{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:FFRS4ALHE3F2NIFIRKVKSKXPLQ","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":"2e70424f1261ae3f0a3f65d2bf6609393da8770d0c738bbd3095259f8e66ddbb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-12-09T05:54:28Z","title_canon_sha256":"80c70a5aaf14864e81178357bbd0f6c54d4893eeaf0cb5a90bb7fa4a5a5646aa"},"schema_version":"1.0","source":{"id":"1312.2311","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.2311","created_at":"2026-05-18T02:41:08Z"},{"alias_kind":"arxiv_version","alias_value":"1312.2311v2","created_at":"2026-05-18T02:41:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.2311","created_at":"2026-05-18T02:41:08Z"},{"alias_kind":"pith_short_12","alias_value":"FFRS4ALHE3F2","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"FFRS4ALHE3F2NIFI","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"FFRS4ALH","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:ed4e67da801e5308982bc87c21f27bd0a462e487bbd38bb3a02daa5fba682194","target":"graph","created_at":"2026-05-18T02:41:08Z","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 introduce the notion of the $k$-closure of a group of automorphisms of a locally finite tree, and give several examples of the construction. We show that the $k$-closure satisfies a new property of automorphism groups of trees that generalises Tits' Property $P$. We prove that, apart from some degenerate cases, any non-discrete group acting on a tree with this property contains an abstractly simple subgroup.","authors_text":"Christopher C. Banks, George A. Willis, Murray Elder","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-12-09T05:54:28Z","title":"Simple groups of automorphisms of trees determined by their actions on finite subtrees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.2311","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":"sha256:38be676db551073ef7ad9e9081230947ad5e6e373eafc0c5ed4a2f8c34523059","target":"record","created_at":"2026-05-18T02:41:08Z","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":"2e70424f1261ae3f0a3f65d2bf6609393da8770d0c738bbd3095259f8e66ddbb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-12-09T05:54:28Z","title_canon_sha256":"80c70a5aaf14864e81178357bbd0f6c54d4893eeaf0cb5a90bb7fa4a5a5646aa"},"schema_version":"1.0","source":{"id":"1312.2311","kind":"arxiv","version":2}},"canonical_sha256":"29632e016726cba6a0a88aaaa92aef5c2f170621fae3e5c1b9c50826528f125e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"29632e016726cba6a0a88aaaa92aef5c2f170621fae3e5c1b9c50826528f125e","first_computed_at":"2026-05-18T02:41:08.810587Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:08.810587Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lLCUfEcdOp+Vqs6cpyI1ZI9W4E+HZDW13ZTz3v9byJW05Hrs8If/wVc2wZxfua1fyliJJ406+dex2RoDB4NkCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:08.811009Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.2311","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:38be676db551073ef7ad9e9081230947ad5e6e373eafc0c5ed4a2f8c34523059","sha256:ed4e67da801e5308982bc87c21f27bd0a462e487bbd38bb3a02daa5fba682194"],"state_sha256":"47d3d21861727f1d31e806133e1ec133830554caea6e0d9faceb3753fb4ba97f"}