{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:WOJO4SUOJB5H7G547UF3CWYXTK","short_pith_number":"pith:WOJO4SUO","schema_version":"1.0","canonical_sha256":"b392ee4a8e487a7f9bbcfd0bb15b179a88a6e630b536ddbc8fcbf09b4e945186","source":{"kind":"arxiv","id":"1504.07783","version":1},"attestation_state":"computed","paper":{"title":"Presentations of Groups Acting Discontinuously on Direct Products of Hyperbolic Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"\\'Angel del R\\'io, Ann Kiefer, Eric Jespers","submitted_at":"2015-04-29T09:25:28Z","abstract_excerpt":"The problem of describing the group of units $\\mathcal{U}(\\mathbb{Z} G)$ of the integral group ring $\\mathbb{Z} G$ of a finite group $G$ has attracted a lot of attention and providing presentations for such groups is a fundamental problem. Within the context of orders, a central problem is to describe a presentation of the unit group of an order $\\mathcal{O}$ in the simple epimorphic images $A$ of the rational group algebra $\\mathbb{Q} G$. Making use of the presentation part of Poincar\\'e's Polyhedron Theorem, Pita, del R\\'io and Ruiz proposed such a method for a large family of finite groups "},"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":"1504.07783","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-04-29T09:25:28Z","cross_cats_sorted":[],"title_canon_sha256":"4ed1ac4dc39da0e6615a5b19b35a0193dc34d697c164ccb6cc836fcf800037ae","abstract_canon_sha256":"24e3eb94f35eb78d33b9de21d7d6411022881f0a0a6f09dd209dadb631273289"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:17:32.234647Z","signature_b64":"Jzr5lVhgiGjMvb7o1xOFV+cqxplrfnXLPGIfz6238Ta275kwwkHgz8lwUlQgcgR5vmEvgcK5BVq8HAOTrkfNDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b392ee4a8e487a7f9bbcfd0bb15b179a88a6e630b536ddbc8fcbf09b4e945186","last_reissued_at":"2026-05-18T02:17:32.234001Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:17:32.234001Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Presentations of Groups Acting Discontinuously on Direct Products of Hyperbolic Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"\\'Angel del R\\'io, Ann Kiefer, Eric Jespers","submitted_at":"2015-04-29T09:25:28Z","abstract_excerpt":"The problem of describing the group of units $\\mathcal{U}(\\mathbb{Z} G)$ of the integral group ring $\\mathbb{Z} G$ of a finite group $G$ has attracted a lot of attention and providing presentations for such groups is a fundamental problem. Within the context of orders, a central problem is to describe a presentation of the unit group of an order $\\mathcal{O}$ in the simple epimorphic images $A$ of the rational group algebra $\\mathbb{Q} G$. Making use of the presentation part of Poincar\\'e's Polyhedron Theorem, Pita, del R\\'io and Ruiz proposed such a method for a large family of finite groups "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.07783","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":"1504.07783","created_at":"2026-05-18T02:17:32.234086+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.07783v1","created_at":"2026-05-18T02:17:32.234086+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.07783","created_at":"2026-05-18T02:17:32.234086+00:00"},{"alias_kind":"pith_short_12","alias_value":"WOJO4SUOJB5H","created_at":"2026-05-18T12:29:47.479230+00:00"},{"alias_kind":"pith_short_16","alias_value":"WOJO4SUOJB5H7G54","created_at":"2026-05-18T12:29:47.479230+00:00"},{"alias_kind":"pith_short_8","alias_value":"WOJO4SUO","created_at":"2026-05-18T12:29:47.479230+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/WOJO4SUOJB5H7G547UF3CWYXTK","json":"https://pith.science/pith/WOJO4SUOJB5H7G547UF3CWYXTK.json","graph_json":"https://pith.science/api/pith-number/WOJO4SUOJB5H7G547UF3CWYXTK/graph.json","events_json":"https://pith.science/api/pith-number/WOJO4SUOJB5H7G547UF3CWYXTK/events.json","paper":"https://pith.science/paper/WOJO4SUO"},"agent_actions":{"view_html":"https://pith.science/pith/WOJO4SUOJB5H7G547UF3CWYXTK","download_json":"https://pith.science/pith/WOJO4SUOJB5H7G547UF3CWYXTK.json","view_paper":"https://pith.science/paper/WOJO4SUO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.07783&json=true","fetch_graph":"https://pith.science/api/pith-number/WOJO4SUOJB5H7G547UF3CWYXTK/graph.json","fetch_events":"https://pith.science/api/pith-number/WOJO4SUOJB5H7G547UF3CWYXTK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WOJO4SUOJB5H7G547UF3CWYXTK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WOJO4SUOJB5H7G547UF3CWYXTK/action/storage_attestation","attest_author":"https://pith.science/pith/WOJO4SUOJB5H7G547UF3CWYXTK/action/author_attestation","sign_citation":"https://pith.science/pith/WOJO4SUOJB5H7G547UF3CWYXTK/action/citation_signature","submit_replication":"https://pith.science/pith/WOJO4SUOJB5H7G547UF3CWYXTK/action/replication_record"}},"created_at":"2026-05-18T02:17:32.234086+00:00","updated_at":"2026-05-18T02:17:32.234086+00:00"}