{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:2OLE6NYBQ3UWUPWPFN4FDBJAJT","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"d3d0e1d59ef885f7d8e18f28e32976e50a82282af3a4e54bb8b23dd967761f56","cross_cats_sorted":["math.DG","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-01-24T23:33:01Z","title_canon_sha256":"518ff68a1a3ed53d9773936b04ea9a0776af9ae18ada99004240a612909312c0"},"schema_version":"1.0","source":{"id":"1801.08239","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.08239","created_at":"2026-05-17T23:57:48Z"},{"alias_kind":"arxiv_version","alias_value":"1801.08239v3","created_at":"2026-05-17T23:57:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.08239","created_at":"2026-05-17T23:57:48Z"},{"alias_kind":"pith_short_12","alias_value":"2OLE6NYBQ3UW","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"2OLE6NYBQ3UWUPWP","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"2OLE6NYB","created_at":"2026-05-18T12:32:02Z"}],"graph_snapshots":[{"event_id":"sha256:f1f12fd3faa1f69e966daf8ddfce6e329dc5a5602fc4c1fc97b2ad10bba8bcba","target":"graph","created_at":"2026-05-17T23:57:48Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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.","authors_text":"Beibei Liu, Michael Kapovich","cross_cats":["math.DG","math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-01-24T23:33:01Z","title":"Geometric finiteness in negatively pinched Hadamard manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.08239","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:d8b4917c00a70de37c2e5f0b25bb37028a5a20a768897f7bfc1dad649d77d422","target":"record","created_at":"2026-05-17T23:57:48Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"d3d0e1d59ef885f7d8e18f28e32976e50a82282af3a4e54bb8b23dd967761f56","cross_cats_sorted":["math.DG","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-01-24T23:33:01Z","title_canon_sha256":"518ff68a1a3ed53d9773936b04ea9a0776af9ae18ada99004240a612909312c0"},"schema_version":"1.0","source":{"id":"1801.08239","kind":"arxiv","version":3}},"canonical_sha256":"d3964f370186e96a3ecf2b785185204cf235a1b0f77e84aa57a4ef3931211dbf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d3964f370186e96a3ecf2b785185204cf235a1b0f77e84aa57a4ef3931211dbf","first_computed_at":"2026-05-17T23:57:48.681693Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:48.681693Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"44LbgvLLf+1JxdlB6rHuGk7mIhfKBGjMdjwMbDqEGnyD4ixA/Fh5PgG+2Jt05swsen9ZoqiZKyfB1sMyhD77Cg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:48.682114Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.08239","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d8b4917c00a70de37c2e5f0b25bb37028a5a20a768897f7bfc1dad649d77d422","sha256:f1f12fd3faa1f69e966daf8ddfce6e329dc5a5602fc4c1fc97b2ad10bba8bcba"],"state_sha256":"143db3162b56ed7a4e21b3384a121f630a55520b321daf3ce332f8beccb3aee0"}