{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:2OLE6NYBQ3UWUPWPFN4FDBJAJT","short_pith_number":"pith:2OLE6NYB","schema_version":"1.0","canonical_sha256":"d3964f370186e96a3ecf2b785185204cf235a1b0f77e84aa57a4ef3931211dbf","source":{"kind":"arxiv","id":"1801.08239","version":3},"attestation_state":"computed","paper":{"title":"Geometric finiteness in negatively pinched Hadamard manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.GT"],"primary_cat":"math.GR","authors_text":"Beibei Liu, Michael Kapovich","submitted_at":"2018-01-24T23:33:01Z","abstract_excerpt":"In this paper, we generalize Bonahon's characterization of geometrically infinite torsion-free discrete subgroups of PSL(2, $\\mathbb{C}$) to geometrically infinite discrete subgroups $\\Gamma$ of isometries of negatively pinched Hadamard manifolds $X$. We then generalize a theorem of Bishop to prove that every discrete geometrically infinite isometry subgroup $\\Gamma$ has a set of nonconical limit points with the cardinality of the continuum."},"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":"1801.08239","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-01-24T23:33:01Z","cross_cats_sorted":["math.DG","math.GT"],"title_canon_sha256":"518ff68a1a3ed53d9773936b04ea9a0776af9ae18ada99004240a612909312c0","abstract_canon_sha256":"d3d0e1d59ef885f7d8e18f28e32976e50a82282af3a4e54bb8b23dd967761f56"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:48.682114Z","signature_b64":"44LbgvLLf+1JxdlB6rHuGk7mIhfKBGjMdjwMbDqEGnyD4ixA/Fh5PgG+2Jt05swsen9ZoqiZKyfB1sMyhD77Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d3964f370186e96a3ecf2b785185204cf235a1b0f77e84aa57a4ef3931211dbf","last_reissued_at":"2026-05-17T23:57:48.681693Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:48.681693Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Geometric finiteness in negatively pinched Hadamard manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.GT"],"primary_cat":"math.GR","authors_text":"Beibei Liu, Michael Kapovich","submitted_at":"2018-01-24T23:33:01Z","abstract_excerpt":"In this paper, we generalize Bonahon's characterization of geometrically infinite torsion-free discrete subgroups of PSL(2, $\\mathbb{C}$) to geometrically infinite discrete subgroups $\\Gamma$ of isometries of negatively pinched Hadamard manifolds $X$. We then generalize a theorem of Bishop to prove that every discrete geometrically infinite isometry subgroup $\\Gamma$ has a set of nonconical limit points with the cardinality of the continuum."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.08239","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":"1801.08239","created_at":"2026-05-17T23:57:48.681765+00:00"},{"alias_kind":"arxiv_version","alias_value":"1801.08239v3","created_at":"2026-05-17T23:57:48.681765+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.08239","created_at":"2026-05-17T23:57:48.681765+00:00"},{"alias_kind":"pith_short_12","alias_value":"2OLE6NYBQ3UW","created_at":"2026-05-18T12:32:02.567920+00:00"},{"alias_kind":"pith_short_16","alias_value":"2OLE6NYBQ3UWUPWP","created_at":"2026-05-18T12:32:02.567920+00:00"},{"alias_kind":"pith_short_8","alias_value":"2OLE6NYB","created_at":"2026-05-18T12:32:02.567920+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/2OLE6NYBQ3UWUPWPFN4FDBJAJT","json":"https://pith.science/pith/2OLE6NYBQ3UWUPWPFN4FDBJAJT.json","graph_json":"https://pith.science/api/pith-number/2OLE6NYBQ3UWUPWPFN4FDBJAJT/graph.json","events_json":"https://pith.science/api/pith-number/2OLE6NYBQ3UWUPWPFN4FDBJAJT/events.json","paper":"https://pith.science/paper/2OLE6NYB"},"agent_actions":{"view_html":"https://pith.science/pith/2OLE6NYBQ3UWUPWPFN4FDBJAJT","download_json":"https://pith.science/pith/2OLE6NYBQ3UWUPWPFN4FDBJAJT.json","view_paper":"https://pith.science/paper/2OLE6NYB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1801.08239&json=true","fetch_graph":"https://pith.science/api/pith-number/2OLE6NYBQ3UWUPWPFN4FDBJAJT/graph.json","fetch_events":"https://pith.science/api/pith-number/2OLE6NYBQ3UWUPWPFN4FDBJAJT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2OLE6NYBQ3UWUPWPFN4FDBJAJT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2OLE6NYBQ3UWUPWPFN4FDBJAJT/action/storage_attestation","attest_author":"https://pith.science/pith/2OLE6NYBQ3UWUPWPFN4FDBJAJT/action/author_attestation","sign_citation":"https://pith.science/pith/2OLE6NYBQ3UWUPWPFN4FDBJAJT/action/citation_signature","submit_replication":"https://pith.science/pith/2OLE6NYBQ3UWUPWPFN4FDBJAJT/action/replication_record"}},"created_at":"2026-05-17T23:57:48.681765+00:00","updated_at":"2026-05-17T23:57:48.681765+00:00"}