{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:UDOQ2TF4SOOXRAK6B6ORERJUPO","short_pith_number":"pith:UDOQ2TF4","schema_version":"1.0","canonical_sha256":"a0dd0d4cbc939d78815e0f9d1245347ba343407c60825bc621d14091c9387d22","source":{"kind":"arxiv","id":"1701.02452","version":1},"attestation_state":"computed","paper":{"title":"Finding generators and relations for groups acting on the hyperbolic ball","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Donald I. Cartwright, Tim Steger","submitted_at":"2017-01-10T07:20:58Z","abstract_excerpt":"In order to enumerate the fake projective planes, as announced in~\\cite{CS}, we found explicit generators and a presentation for each maximal arithmetic subgroup $\\bar\\Gamma$ of~$PU(2,1)$ for which the (appropriately normalized) covolume equals~$1/N$ for some integer~$N\\ge1$. Prasad and Yeung \\cite{PY1,PY2} had given a list of all such $\\bar\\Gamma$ (up to equivalence).\n  The generators were found by a computer search which uses the natural action of $PU(2,1)$ on the unit ball $B(\\C^2)$ in~$\\C^2$. Our main results here give criteria which ensure that the computer search has found sufficiently m"},"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":"1701.02452","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-01-10T07:20:58Z","cross_cats_sorted":[],"title_canon_sha256":"a2426fc69d85252d8d06a7633feb1f92cbba65ddc073f368c4d9ca69aeff50b4","abstract_canon_sha256":"5f247b06a66115e8ebdd1988d43c5d2110928023b0325ebbb12f2533aa3e40b9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:04.228705Z","signature_b64":"sPLRuLTW2W4TWoEVY53KybxQMiwcaIFxw2sxPNGa5ZNZj7diup9vJTrPaN/GiSLF5Nr1BpzeKxIMOqVZvYaRCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a0dd0d4cbc939d78815e0f9d1245347ba343407c60825bc621d14091c9387d22","last_reissued_at":"2026-05-18T00:53:04.228070Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:04.228070Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Finding generators and relations for groups acting on the hyperbolic ball","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Donald I. Cartwright, Tim Steger","submitted_at":"2017-01-10T07:20:58Z","abstract_excerpt":"In order to enumerate the fake projective planes, as announced in~\\cite{CS}, we found explicit generators and a presentation for each maximal arithmetic subgroup $\\bar\\Gamma$ of~$PU(2,1)$ for which the (appropriately normalized) covolume equals~$1/N$ for some integer~$N\\ge1$. Prasad and Yeung \\cite{PY1,PY2} had given a list of all such $\\bar\\Gamma$ (up to equivalence).\n  The generators were found by a computer search which uses the natural action of $PU(2,1)$ on the unit ball $B(\\C^2)$ in~$\\C^2$. Our main results here give criteria which ensure that the computer search has found sufficiently m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.02452","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":"1701.02452","created_at":"2026-05-18T00:53:04.228167+00:00"},{"alias_kind":"arxiv_version","alias_value":"1701.02452v1","created_at":"2026-05-18T00:53:04.228167+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.02452","created_at":"2026-05-18T00:53:04.228167+00:00"},{"alias_kind":"pith_short_12","alias_value":"UDOQ2TF4SOOX","created_at":"2026-05-18T12:31:46.661854+00:00"},{"alias_kind":"pith_short_16","alias_value":"UDOQ2TF4SOOXRAK6","created_at":"2026-05-18T12:31:46.661854+00:00"},{"alias_kind":"pith_short_8","alias_value":"UDOQ2TF4","created_at":"2026-05-18T12:31:46.661854+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/UDOQ2TF4SOOXRAK6B6ORERJUPO","json":"https://pith.science/pith/UDOQ2TF4SOOXRAK6B6ORERJUPO.json","graph_json":"https://pith.science/api/pith-number/UDOQ2TF4SOOXRAK6B6ORERJUPO/graph.json","events_json":"https://pith.science/api/pith-number/UDOQ2TF4SOOXRAK6B6ORERJUPO/events.json","paper":"https://pith.science/paper/UDOQ2TF4"},"agent_actions":{"view_html":"https://pith.science/pith/UDOQ2TF4SOOXRAK6B6ORERJUPO","download_json":"https://pith.science/pith/UDOQ2TF4SOOXRAK6B6ORERJUPO.json","view_paper":"https://pith.science/paper/UDOQ2TF4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1701.02452&json=true","fetch_graph":"https://pith.science/api/pith-number/UDOQ2TF4SOOXRAK6B6ORERJUPO/graph.json","fetch_events":"https://pith.science/api/pith-number/UDOQ2TF4SOOXRAK6B6ORERJUPO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UDOQ2TF4SOOXRAK6B6ORERJUPO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UDOQ2TF4SOOXRAK6B6ORERJUPO/action/storage_attestation","attest_author":"https://pith.science/pith/UDOQ2TF4SOOXRAK6B6ORERJUPO/action/author_attestation","sign_citation":"https://pith.science/pith/UDOQ2TF4SOOXRAK6B6ORERJUPO/action/citation_signature","submit_replication":"https://pith.science/pith/UDOQ2TF4SOOXRAK6B6ORERJUPO/action/replication_record"}},"created_at":"2026-05-18T00:53:04.228167+00:00","updated_at":"2026-05-18T00:53:04.228167+00:00"}