{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:BYS3KZKSYP6C4QLLPYQILCZDLQ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"f0bac385a3b3bf7cf7759a2d4af07fc6403aec52b0a1fae8bf33032c828db64b","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-09-26T09:52:35Z","title_canon_sha256":"3b65cd2a91de7e7719b51698a041672a5a3b9347d96c1f523de0b70b1096f5bd"},"schema_version":"1.0","source":{"id":"1409.7518","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.7518","created_at":"2026-05-18T02:28:20Z"},{"alias_kind":"arxiv_version","alias_value":"1409.7518v1","created_at":"2026-05-18T02:28:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.7518","created_at":"2026-05-18T02:28:20Z"},{"alias_kind":"pith_short_12","alias_value":"BYS3KZKSYP6C","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"BYS3KZKSYP6C4QLL","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"BYS3KZKS","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:3b2fb79df28668f81d60aee210e2fa00f36bb162f979dc9894c90bbeaaa29be9","target":"graph","created_at":"2026-05-18T02:28:20Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We prove that if $G$ is a finite simple group which is the unit group of a ring, then $G$ is isomorphic to either (a) a cyclic group of order 2; (b) a cyclic group of prime order $2^k -1$ for some $k$; or (c) a projective special linear group $PSL_n(\\mathbb{F}_2)$ for some $n \\geq 3$. Moreover, these groups do (trivially) all occur as unit groups. We deduce this classification from a more general result, which holds for groups $G$ with no non-trivial normal 2-subgroup.","authors_text":"Christopher Davis, Tommy Occhipinti","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-09-26T09:52:35Z","title":"Which finite simple groups are unit groups?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.7518","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:5fa59f9b337cebbf0dddd096b42029ab002b9ab036f14ce776421b35777c719c","target":"record","created_at":"2026-05-18T02:28:20Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"f0bac385a3b3bf7cf7759a2d4af07fc6403aec52b0a1fae8bf33032c828db64b","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-09-26T09:52:35Z","title_canon_sha256":"3b65cd2a91de7e7719b51698a041672a5a3b9347d96c1f523de0b70b1096f5bd"},"schema_version":"1.0","source":{"id":"1409.7518","kind":"arxiv","version":1}},"canonical_sha256":"0e25b56552c3fc2e416b7e20858b235c0834a3377bb1ac422875ab859dd9b7f5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0e25b56552c3fc2e416b7e20858b235c0834a3377bb1ac422875ab859dd9b7f5","first_computed_at":"2026-05-18T02:28:20.553118Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:20.553118Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fCRyMG/wRwJV79DyLXERgj23G+TFgtpjT5fiAoFjZqOtZ5+nY3zSdOxZVc2NdAEngTL66zIvklPluIPjoHUYBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:20.553824Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.7518","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5fa59f9b337cebbf0dddd096b42029ab002b9ab036f14ce776421b35777c719c","sha256:3b2fb79df28668f81d60aee210e2fa00f36bb162f979dc9894c90bbeaaa29be9"],"state_sha256":"ff95acee24cc6da8a78554e40b61e00dc9e756f8d7f3730672b74d5f3c0d1673"}