{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:FOG3WFBVGL4IBWS2FM57GDIF5L","short_pith_number":"pith:FOG3WFBV","schema_version":"1.0","canonical_sha256":"2b8dbb143532f880da5a2b3bf30d05eaff34bf4578a481baeae033acb4a382f2","source":{"kind":"arxiv","id":"1411.1140","version":1},"attestation_state":"computed","paper":{"title":"A fake plane via 2-adic uniformization with torsion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.AG","authors_text":"Daniel Allcock, Fumiharu Kato","submitted_at":"2014-11-05T03:42:58Z","abstract_excerpt":"We adapt the theory of non-Archimedean uniformization to construct a smooth surface from a lattice in PGL3(Q2) that has nontrivial torsion. It turns out to be a fake projective plane, commensurable with Mumford's fake plane yet distinct from it and the other fake planes that arise from 2-adic uniformization by torsion-free groups. As part of the proof, and of independent interest, we compute the homotopy type of the Berkovich space of our plane."},"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":"1411.1140","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-11-05T03:42:58Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"aadba71f327669036ffb050f9db4ba4122ba6834d8aa2e718be4ed86f4c632db","abstract_canon_sha256":"57aa8dac1b5089d4b01f136e9b140d248844740fd881a44df29d9d87cb79369b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:38:36.222046Z","signature_b64":"KJX3dKaCGK1FnD6p3PACyiXozqWffNyjUuYuCc5DW8S1Cyhh4NkRihUtSrRC1iN+d3A37MNuhNP0yg84j1BOAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2b8dbb143532f880da5a2b3bf30d05eaff34bf4578a481baeae033acb4a382f2","last_reissued_at":"2026-05-18T02:38:36.221430Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:38:36.221430Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A fake plane via 2-adic uniformization with torsion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.AG","authors_text":"Daniel Allcock, Fumiharu Kato","submitted_at":"2014-11-05T03:42:58Z","abstract_excerpt":"We adapt the theory of non-Archimedean uniformization to construct a smooth surface from a lattice in PGL3(Q2) that has nontrivial torsion. It turns out to be a fake projective plane, commensurable with Mumford's fake plane yet distinct from it and the other fake planes that arise from 2-adic uniformization by torsion-free groups. As part of the proof, and of independent interest, we compute the homotopy type of the Berkovich space of our plane."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.1140","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":"1411.1140","created_at":"2026-05-18T02:38:36.221524+00:00"},{"alias_kind":"arxiv_version","alias_value":"1411.1140v1","created_at":"2026-05-18T02:38:36.221524+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.1140","created_at":"2026-05-18T02:38:36.221524+00:00"},{"alias_kind":"pith_short_12","alias_value":"FOG3WFBVGL4I","created_at":"2026-05-18T12:28:28.263976+00:00"},{"alias_kind":"pith_short_16","alias_value":"FOG3WFBVGL4IBWS2","created_at":"2026-05-18T12:28:28.263976+00:00"},{"alias_kind":"pith_short_8","alias_value":"FOG3WFBV","created_at":"2026-05-18T12:28:28.263976+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/FOG3WFBVGL4IBWS2FM57GDIF5L","json":"https://pith.science/pith/FOG3WFBVGL4IBWS2FM57GDIF5L.json","graph_json":"https://pith.science/api/pith-number/FOG3WFBVGL4IBWS2FM57GDIF5L/graph.json","events_json":"https://pith.science/api/pith-number/FOG3WFBVGL4IBWS2FM57GDIF5L/events.json","paper":"https://pith.science/paper/FOG3WFBV"},"agent_actions":{"view_html":"https://pith.science/pith/FOG3WFBVGL4IBWS2FM57GDIF5L","download_json":"https://pith.science/pith/FOG3WFBVGL4IBWS2FM57GDIF5L.json","view_paper":"https://pith.science/paper/FOG3WFBV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1411.1140&json=true","fetch_graph":"https://pith.science/api/pith-number/FOG3WFBVGL4IBWS2FM57GDIF5L/graph.json","fetch_events":"https://pith.science/api/pith-number/FOG3WFBVGL4IBWS2FM57GDIF5L/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FOG3WFBVGL4IBWS2FM57GDIF5L/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FOG3WFBVGL4IBWS2FM57GDIF5L/action/storage_attestation","attest_author":"https://pith.science/pith/FOG3WFBVGL4IBWS2FM57GDIF5L/action/author_attestation","sign_citation":"https://pith.science/pith/FOG3WFBVGL4IBWS2FM57GDIF5L/action/citation_signature","submit_replication":"https://pith.science/pith/FOG3WFBVGL4IBWS2FM57GDIF5L/action/replication_record"}},"created_at":"2026-05-18T02:38:36.221524+00:00","updated_at":"2026-05-18T02:38:36.221524+00:00"}