{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:DKAMT5J5BNS4577KZJICMAUP6F","short_pith_number":"pith:DKAMT5J5","schema_version":"1.0","canonical_sha256":"1a80c9f53d0b65ceffeaca5026028ff14401b7f80dfe93106e3eb3754377edb5","source":{"kind":"arxiv","id":"1801.04561","version":2},"attestation_state":"computed","paper":{"title":"Regular orbits of sporadic simple groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.RT","authors_text":"E. A. O'Brien, Joanna B. Fawcett, J\\\"urgen M\\\"uller, Robert A. Wilson","submitted_at":"2018-01-14T14:17:06Z","abstract_excerpt":"Given a finite group $G$ and a faithful irreducible $FG$-module $V$ where $F$ has prime order, does $G$ have a regular orbit on $V$? This problem is equivalent to determining which primitive permutation groups of affine type have a base of size 2. Let $G$ be a covering group of an almost simple group whose socle $T$ is sporadic, and let $V$ be a faithful irreducible $FG$-module where $F$ has prime order dividing $|G|$. We classify the pairs $(G,V)$ for which $G$ has no regular orbit on $V$, and determine the minimal base size of $G$ in its action on $V$. To obtain this classification, for each"},"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":"1801.04561","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-01-14T14:17:06Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"a5969c07d6ded6188648a0e4383ddf2d0a5d73df186e3e9939ad681b01c8a866","abstract_canon_sha256":"e2067b4128fe5f3d497306aeacfbf575e4bdb79e4a159760b0b86b31722ef6ab"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:07.713779Z","signature_b64":"w+gYkzLIG4yAYJvyfKLPGAM3Y3rNbVLK7RvRxBpOY4+jwcInhUhLYuE3Yfcr3otgZxZyL4+Bk3XqZ0bJDpnWBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1a80c9f53d0b65ceffeaca5026028ff14401b7f80dfe93106e3eb3754377edb5","last_reissued_at":"2026-05-17T23:57:07.713334Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:07.713334Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Regular orbits of sporadic simple groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.RT","authors_text":"E. A. O'Brien, Joanna B. Fawcett, J\\\"urgen M\\\"uller, Robert A. Wilson","submitted_at":"2018-01-14T14:17:06Z","abstract_excerpt":"Given a finite group $G$ and a faithful irreducible $FG$-module $V$ where $F$ has prime order, does $G$ have a regular orbit on $V$? This problem is equivalent to determining which primitive permutation groups of affine type have a base of size 2. Let $G$ be a covering group of an almost simple group whose socle $T$ is sporadic, and let $V$ be a faithful irreducible $FG$-module where $F$ has prime order dividing $|G|$. We classify the pairs $(G,V)$ for which $G$ has no regular orbit on $V$, and determine the minimal base size of $G$ in its action on $V$. To obtain this classification, for each"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.04561","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":"1801.04561","created_at":"2026-05-17T23:57:07.713396+00:00"},{"alias_kind":"arxiv_version","alias_value":"1801.04561v2","created_at":"2026-05-17T23:57:07.713396+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.04561","created_at":"2026-05-17T23:57:07.713396+00:00"},{"alias_kind":"pith_short_12","alias_value":"DKAMT5J5BNS4","created_at":"2026-05-18T12:32:19.392346+00:00"},{"alias_kind":"pith_short_16","alias_value":"DKAMT5J5BNS4577K","created_at":"2026-05-18T12:32:19.392346+00:00"},{"alias_kind":"pith_short_8","alias_value":"DKAMT5J5","created_at":"2026-05-18T12:32:19.392346+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/DKAMT5J5BNS4577KZJICMAUP6F","json":"https://pith.science/pith/DKAMT5J5BNS4577KZJICMAUP6F.json","graph_json":"https://pith.science/api/pith-number/DKAMT5J5BNS4577KZJICMAUP6F/graph.json","events_json":"https://pith.science/api/pith-number/DKAMT5J5BNS4577KZJICMAUP6F/events.json","paper":"https://pith.science/paper/DKAMT5J5"},"agent_actions":{"view_html":"https://pith.science/pith/DKAMT5J5BNS4577KZJICMAUP6F","download_json":"https://pith.science/pith/DKAMT5J5BNS4577KZJICMAUP6F.json","view_paper":"https://pith.science/paper/DKAMT5J5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1801.04561&json=true","fetch_graph":"https://pith.science/api/pith-number/DKAMT5J5BNS4577KZJICMAUP6F/graph.json","fetch_events":"https://pith.science/api/pith-number/DKAMT5J5BNS4577KZJICMAUP6F/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DKAMT5J5BNS4577KZJICMAUP6F/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DKAMT5J5BNS4577KZJICMAUP6F/action/storage_attestation","attest_author":"https://pith.science/pith/DKAMT5J5BNS4577KZJICMAUP6F/action/author_attestation","sign_citation":"https://pith.science/pith/DKAMT5J5BNS4577KZJICMAUP6F/action/citation_signature","submit_replication":"https://pith.science/pith/DKAMT5J5BNS4577KZJICMAUP6F/action/replication_record"}},"created_at":"2026-05-17T23:57:07.713396+00:00","updated_at":"2026-05-17T23:57:07.713396+00:00"}