{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:G57ATPY56LT7TKBPFHO7UQRZT3","short_pith_number":"pith:G57ATPY5","schema_version":"1.0","canonical_sha256":"377e09bf1df2e7f9a82f29ddfa42399ee7e94d05c7d1e1812a491d7abc993402","source":{"kind":"arxiv","id":"2411.09069","version":1},"attestation_state":"computed","paper":{"title":"The Higman--Thompson groups $V_n$ are $(2,2,2)$-generated","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Eduard Schesler, Rachel Skipper, Xiaolei Wu","submitted_at":"2024-11-13T22:50:08Z","abstract_excerpt":"We provide a family of generating sets $S_{\\alpha}$ of the Higman--Thompson groups $V_n$ that are parametrized by certain sequences $\\alpha$ of elements in $V_n$. These generating sets consist of $3$ involutions $\\sigma$, $\\tau$, and $s_{\\alpha}$, where the latter involution is inspired by the class of spinal elements in the theory of branch groups. In particular this shows the existence of generating sets of $V_n$ that consist of $3$ involutions."},"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":"2411.09069","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2024-11-13T22:50:08Z","cross_cats_sorted":[],"title_canon_sha256":"8c247975b354d102f18611f7f45eed1d25bf96c69d2c32c0c3b8c8b7563f3a63","abstract_canon_sha256":"b1f639f968703a9e2b7eaec44451634946228fff53e629030268a7995bb6865e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:35:19.359698Z","signature_b64":"OH9cjxLOjK6+zrfR1ti1SFJca19TMCox35CqJhyHDXlxuM/lrFi+Et/TI/joO5eXUKqeIEpjTOXL98t3vtF3DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"377e09bf1df2e7f9a82f29ddfa42399ee7e94d05c7d1e1812a491d7abc993402","last_reissued_at":"2026-07-05T09:35:19.359235Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:35:19.359235Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Higman--Thompson groups $V_n$ are $(2,2,2)$-generated","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Eduard Schesler, Rachel Skipper, Xiaolei Wu","submitted_at":"2024-11-13T22:50:08Z","abstract_excerpt":"We provide a family of generating sets $S_{\\alpha}$ of the Higman--Thompson groups $V_n$ that are parametrized by certain sequences $\\alpha$ of elements in $V_n$. These generating sets consist of $3$ involutions $\\sigma$, $\\tau$, and $s_{\\alpha}$, where the latter involution is inspired by the class of spinal elements in the theory of branch groups. In particular this shows the existence of generating sets of $V_n$ that consist of $3$ involutions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.09069","kind":"arxiv","version":1},"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/2411.09069/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":"2411.09069","created_at":"2026-07-05T09:35:19.359292+00:00"},{"alias_kind":"arxiv_version","alias_value":"2411.09069v1","created_at":"2026-07-05T09:35:19.359292+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.09069","created_at":"2026-07-05T09:35:19.359292+00:00"},{"alias_kind":"pith_short_12","alias_value":"G57ATPY56LT7","created_at":"2026-07-05T09:35:19.359292+00:00"},{"alias_kind":"pith_short_16","alias_value":"G57ATPY56LT7TKBP","created_at":"2026-07-05T09:35:19.359292+00:00"},{"alias_kind":"pith_short_8","alias_value":"G57ATPY5","created_at":"2026-07-05T09:35:19.359292+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2507.06599","citing_title":"Minimal sofic shift on a group that is not finitely-generated","ref_index":35,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/G57ATPY56LT7TKBPFHO7UQRZT3","json":"https://pith.science/pith/G57ATPY56LT7TKBPFHO7UQRZT3.json","graph_json":"https://pith.science/api/pith-number/G57ATPY56LT7TKBPFHO7UQRZT3/graph.json","events_json":"https://pith.science/api/pith-number/G57ATPY56LT7TKBPFHO7UQRZT3/events.json","paper":"https://pith.science/paper/G57ATPY5"},"agent_actions":{"view_html":"https://pith.science/pith/G57ATPY56LT7TKBPFHO7UQRZT3","download_json":"https://pith.science/pith/G57ATPY56LT7TKBPFHO7UQRZT3.json","view_paper":"https://pith.science/paper/G57ATPY5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2411.09069&json=true","fetch_graph":"https://pith.science/api/pith-number/G57ATPY56LT7TKBPFHO7UQRZT3/graph.json","fetch_events":"https://pith.science/api/pith-number/G57ATPY56LT7TKBPFHO7UQRZT3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/G57ATPY56LT7TKBPFHO7UQRZT3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/G57ATPY56LT7TKBPFHO7UQRZT3/action/storage_attestation","attest_author":"https://pith.science/pith/G57ATPY56LT7TKBPFHO7UQRZT3/action/author_attestation","sign_citation":"https://pith.science/pith/G57ATPY56LT7TKBPFHO7UQRZT3/action/citation_signature","submit_replication":"https://pith.science/pith/G57ATPY56LT7TKBPFHO7UQRZT3/action/replication_record"}},"created_at":"2026-07-05T09:35:19.359292+00:00","updated_at":"2026-07-05T09:35:19.359292+00:00"}