{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:CRMSS6YBJQALY2Q2QDYNMTBS2B","short_pith_number":"pith:CRMSS6YB","schema_version":"1.0","canonical_sha256":"1459297b014c00bc6a1a80f0d64c32d05fde7e98a88b89c493a669c7e7c69de0","source":{"kind":"arxiv","id":"1410.7535","version":2},"attestation_state":"computed","paper":{"title":"Finite groups of automorphisms of Enriques surfaces and the Mathieu group $M_{12}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.AG","authors_text":"Hisanori Ohashi, Shigeru Mukai","submitted_at":"2014-10-28T07:17:53Z","abstract_excerpt":"An action of a group $G$ on an Enriques surface $S$ is called Mathieu if it acts on $H^0(2K_S)$ trivially and every element of order 2, 4 has Lefschetz number 4. A finite group $G$ has a Mathieu action on some Enriques surface if and only if it is isomorphic to a subgroup of the symmetric group $\\mathfrak{S}_6$ of degree 6 and the order $|G|$ is not divisible by $2^4$. Explicit Mathieu actions of the three groups $\\mathfrak S_5, N_{72}$ and $\\mathfrak A_6$, together with non-Mathieu one of $H_{192}$, on polarized Enriques surfaces of degree 30, 18, 10 and 6, respectively, are constructed witho"},"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":"1410.7535","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-10-28T07:17:53Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"f76ed1a6f09df933d51d4415f81d62eacffc0962728a627042649a1dce499e73","abstract_canon_sha256":"34ab64d3c930d6653ce67eee6bce3ffaabbdf0900bb059c2dd3c061e41b9d6ac"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:19:00.857477Z","signature_b64":"2X9y6zmXxV2Q053mtMWMmnRai/TM4j4OW/vvM6aTp/5vhlGBg5lydvtG1tQHaRGOi0PI/wb3P6ufpYZGGYT5DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1459297b014c00bc6a1a80f0d64c32d05fde7e98a88b89c493a669c7e7c69de0","last_reissued_at":"2026-05-18T02:19:00.856954Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:19:00.856954Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Finite groups of automorphisms of Enriques surfaces and the Mathieu group $M_{12}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.AG","authors_text":"Hisanori Ohashi, Shigeru Mukai","submitted_at":"2014-10-28T07:17:53Z","abstract_excerpt":"An action of a group $G$ on an Enriques surface $S$ is called Mathieu if it acts on $H^0(2K_S)$ trivially and every element of order 2, 4 has Lefschetz number 4. A finite group $G$ has a Mathieu action on some Enriques surface if and only if it is isomorphic to a subgroup of the symmetric group $\\mathfrak{S}_6$ of degree 6 and the order $|G|$ is not divisible by $2^4$. Explicit Mathieu actions of the three groups $\\mathfrak S_5, N_{72}$ and $\\mathfrak A_6$, together with non-Mathieu one of $H_{192}$, on polarized Enriques surfaces of degree 30, 18, 10 and 6, respectively, are constructed witho"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.7535","kind":"arxiv","version":2},"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":"1410.7535","created_at":"2026-05-18T02:19:00.857033+00:00"},{"alias_kind":"arxiv_version","alias_value":"1410.7535v2","created_at":"2026-05-18T02:19:00.857033+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.7535","created_at":"2026-05-18T02:19:00.857033+00:00"},{"alias_kind":"pith_short_12","alias_value":"CRMSS6YBJQAL","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_16","alias_value":"CRMSS6YBJQALY2Q2","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_8","alias_value":"CRMSS6YB","created_at":"2026-05-18T12:28:22.404517+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/CRMSS6YBJQALY2Q2QDYNMTBS2B","json":"https://pith.science/pith/CRMSS6YBJQALY2Q2QDYNMTBS2B.json","graph_json":"https://pith.science/api/pith-number/CRMSS6YBJQALY2Q2QDYNMTBS2B/graph.json","events_json":"https://pith.science/api/pith-number/CRMSS6YBJQALY2Q2QDYNMTBS2B/events.json","paper":"https://pith.science/paper/CRMSS6YB"},"agent_actions":{"view_html":"https://pith.science/pith/CRMSS6YBJQALY2Q2QDYNMTBS2B","download_json":"https://pith.science/pith/CRMSS6YBJQALY2Q2QDYNMTBS2B.json","view_paper":"https://pith.science/paper/CRMSS6YB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1410.7535&json=true","fetch_graph":"https://pith.science/api/pith-number/CRMSS6YBJQALY2Q2QDYNMTBS2B/graph.json","fetch_events":"https://pith.science/api/pith-number/CRMSS6YBJQALY2Q2QDYNMTBS2B/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CRMSS6YBJQALY2Q2QDYNMTBS2B/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CRMSS6YBJQALY2Q2QDYNMTBS2B/action/storage_attestation","attest_author":"https://pith.science/pith/CRMSS6YBJQALY2Q2QDYNMTBS2B/action/author_attestation","sign_citation":"https://pith.science/pith/CRMSS6YBJQALY2Q2QDYNMTBS2B/action/citation_signature","submit_replication":"https://pith.science/pith/CRMSS6YBJQALY2Q2QDYNMTBS2B/action/replication_record"}},"created_at":"2026-05-18T02:19:00.857033+00:00","updated_at":"2026-05-18T02:19:00.857033+00:00"}