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This class contains many generalisations of the Higman-Thompson groups $G_{n,r}$, and the Rational group $\\mathcal{R}_{2}$ of Grigorchuk, Nekrashevych, and Suchanski{\\u \\i}. We also demonstrate that for generalisations $T_{n,r}$ of R. Thompson's group $T$, $\\mathrm{Aut}(\\mathrm{Aut}(T_{n,r}))= \\mathrm{Aut}(T_{n,r})$. In the case of the groups $G_{n,r}$ and $T_{n,r}$ our results extend results of Brin and Guzm{\\' a}n for T"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1908.03815","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-08-10T21:53:08Z","cross_cats_sorted":[],"title_canon_sha256":"d54201efd79fe8addcb4e953441708665521f949aa2e8bcd437d8d814a08aa90","abstract_canon_sha256":"6d184422ad5a4209b54071869bbf084bf84b9392c35bee52a41a1b61401181a7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:28:17.785171Z","signature_b64":"zNI0cThVmzZWK+ZP4Geh5aIrkFlcqCeQzOT6xBJo5roVpOxOs1gVJllXBQhYfGYlNnFa9+KSQy9biFIGJMclBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f91147ab8e0b2b40cd40588d10638ae243498c7404e4ebe83eb7aecfd1ff28ea","last_reissued_at":"2026-07-05T01:28:17.784775Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:28:17.784775Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Automorphism towers of groups of homeomorphisms of Cantor space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Feyishayo Olukoya","submitted_at":"2019-08-10T21:53:08Z","abstract_excerpt":"We show that for any full and sufficiently transitive (i.e. \\textit{flexible}) group $G$ of homeomorphisms of Cantor space, $\\mathrm{Aut}(\\mathrm{Aut}(G)) = \\mathrm{Aut}(G)$. 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In the case of the groups $G_{n,r}$ and $T_{n,r}$ our results extend results of Brin and Guzm{\\' a}n for T"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.03815","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.03815/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1908.03815","created_at":"2026-07-05T01:28:17.784834+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.03815v2","created_at":"2026-07-05T01:28:17.784834+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.03815","created_at":"2026-07-05T01:28:17.784834+00:00"},{"alias_kind":"pith_short_12","alias_value":"7EIUPK4OBMVU","created_at":"2026-07-05T01:28:17.784834+00:00"},{"alias_kind":"pith_short_16","alias_value":"7EIUPK4OBMVUBTKA","created_at":"2026-07-05T01:28:17.784834+00:00"},{"alias_kind":"pith_short_8","alias_value":"7EIUPK4O","created_at":"2026-07-05T01:28:17.784834+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7EIUPK4OBMVUBTKALCGRAY4K4J","json":"https://pith.science/pith/7EIUPK4OBMVUBTKALCGRAY4K4J.json","graph_json":"https://pith.science/api/pith-number/7EIUPK4OBMVUBTKALCGRAY4K4J/graph.json","events_json":"https://pith.science/api/pith-number/7EIUPK4OBMVUBTKALCGRAY4K4J/events.json","paper":"https://pith.science/paper/7EIUPK4O"},"agent_actions":{"view_html":"https://pith.science/pith/7EIUPK4OBMVUBTKALCGRAY4K4J","download_json":"https://pith.science/pith/7EIUPK4OBMVUBTKALCGRAY4K4J.json","view_paper":"https://pith.science/paper/7EIUPK4O","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.03815&json=true","fetch_graph":"https://pith.science/api/pith-number/7EIUPK4OBMVUBTKALCGRAY4K4J/graph.json","fetch_events":"https://pith.science/api/pith-number/7EIUPK4OBMVUBTKALCGRAY4K4J/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7EIUPK4OBMVUBTKALCGRAY4K4J/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7EIUPK4OBMVUBTKALCGRAY4K4J/action/storage_attestation","attest_author":"https://pith.science/pith/7EIUPK4OBMVUBTKALCGRAY4K4J/action/author_attestation","sign_citation":"https://pith.science/pith/7EIUPK4OBMVUBTKALCGRAY4K4J/action/citation_signature","submit_replication":"https://pith.science/pith/7EIUPK4OBMVUBTKALCGRAY4K4J/action/replication_record"}},"created_at":"2026-07-05T01:28:17.784834+00:00","updated_at":"2026-07-05T01:28:17.784834+00:00"}