{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:UUYNDBN3ROWZT2U7JINBBPGAGW","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":"52621101b4ae6ee28ee39dcc4c52278e4cdcee79f70e8a6ba684f85508ba2c82","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-05-04T01:54:49Z","title_canon_sha256":"6a6fd98bd49a2811a78f20e941d23199910259856ebb5757f975add4c42cc92f"},"schema_version":"1.0","source":{"id":"1105.0719","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.0719","created_at":"2026-05-18T03:51:58Z"},{"alias_kind":"arxiv_version","alias_value":"1105.0719v4","created_at":"2026-05-18T03:51:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.0719","created_at":"2026-05-18T03:51:58Z"},{"alias_kind":"pith_short_12","alias_value":"UUYNDBN3ROWZ","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"UUYNDBN3ROWZT2U7","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"UUYNDBN3","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:4cd0a64499fd69e5f980184129d5f2022674296c2d6248876eb8a23cab2449f0","target":"graph","created_at":"2026-05-18T03:51:58Z","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":"In the paper we discuss the algebraic structure of topological full group $[[T]]$ of a Cantor minimal system $(X,T)$. We show that the topological full group $[[T]]$ has the structure similar to a union of permutational wreath products of group $\\mathbb Z$. This allows us to prove that the topological full groups are locally embeddable into finite groups; give an elmentary proof of the fact that group $[[T]]'$ is infinitely presented; and provide explicit examples of maximal locally finite subgroups of $[[T]]$. We also show that the commutator subgroup $[[T]]'$, which is simple and finitely-ge","authors_text":"Konstantin Medynets, Rostislav Grigorchuk","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-05-04T01:54:49Z","title":"On Algebraic Properties of Topological Full Groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.0719","kind":"arxiv","version":4},"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:ed3505da287fb140bec4f46a49cae301947e01ee0963eb0715c6a286a1f3c613","target":"record","created_at":"2026-05-18T03:51:58Z","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":"52621101b4ae6ee28ee39dcc4c52278e4cdcee79f70e8a6ba684f85508ba2c82","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-05-04T01:54:49Z","title_canon_sha256":"6a6fd98bd49a2811a78f20e941d23199910259856ebb5757f975add4c42cc92f"},"schema_version":"1.0","source":{"id":"1105.0719","kind":"arxiv","version":4}},"canonical_sha256":"a530d185bb8bad99ea9f4a1a10bcc035a60225b7ae38aea061bef0647df8d633","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a530d185bb8bad99ea9f4a1a10bcc035a60225b7ae38aea061bef0647df8d633","first_computed_at":"2026-05-18T03:51:58.650850Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:51:58.650850Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6Y07x0ru1MwKviQUZJF4VanNEqEYx+DqUzsIqmGngifyQBSqLMpMsKYCZM8hnR+XnSNL90CVITxzl3PrfDdZDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:51:58.651576Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.0719","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ed3505da287fb140bec4f46a49cae301947e01ee0963eb0715c6a286a1f3c613","sha256:4cd0a64499fd69e5f980184129d5f2022674296c2d6248876eb8a23cab2449f0"],"state_sha256":"daee4926f19d0ce7aad48ba81ad95924da93c0dbdacc2c41a7310aad35911d26"}