP3SGFO/action/author_attestation","sign_citation":"https://pith.science/pith/Y3NSTE7XNGUVQBXBZJ5VP3SGFO/action/citation_signature","submit_replication":"https://pith.science/pith/Y3NSTE7XNGUVQBXBZJ5VP3SGFO/action/replication_record"}},"created_at":"2026-05-18T00:12:57.676342+00:00","updated_at":"2026-05-18T00:12:57.676342+00:00"}