{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2003:XPRYKBQP5JYVCOVZEF7EAYZ5M2","short_pith_number":"pith:XPRYKBQP","schema_version":"1.0","canonical_sha256":"bbe385060fea71513ab9217e40633d66b4ce4744e3ca99ebd2399e4eb749313d","source":{"kind":"arxiv","id":"math/0308274","version":3},"attestation_state":"computed","paper":{"title":"Parabolic isometries of CAT(0) spaces and CAT(0) dimensions","license":"","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"Koji Fujiwara, Saeko Yamagata, Takashi Shioya","submitted_at":"2003-08-28T11:37:52Z","abstract_excerpt":"We study discrete groups from the view point of a dimension gap in connection to CAT(0) geometry. Developing studies by Brady-Crisp and Bridson, we show that there exist finitely presented groups of geometric dimension 2 which do not act properly on any proper CAT(0) spaces of dimension 2 by isometries, although such actions exist on CAT(0) spaces of dimension 3.\n  Another example is the fundamental group, G, of a complete, non-compact, complex hyperbolic manifold M with finite volume, of complex-dimension n > 1. The group G is acting on the universal cover of M, which is isometric to H^n_C. I"},"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":"math/0308274","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.GT","submitted_at":"2003-08-28T11:37:52Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"a77e00beefa21a3d38bacdfe970f3d9b33752cac545540c61c1aadc9aa5a4b71","abstract_canon_sha256":"b186a2a18bdc2e57dd6d077e019279f48247073a643ef1e7868907dc5a228527"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:32.618386Z","signature_b64":"ZbtMYcuoXRaxXJ/NG7ZZykIvCk5Z2WCIOnX5nqyNuGYZoCQML82wj0/2qhbUImHxaFXQhx15Znynka4TIP/qCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bbe385060fea71513ab9217e40633d66b4ce4744e3ca99ebd2399e4eb749313d","last_reissued_at":"2026-05-18T02:41:32.618008Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:32.618008Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Parabolic isometries of CAT(0) spaces and CAT(0) dimensions","license":"","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"Koji Fujiwara, Saeko Yamagata, Takashi Shioya","submitted_at":"2003-08-28T11:37:52Z","abstract_excerpt":"We study discrete groups from the view point of a dimension gap in connection to CAT(0) geometry. Developing studies by Brady-Crisp and Bridson, we show that there exist finitely presented groups of geometric dimension 2 which do not act properly on any proper CAT(0) spaces of dimension 2 by isometries, although such actions exist on CAT(0) spaces of dimension 3.\n  Another example is the fundamental group, G, of a complete, non-compact, complex hyperbolic manifold M with finite volume, of complex-dimension n > 1. The group G is acting on the universal cover of M, which is isometric to H^n_C. I"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0308274","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":"math/0308274","created_at":"2026-05-18T02:41:32.618071+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0308274v3","created_at":"2026-05-18T02:41:32.618071+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0308274","created_at":"2026-05-18T02:41:32.618071+00:00"},{"alias_kind":"pith_short_12","alias_value":"XPRYKBQP5JYV","created_at":"2026-05-18T12:25:52.051335+00:00"},{"alias_kind":"pith_short_16","alias_value":"XPRYKBQP5JYVCOVZ","created_at":"2026-05-18T12:25:52.051335+00:00"},{"alias_kind":"pith_short_8","alias_value":"XPRYKBQP","created_at":"2026-05-18T12:25:52.051335+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/XPRYKBQP5JYVCOVZEF7EAYZ5M2","json":"https://pith.science/pith/XPRYKBQP5JYVCOVZEF7EAYZ5M2.json","graph_json":"https://pith.science/api/pith-number/XPRYKBQP5JYVCOVZEF7EAYZ5M2/graph.json","events_json":"https://pith.science/api/pith-number/XPRYKBQP5JYVCOVZEF7EAYZ5M2/events.json","paper":"https://pith.science/paper/XPRYKBQP"},"agent_actions":{"view_html":"https://pith.science/pith/XPRYKBQP5JYVCOVZEF7EAYZ5M2","download_json":"https://pith.science/pith/XPRYKBQP5JYVCOVZEF7EAYZ5M2.json","view_paper":"https://pith.science/paper/XPRYKBQP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0308274&json=true","fetch_graph":"https://pith.science/api/pith-number/XPRYKBQP5JYVCOVZEF7EAYZ5M2/graph.json","fetch_events":"https://pith.science/api/pith-number/XPRYKBQP5JYVCOVZEF7EAYZ5M2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XPRYKBQP5JYVCOVZEF7EAYZ5M2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XPRYKBQP5JYVCOVZEF7EAYZ5M2/action/storage_attestation","attest_author":"https://pith.science/pith/XPRYKBQP5JYVCOVZEF7EAYZ5M2/action/author_attestation","sign_citation":"https://pith.science/pith/XPRYKBQP5JYVCOVZEF7EAYZ5M2/action/citation_signature","submit_replication":"https://pith.science/pith/XPRYKBQP5JYVCOVZEF7EAYZ5M2/action/replication_record"}},"created_at":"2026-05-18T02:41:32.618071+00:00","updated_at":"2026-05-18T02:41:32.618071+00:00"}