{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:FHKA3GLNWSX65GS2XQNSOSPSPT","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":"bfcd17de25befa3b8705dcaa22ac125d887180167f27947c517ca86653a961d0","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-01-09T14:32:10Z","title_canon_sha256":"3be9da26b2841d6437b6ef0fbd67b1edbf1b44ffc6a00d3817b48b2f3a5e8c4b"},"schema_version":"1.0","source":{"id":"1401.2017","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.2017","created_at":"2026-05-18T02:59:20Z"},{"alias_kind":"arxiv_version","alias_value":"1401.2017v1","created_at":"2026-05-18T02:59:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.2017","created_at":"2026-05-18T02:59:20Z"},{"alias_kind":"pith_short_12","alias_value":"FHKA3GLNWSX6","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"FHKA3GLNWSX65GS2","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"FHKA3GLN","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:fa8d57bc3e1acf7bf2911b3904bd366d30305e6b6584ea5f873b787743af7ecb","target":"graph","created_at":"2026-05-18T02:59:20Z","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 show that for a wide class of groups of finite Morley rank the presence of a split $BN$-pair of Tits rank $1$ forces the group to be of the form $\\operatorname{PSL}_2$ and the $BN$-pair to be standard. Our approach is via the theory of Moufang sets. Specifically, we investigate infinite and so-called hereditarily proper Moufang sets of finite Morley rank in the case where the little projective group has no infinite elementary abelian $2$-subgroups and show that all such Moufang sets are standard (and thus associated to $\\operatorname{PSL}_2(F)$ for $F$ an algebraically closed field of chara","authors_text":"Joshua Wiscons","cross_cats":["math.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-01-09T14:32:10Z","title":"Moufang sets of finite Morley rank of odd type"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.2017","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":"sha256:4a66f99c6e02f67e4df7b064197d5e2ce4283bd222080fcfb009f03821bf5cd8","target":"record","created_at":"2026-05-18T02:59:20Z","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":"bfcd17de25befa3b8705dcaa22ac125d887180167f27947c517ca86653a961d0","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-01-09T14:32:10Z","title_canon_sha256":"3be9da26b2841d6437b6ef0fbd67b1edbf1b44ffc6a00d3817b48b2f3a5e8c4b"},"schema_version":"1.0","source":{"id":"1401.2017","kind":"arxiv","version":1}},"canonical_sha256":"29d40d996db4afee9a5abc1b2749f27cec9343026476c520ac5e6318bb13d1ff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"29d40d996db4afee9a5abc1b2749f27cec9343026476c520ac5e6318bb13d1ff","first_computed_at":"2026-05-18T02:59:20.266922Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:59:20.266922Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Oulvau72kVzcyIs0R/7F3mMS09yHrKaK1sJB9w1PE1kjqCbISt6dTNxpJQUlohyun0t77cCDRwVj0/u9BSmnDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:59:20.267898Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.2017","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4a66f99c6e02f67e4df7b064197d5e2ce4283bd222080fcfb009f03821bf5cd8","sha256:fa8d57bc3e1acf7bf2911b3904bd366d30305e6b6584ea5f873b787743af7ecb"],"state_sha256":"e03f9aeffdd9eaced63a8ad3da567db0516d57d123a87b166a1cfb0a51f93992"}