{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:GNTWAJFAKKSVF4XZQRFPJ3UN2M","short_pith_number":"pith:GNTWAJFA","schema_version":"1.0","canonical_sha256":"33676024a052a552f2f9844af4ee8dd31a2f67cee9a1f4b0b2b3dd9efa736c4d","source":{"kind":"arxiv","id":"2405.14287","version":1},"attestation_state":"computed","paper":{"title":"Maps, simple groups, and arc-transitive graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GR","authors_text":"Cheryl E. Praeger, Martin W. Liebeck","submitted_at":"2024-05-23T08:02:41Z","abstract_excerpt":"We determine all factorisations $X=AB$, where $X$ is a finite almost simple group and $A,B$ are core-free subgroups such that $A\\cap B$ is cyclic or dihedral. As a main application, we classify the graphs $\\Gamma$ admitting an almost simple arc-transitive group $X$ of automorphisms, such that $\\Gamma$ has a 2-cell embedding as a map on a closed surface admitting a core-free arc-transitive subgroup $G$ of $X$. We prove that apart from the case where $X$ and $G$ have socles $A_n$ and $A_{n-1}$ respectively, the only such graphs are the complete graphs $K_n$ with $n$ a prime power, the Johnson gr"},"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":"2405.14287","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2024-05-23T08:02:41Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"e29146f626285cb80b4423a751e560826696d1131b86ab044cffa5816849b161","abstract_canon_sha256":"4beb60e99900b1b605eeecd8812da4a4d37f234991bc04db8cc488bb9af46c9b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:22:12.336525Z","signature_b64":"sogjOB1NC7NQJm+FzIUWrbmG6NY0vxGWCDDOB8CHzLhuPdnHMnNXDZQRgghROfA0SqAFIjD/AGAallRqyAVtDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"33676024a052a552f2f9844af4ee8dd31a2f67cee9a1f4b0b2b3dd9efa736c4d","last_reissued_at":"2026-07-05T08:22:12.336068Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:22:12.336068Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Maps, simple groups, and arc-transitive graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GR","authors_text":"Cheryl E. Praeger, Martin W. Liebeck","submitted_at":"2024-05-23T08:02:41Z","abstract_excerpt":"We determine all factorisations $X=AB$, where $X$ is a finite almost simple group and $A,B$ are core-free subgroups such that $A\\cap B$ is cyclic or dihedral. As a main application, we classify the graphs $\\Gamma$ admitting an almost simple arc-transitive group $X$ of automorphisms, such that $\\Gamma$ has a 2-cell embedding as a map on a closed surface admitting a core-free arc-transitive subgroup $G$ of $X$. We prove that apart from the case where $X$ and $G$ have socles $A_n$ and $A_{n-1}$ respectively, the only such graphs are the complete graphs $K_n$ with $n$ a prime power, the Johnson gr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.14287","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2405.14287/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2405.14287","created_at":"2026-07-05T08:22:12.336111+00:00"},{"alias_kind":"arxiv_version","alias_value":"2405.14287v1","created_at":"2026-07-05T08:22:12.336111+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.14287","created_at":"2026-07-05T08:22:12.336111+00:00"},{"alias_kind":"pith_short_12","alias_value":"GNTWAJFAKKSV","created_at":"2026-07-05T08:22:12.336111+00:00"},{"alias_kind":"pith_short_16","alias_value":"GNTWAJFAKKSVF4XZ","created_at":"2026-07-05T08:22:12.336111+00:00"},{"alias_kind":"pith_short_8","alias_value":"GNTWAJFA","created_at":"2026-07-05T08:22:12.336111+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/GNTWAJFAKKSVF4XZQRFPJ3UN2M","json":"https://pith.science/pith/GNTWAJFAKKSVF4XZQRFPJ3UN2M.json","graph_json":"https://pith.science/api/pith-number/GNTWAJFAKKSVF4XZQRFPJ3UN2M/graph.json","events_json":"https://pith.science/api/pith-number/GNTWAJFAKKSVF4XZQRFPJ3UN2M/events.json","paper":"https://pith.science/paper/GNTWAJFA"},"agent_actions":{"view_html":"https://pith.science/pith/GNTWAJFAKKSVF4XZQRFPJ3UN2M","download_json":"https://pith.science/pith/GNTWAJFAKKSVF4XZQRFPJ3UN2M.json","view_paper":"https://pith.science/paper/GNTWAJFA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2405.14287&json=true","fetch_graph":"https://pith.science/api/pith-number/GNTWAJFAKKSVF4XZQRFPJ3UN2M/graph.json","fetch_events":"https://pith.science/api/pith-number/GNTWAJFAKKSVF4XZQRFPJ3UN2M/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GNTWAJFAKKSVF4XZQRFPJ3UN2M/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GNTWAJFAKKSVF4XZQRFPJ3UN2M/action/storage_attestation","attest_author":"https://pith.science/pith/GNTWAJFAKKSVF4XZQRFPJ3UN2M/action/author_attestation","sign_citation":"https://pith.science/pith/GNTWAJFAKKSVF4XZQRFPJ3UN2M/action/citation_signature","submit_replication":"https://pith.science/pith/GNTWAJFAKKSVF4XZQRFPJ3UN2M/action/replication_record"}},"created_at":"2026-07-05T08:22:12.336111+00:00","updated_at":"2026-07-05T08:22:12.336111+00:00"}