{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:6VJSJEUQSGNDMQ7H62VVSUPKIL","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":"a3311ffed46ee5684fd2d294666181dface06badd6f73b9bf0fdb40fb3863a31","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2021-06-09T15:52:39Z","title_canon_sha256":"95955d9ca652c1cb8fb74050dd06269fd17f14d4a5d274a892521bf1f45bf33e"},"schema_version":"1.0","source":{"id":"2106.05154","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2106.05154","created_at":"2026-07-05T02:56:40Z"},{"alias_kind":"arxiv_version","alias_value":"2106.05154v2","created_at":"2026-07-05T02:56:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.05154","created_at":"2026-07-05T02:56:40Z"},{"alias_kind":"pith_short_12","alias_value":"6VJSJEUQSGND","created_at":"2026-07-05T02:56:40Z"},{"alias_kind":"pith_short_16","alias_value":"6VJSJEUQSGNDMQ7H","created_at":"2026-07-05T02:56:40Z"},{"alias_kind":"pith_short_8","alias_value":"6VJSJEUQ","created_at":"2026-07-05T02:56:40Z"}],"graph_snapshots":[{"event_id":"sha256:e55239212b8c4d8ab63038f3fae93abfab54793d21546ff5f4c7140cb62f3a2e","target":"graph","created_at":"2026-07-05T02:56:40Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2106.05154/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A permutation group is {\\it binary} if its orbits on $k$-tuples, for any integer $k\\geq 2$, can be deduced from its orbits on $2$-tuples. Cherlin conjectured that a finite primitive binary permutation group $G$ must lie in one of three known families. In this paper we complete the proof of this conjecture. To do this we study the case where the group $G$ is almost simple of Lie type.","authors_text":"Martin W. Liebeck, Nick Gill, Pablo Spiga","cross_cats":["math.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2021-06-09T15:52:39Z","title":"Cherlin's conjecture on finite primitive binary permutation groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.05154","kind":"arxiv","version":2},"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":"sha256:172eb6f6d19d0206613a4874159a6cd80730296df603503bc6d1786c1855b1c8","target":"record","created_at":"2026-07-05T02:56:40Z","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":"a3311ffed46ee5684fd2d294666181dface06badd6f73b9bf0fdb40fb3863a31","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2021-06-09T15:52:39Z","title_canon_sha256":"95955d9ca652c1cb8fb74050dd06269fd17f14d4a5d274a892521bf1f45bf33e"},"schema_version":"1.0","source":{"id":"2106.05154","kind":"arxiv","version":2}},"canonical_sha256":"f553249290919a3643e7f6ab5951ea42e2f21dcca02a456dcdd99babe6694d3e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f553249290919a3643e7f6ab5951ea42e2f21dcca02a456dcdd99babe6694d3e","first_computed_at":"2026-07-05T02:56:40.058286Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:56:40.058286Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DmVx7CHOWH4vIz2guBIsa1ZPMLV5cjtpb9/dAS3AIgyNMnLRjdGf5po/Efxa4UgR1aoGrUvQjdGXNz5mWsMFCg==","signature_status":"signed_v1","signed_at":"2026-07-05T02:56:40.058681Z","signed_message":"canonical_sha256_bytes"},"source_id":"2106.05154","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:172eb6f6d19d0206613a4874159a6cd80730296df603503bc6d1786c1855b1c8","sha256:e55239212b8c4d8ab63038f3fae93abfab54793d21546ff5f4c7140cb62f3a2e"],"state_sha256":"ba188fefb8d3803bc7a078532530fbaa5849f64026eae810996a88e05c9a7900"}