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In a natural way, $M_m(L_r^{\\otimes t})$ is a partially ordered ring with involution. Let $PU_m(L_r^{\\otimes t})$ denote the group of positive unitary elements. We show that $PU_m(L_r^{\\otimes t})$ is isomorphic to the Brin-Higman-Thompson group $t V_{r,m}$; the case $t =1$ was found by Pardo, that is, $PU_m(L_r)$ is isomorphic to 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":"1112.1606","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-12-07T16:10:28Z","cross_cats_sorted":[],"title_canon_sha256":"a58699d7fa4de29dc0b707219c7e54f218b424c05f09e488570dffb608f3de0b","abstract_canon_sha256":"7e0429526856ab224a616f56a9ad4332e3866d3d0dbe50965333e6ea7f4aa373"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:48:26.275104Z","signature_b64":"r3B7gEfJQqcsKTuRaz8LE+ZqjxIH9E3B2IpqRKkSHWTrV3I2wAefu59PUPKo6ekCZ6y4kA4/WmR4pEydi/F4BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"51091b5bd9ee6c6baeccb50be67eb55b95596d77c6debabbade4d59cd12867d2","last_reissued_at":"2026-05-18T02:48:26.274591Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:48:26.274591Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Isomorphisms of Brin-Higman-Thompson groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Conchita Mart\\'inez-P\\'erez, Warren Dicks","submitted_at":"2011-12-07T16:10:28Z","abstract_excerpt":"Let $m, m', r, r',t, t'$ be positive integers with $r, r' \\ge 2$. Let $L_r$ denote the ring that is universal with an invertible $1 \\times r$ matrix. Let $M_m(L_r^{\\otimes t})$ denote the ring of $m \\times m$ matrices over the tensor product of $t$ copies of $L_r$. In a natural way, $M_m(L_r^{\\otimes t})$ is a partially ordered ring with involution. Let $PU_m(L_r^{\\otimes t})$ denote the group of positive unitary elements. We show that $PU_m(L_r^{\\otimes t})$ is isomorphic to the Brin-Higman-Thompson group $t V_{r,m}$; the case $t =1$ was found by Pardo, that is, $PU_m(L_r)$ is isomorphic to t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.1606","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1112.1606","created_at":"2026-05-18T02:48:26.274667+00:00"},{"alias_kind":"arxiv_version","alias_value":"1112.1606v3","created_at":"2026-05-18T02:48:26.274667+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.1606","created_at":"2026-05-18T02:48:26.274667+00:00"},{"alias_kind":"pith_short_12","alias_value":"KEERWW6Z5ZWG","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_16","alias_value":"KEERWW6Z5ZWGXLWM","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_8","alias_value":"KEERWW6Z","created_at":"2026-05-18T12:26:32.869790+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/KEERWW6Z5ZWGXLWMWUF6M7VVLO","json":"https://pith.science/pith/KEERWW6Z5ZWGXLWMWUF6M7VVLO.json","graph_json":"https://pith.science/api/pith-number/KEERWW6Z5ZWGXLWMWUF6M7VVLO/graph.json","events_json":"https://pith.science/api/pith-number/KEERWW6Z5ZWGXLWMWUF6M7VVLO/events.json","paper":"https://pith.science/paper/KEERWW6Z"},"agent_actions":{"view_html":"https://pith.science/pith/KEERWW6Z5ZWGXLWMWUF6M7VVLO","download_json":"https://pith.science/pith/KEERWW6Z5ZWGXLWMWUF6M7VVLO.json","view_paper":"https://pith.science/paper/KEERWW6Z","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1112.1606&json=true","fetch_graph":"https://pith.science/api/pith-number/KEERWW6Z5ZWGXLWMWUF6M7VVLO/graph.json","fetch_events":"https://pith.science/api/pith-number/KEERWW6Z5ZWGXLWMWUF6M7VVLO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KEERWW6Z5ZWGXLWMWUF6M7VVLO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KEERWW6Z5ZWGXLWMWUF6M7VVLO/action/storage_attestation","attest_author":"https://pith.science/pith/KEERWW6Z5ZWGXLWMWUF6M7VVLO/action/author_attestation","sign_citation":"https://pith.science/pith/KEERWW6Z5ZWGXLWMWUF6M7VVLO/action/citation_signature","submit_replication":"https://pith.science/pith/KEERWW6Z5ZWGXLWMWUF6M7VVLO/action/replication_record"}},"created_at":"2026-05-18T02:48:26.274667+00:00","updated_at":"2026-05-18T02:48:26.274667+00:00"}