{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:26J4VXC4BSUWCN4A23ZSESOSWO","short_pith_number":"pith:26J4VXC4","schema_version":"1.0","canonical_sha256":"d793cadc5c0ca9613780d6f32249d2b3bbe0fffd325ce29732d2886f7727403a","source":{"kind":"arxiv","id":"1004.1751","version":1},"attestation_state":"computed","paper":{"title":"Limit sets and commensurability of Kleinian groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"Wen-yuan Yang, Yue-ping Jiang","submitted_at":"2010-04-10T23:14:17Z","abstract_excerpt":"In this paper, we obtain several results on the commensurability of two Kleinian groups and their limit sets. We prove that two finitely generated subgroups $G_1$ and $G_2$ of an infinite co-volume Kleinian group $G \\subset \\Isom(\\mathbf{H}^3)$ having $\\Lambda(G_1) = \\Lambda(G_2)$ are commensurable. In particular, it is proved that any finitely generated subgroup $H$ of a Kleinian group $G \\subset \\Isom(\\mathbf{H}^3)$ with $\\Lambda(H) = \\Lambda(G)$ is of finite index if and only if $H$ is not a virtually fiber subgroup."},"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":"1004.1751","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-04-10T23:14:17Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"18ff2fa44ad3d73a74be50d897ae0bebdb8195690975e6ca61e03969fdc2cd99","abstract_canon_sha256":"6c2837f26b4cf4ac4205fef0e2941a75f8a10e1bda0fe23096cb94eca8631dab"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:40:55.955452Z","signature_b64":"6Xr5Hw2znWNqZlGAc8d+BMNpNSWVff59429J9BA638ypS42BXPTxkiFoJlz90/X8VgSi/8EEzzss8ezCA18BDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d793cadc5c0ca9613780d6f32249d2b3bbe0fffd325ce29732d2886f7727403a","last_reissued_at":"2026-05-18T04:40:55.954936Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:40:55.954936Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Limit sets and commensurability of Kleinian groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"Wen-yuan Yang, Yue-ping Jiang","submitted_at":"2010-04-10T23:14:17Z","abstract_excerpt":"In this paper, we obtain several results on the commensurability of two Kleinian groups and their limit sets. We prove that two finitely generated subgroups $G_1$ and $G_2$ of an infinite co-volume Kleinian group $G \\subset \\Isom(\\mathbf{H}^3)$ having $\\Lambda(G_1) = \\Lambda(G_2)$ are commensurable. In particular, it is proved that any finitely generated subgroup $H$ of a Kleinian group $G \\subset \\Isom(\\mathbf{H}^3)$ with $\\Lambda(H) = \\Lambda(G)$ is of finite index if and only if $H$ is not a virtually fiber subgroup."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.1751","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":""},"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":"1004.1751","created_at":"2026-05-18T04:40:55.955011+00:00"},{"alias_kind":"arxiv_version","alias_value":"1004.1751v1","created_at":"2026-05-18T04:40:55.955011+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.1751","created_at":"2026-05-18T04:40:55.955011+00:00"},{"alias_kind":"pith_short_12","alias_value":"26J4VXC4BSUW","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_16","alias_value":"26J4VXC4BSUWCN4A","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_8","alias_value":"26J4VXC4","created_at":"2026-05-18T12:26:03.138858+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/26J4VXC4BSUWCN4A23ZSESOSWO","json":"https://pith.science/pith/26J4VXC4BSUWCN4A23ZSESOSWO.json","graph_json":"https://pith.science/api/pith-number/26J4VXC4BSUWCN4A23ZSESOSWO/graph.json","events_json":"https://pith.science/api/pith-number/26J4VXC4BSUWCN4A23ZSESOSWO/events.json","paper":"https://pith.science/paper/26J4VXC4"},"agent_actions":{"view_html":"https://pith.science/pith/26J4VXC4BSUWCN4A23ZSESOSWO","download_json":"https://pith.science/pith/26J4VXC4BSUWCN4A23ZSESOSWO.json","view_paper":"https://pith.science/paper/26J4VXC4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1004.1751&json=true","fetch_graph":"https://pith.science/api/pith-number/26J4VXC4BSUWCN4A23ZSESOSWO/graph.json","fetch_events":"https://pith.science/api/pith-number/26J4VXC4BSUWCN4A23ZSESOSWO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/26J4VXC4BSUWCN4A23ZSESOSWO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/26J4VXC4BSUWCN4A23ZSESOSWO/action/storage_attestation","attest_author":"https://pith.science/pith/26J4VXC4BSUWCN4A23ZSESOSWO/action/author_attestation","sign_citation":"https://pith.science/pith/26J4VXC4BSUWCN4A23ZSESOSWO/action/citation_signature","submit_replication":"https://pith.science/pith/26J4VXC4BSUWCN4A23ZSESOSWO/action/replication_record"}},"created_at":"2026-05-18T04:40:55.955011+00:00","updated_at":"2026-05-18T04:40:55.955011+00:00"}