{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:F5FDE35RPJO5N5URY7PGFAXYZJ","short_pith_number":"pith:F5FDE35R","canonical_record":{"source":{"id":"1304.5549","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-04-19T21:09:54Z","cross_cats_sorted":["math.AG","math.NT"],"title_canon_sha256":"75a1dbe4ee2481698bab61057ddf01db7238bab9e1fa4fcd9c4ebb4b425f66a6","abstract_canon_sha256":"3b7303f58c588b61e4966520558310e11bc65eef14c75c3e6b0c4196f9939b4a"},"schema_version":"1.0"},"canonical_sha256":"2f4a326fb17a5dd6f691c7de6282f8ca4dc01b786e8e4edb1c19457118ce1b65","source":{"kind":"arxiv","id":"1304.5549","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.5549","created_at":"2026-05-18T03:27:31Z"},{"alias_kind":"arxiv_version","alias_value":"1304.5549v1","created_at":"2026-05-18T03:27:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.5549","created_at":"2026-05-18T03:27:31Z"},{"alias_kind":"pith_short_12","alias_value":"F5FDE35RPJO5","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"F5FDE35RPJO5N5UR","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"F5FDE35R","created_at":"2026-05-18T12:27:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:F5FDE35RPJO5N5URY7PGFAXYZJ","target":"record","payload":{"canonical_record":{"source":{"id":"1304.5549","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-04-19T21:09:54Z","cross_cats_sorted":["math.AG","math.NT"],"title_canon_sha256":"75a1dbe4ee2481698bab61057ddf01db7238bab9e1fa4fcd9c4ebb4b425f66a6","abstract_canon_sha256":"3b7303f58c588b61e4966520558310e11bc65eef14c75c3e6b0c4196f9939b4a"},"schema_version":"1.0"},"canonical_sha256":"2f4a326fb17a5dd6f691c7de6282f8ca4dc01b786e8e4edb1c19457118ce1b65","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:27:31.723778Z","signature_b64":"IAMAMO/jygAMm+FmAc9ehKUGa3OhKJ9xEsR+5mnlUpCh0/mU2AWmNn8tdXy9r6a3Vdk375xpg1ZobNaSNaS1Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2f4a326fb17a5dd6f691c7de6282f8ca4dc01b786e8e4edb1c19457118ce1b65","last_reissued_at":"2026-05-18T03:27:31.723180Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:27:31.723180Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.5549","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:27:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pfQoEIWYuIStlZTpuM3DQDyRDcjMC9ecdwRaxh3JOLZCftAPSnwdcmur3TX06o1YUkvgC4bmvr1tJ0JqdwKTBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T20:28:50.981633Z"},"content_sha256":"4d7b3c52ccd31c1c55f2f64b84048b20c1cf6925c5e5601f2058cce3ee949775","schema_version":"1.0","event_id":"sha256:4d7b3c52ccd31c1c55f2f64b84048b20c1cf6925c5e5601f2058cce3ee949775"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:F5FDE35RPJO5N5URY7PGFAXYZJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Simply transitive quaternionic lattices of rank 2 over F_q(t) and a non-classical fake quadric","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.NT"],"primary_cat":"math.GR","authors_text":"Alina Vdovina, Jakob Stix","submitted_at":"2013-04-19T21:09:54Z","abstract_excerpt":"We construct an infinite series of simply transitive irreducible lattices in PGL_2(F_q((t))) \\times PGL_2(F_q((t))) by means of a quaternion algebra over F_q(t). The lattices depend on an odd prime power q = p^r and a parameter \\tau\\ in F_q^* different from 1, and are the fundamental group of a square complex with just one vertex and universal covering T_{q+1} \\times T_{q+1}, a product of trees with constant valency q + 1.\n  Our lattices give rise via non-archimedian uniformization to smooth projective surfaces of general type over F_q((t)) with ample canonical class, Chern ratio (c_1)^2/c_2 ="},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.5549","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:27:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x2ZSCA6iPFwgWlLUpgqNkJhFR5g+CT0wS2M9c40zVh1qa+UH60mPZsCsBt2xc7rjy5r6Bfzs969TCOX35nFeDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T20:28:50.981988Z"},"content_sha256":"70729267f2a0833d821f836b68aded1e1a6100b2868f296ad8d64c4ec76d2c57","schema_version":"1.0","event_id":"sha256:70729267f2a0833d821f836b68aded1e1a6100b2868f296ad8d64c4ec76d2c57"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F5FDE35RPJO5N5URY7PGFAXYZJ/bundle.json","state_url":"https://pith.science/pith/F5FDE35RPJO5N5URY7PGFAXYZJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F5FDE35RPJO5N5URY7PGFAXYZJ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-30T20:28:50Z","links":{"resolver":"https://pith.science/pith/F5FDE35RPJO5N5URY7PGFAXYZJ","bundle":"https://pith.science/pith/F5FDE35RPJO5N5URY7PGFAXYZJ/bundle.json","state":"https://pith.science/pith/F5FDE35RPJO5N5URY7PGFAXYZJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F5FDE35RPJO5N5URY7PGFAXYZJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:F5FDE35RPJO5N5URY7PGFAXYZJ","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":"3b7303f58c588b61e4966520558310e11bc65eef14c75c3e6b0c4196f9939b4a","cross_cats_sorted":["math.AG","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-04-19T21:09:54Z","title_canon_sha256":"75a1dbe4ee2481698bab61057ddf01db7238bab9e1fa4fcd9c4ebb4b425f66a6"},"schema_version":"1.0","source":{"id":"1304.5549","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.5549","created_at":"2026-05-18T03:27:31Z"},{"alias_kind":"arxiv_version","alias_value":"1304.5549v1","created_at":"2026-05-18T03:27:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.5549","created_at":"2026-05-18T03:27:31Z"},{"alias_kind":"pith_short_12","alias_value":"F5FDE35RPJO5","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"F5FDE35RPJO5N5UR","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"F5FDE35R","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:70729267f2a0833d821f836b68aded1e1a6100b2868f296ad8d64c4ec76d2c57","target":"graph","created_at":"2026-05-18T03:27:31Z","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":"We construct an infinite series of simply transitive irreducible lattices in PGL_2(F_q((t))) \\times PGL_2(F_q((t))) by means of a quaternion algebra over F_q(t). The lattices depend on an odd prime power q = p^r and a parameter \\tau\\ in F_q^* different from 1, and are the fundamental group of a square complex with just one vertex and universal covering T_{q+1} \\times T_{q+1}, a product of trees with constant valency q + 1.\n  Our lattices give rise via non-archimedian uniformization to smooth projective surfaces of general type over F_q((t)) with ample canonical class, Chern ratio (c_1)^2/c_2 =","authors_text":"Alina Vdovina, Jakob Stix","cross_cats":["math.AG","math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-04-19T21:09:54Z","title":"Simply transitive quaternionic lattices of rank 2 over F_q(t) and a non-classical fake quadric"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.5549","kind":"arxiv","version":1},"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":"sha256:4d7b3c52ccd31c1c55f2f64b84048b20c1cf6925c5e5601f2058cce3ee949775","target":"record","created_at":"2026-05-18T03:27:31Z","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":"3b7303f58c588b61e4966520558310e11bc65eef14c75c3e6b0c4196f9939b4a","cross_cats_sorted":["math.AG","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-04-19T21:09:54Z","title_canon_sha256":"75a1dbe4ee2481698bab61057ddf01db7238bab9e1fa4fcd9c4ebb4b425f66a6"},"schema_version":"1.0","source":{"id":"1304.5549","kind":"arxiv","version":1}},"canonical_sha256":"2f4a326fb17a5dd6f691c7de6282f8ca4dc01b786e8e4edb1c19457118ce1b65","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2f4a326fb17a5dd6f691c7de6282f8ca4dc01b786e8e4edb1c19457118ce1b65","first_computed_at":"2026-05-18T03:27:31.723180Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:27:31.723180Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IAMAMO/jygAMm+FmAc9ehKUGa3OhKJ9xEsR+5mnlUpCh0/mU2AWmNn8tdXy9r6a3Vdk375xpg1ZobNaSNaS1Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:27:31.723778Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.5549","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4d7b3c52ccd31c1c55f2f64b84048b20c1cf6925c5e5601f2058cce3ee949775","sha256:70729267f2a0833d821f836b68aded1e1a6100b2868f296ad8d64c4ec76d2c57"],"state_sha256":"a1d392d8011d468026d58d99bc656867e0a65a3141163077c9d4b3f6dead3712"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"88ZjxWSH1ZSKNOrIPAczd8ZpMktrvUP1+Yy0ogalLZN/QGcghlm2pS2GS6RumR5OW5h9kUlk9Z95bMYW28XFBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T20:28:50.984168Z","bundle_sha256":"3170004e7e056e7662f87ee7f8da2755cc5a294c8b03ef20d5ec2779290ef4a8"}}