{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:G56OBMKPY7MAV5CZMNGT5KNPZG","short_pith_number":"pith:G56OBMKP","canonical_record":{"source":{"id":"1901.03894","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-01-12T19:31:41Z","cross_cats_sorted":["math.AG","math.GR"],"title_canon_sha256":"08121ac5cf9988286a3f8abe94b10010f8f2272908ac0ec1b208ae10aa465827","abstract_canon_sha256":"15c3f514746aa2ca0117c15a4608c4ce17bbfe2f42e7037ba2c7860a9ea51de8"},"schema_version":"1.0"},"canonical_sha256":"377ce0b14fc7d80af459634d3ea9afc992070df23d243022f07846addb7185ea","source":{"kind":"arxiv","id":"1901.03894","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.03894","created_at":"2026-05-17T23:53:49Z"},{"alias_kind":"arxiv_version","alias_value":"1901.03894v2","created_at":"2026-05-17T23:53:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.03894","created_at":"2026-05-17T23:53:49Z"},{"alias_kind":"pith_short_12","alias_value":"G56OBMKPY7MA","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"G56OBMKPY7MAV5CZ","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"G56OBMKP","created_at":"2026-05-18T12:33:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:G56OBMKPY7MAV5CZMNGT5KNPZG","target":"record","payload":{"canonical_record":{"source":{"id":"1901.03894","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-01-12T19:31:41Z","cross_cats_sorted":["math.AG","math.GR"],"title_canon_sha256":"08121ac5cf9988286a3f8abe94b10010f8f2272908ac0ec1b208ae10aa465827","abstract_canon_sha256":"15c3f514746aa2ca0117c15a4608c4ce17bbfe2f42e7037ba2c7860a9ea51de8"},"schema_version":"1.0"},"canonical_sha256":"377ce0b14fc7d80af459634d3ea9afc992070df23d243022f07846addb7185ea","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:49.643755Z","signature_b64":"sRtjMb5dhmHaSiHZKuNkRp9pAWfpkddKWbH4Dr5tudWQOjlq2HnP3MCPPs3yPRJtUoqwgK7J87K1Q7bcOAkPBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"377ce0b14fc7d80af459634d3ea9afc992070df23d243022f07846addb7185ea","last_reissued_at":"2026-05-17T23:53:49.643075Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:49.643075Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1901.03894","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:53:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lfraOfxjdA/pIeTi641keibuFQEgWG7X67WKLx0vFBpRo4mq8q48xI/Lj3Z+acMCBkuKN/EzsRi8uiZAqUClDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T17:12:22.522212Z"},"content_sha256":"4013af8f23a0f579653584388b215258a3f57ded8945012e93e24f7f26fa453f","schema_version":"1.0","event_id":"sha256:4013af8f23a0f579653584388b215258a3f57ded8945012e93e24f7f26fa453f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:G56OBMKPY7MAV5CZMNGT5KNPZG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A rigid local system with monodromy group the big Conway group 2.Co_1 and two others with monodromy group the Suzuki group 6.Suz","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.GR"],"primary_cat":"math.NT","authors_text":"Antonio Rojas-Le\\'on, Nicholas M. Katz, Pham Huu Tiep","submitted_at":"2019-01-12T19:31:41Z","abstract_excerpt":"In the first three sections, we develop some basic facts about hypergeometric sheaves on the multiplicative group ${\\mathbb G}_m$ in characteristic $p >0$. In the fourth and fifth sections, we specialize to quite special classses of hypergeomtric sheaves. We give relatively \"simple\" formulas for their trace functions, and a criterion for them to have finite monodromy. In the next section, we prove that three of them have finite monodromy groups.We then give some results on finite complex linear groups.\n  We next use these group theoretic results to show that one of our local systems, of rank $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.03894","kind":"arxiv","version":2},"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":"2026-05-17T23:53:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iWPPwv7da9NdcYa86UquAlr08oFAfQRPg1/WPpvSmDz9Dy0ocg591cvUctUhlLFiv2R1krKRu8ClRtGOISpSAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T17:12:22.522592Z"},"content_sha256":"aa4e9eaaa0524bd0c0be1233e3b8b21185485068490cf744edebabb1cb50b3c6","schema_version":"1.0","event_id":"sha256:aa4e9eaaa0524bd0c0be1233e3b8b21185485068490cf744edebabb1cb50b3c6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/G56OBMKPY7MAV5CZMNGT5KNPZG/bundle.json","state_url":"https://pith.science/pith/G56OBMKPY7MAV5CZMNGT5KNPZG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/G56OBMKPY7MAV5CZMNGT5KNPZG/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":"2026-06-22T17:12:22Z","links":{"resolver":"https://pith.science/pith/G56OBMKPY7MAV5CZMNGT5KNPZG","bundle":"https://pith.science/pith/G56OBMKPY7MAV5CZMNGT5KNPZG/bundle.json","state":"https://pith.science/pith/G56OBMKPY7MAV5CZMNGT5KNPZG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/G56OBMKPY7MAV5CZMNGT5KNPZG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:G56OBMKPY7MAV5CZMNGT5KNPZG","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":"15c3f514746aa2ca0117c15a4608c4ce17bbfe2f42e7037ba2c7860a9ea51de8","cross_cats_sorted":["math.AG","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-01-12T19:31:41Z","title_canon_sha256":"08121ac5cf9988286a3f8abe94b10010f8f2272908ac0ec1b208ae10aa465827"},"schema_version":"1.0","source":{"id":"1901.03894","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.03894","created_at":"2026-05-17T23:53:49Z"},{"alias_kind":"arxiv_version","alias_value":"1901.03894v2","created_at":"2026-05-17T23:53:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.03894","created_at":"2026-05-17T23:53:49Z"},{"alias_kind":"pith_short_12","alias_value":"G56OBMKPY7MA","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"G56OBMKPY7MAV5CZ","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"G56OBMKP","created_at":"2026-05-18T12:33:18Z"}],"graph_snapshots":[{"event_id":"sha256:aa4e9eaaa0524bd0c0be1233e3b8b21185485068490cf744edebabb1cb50b3c6","target":"graph","created_at":"2026-05-17T23:53:49Z","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":"In the first three sections, we develop some basic facts about hypergeometric sheaves on the multiplicative group ${\\mathbb G}_m$ in characteristic $p >0$. In the fourth and fifth sections, we specialize to quite special classses of hypergeomtric sheaves. We give relatively \"simple\" formulas for their trace functions, and a criterion for them to have finite monodromy. In the next section, we prove that three of them have finite monodromy groups.We then give some results on finite complex linear groups.\n  We next use these group theoretic results to show that one of our local systems, of rank $","authors_text":"Antonio Rojas-Le\\'on, Nicholas M. Katz, Pham Huu Tiep","cross_cats":["math.AG","math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-01-12T19:31:41Z","title":"A rigid local system with monodromy group the big Conway group 2.Co_1 and two others with monodromy group the Suzuki group 6.Suz"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.03894","kind":"arxiv","version":2},"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":"sha256:4013af8f23a0f579653584388b215258a3f57ded8945012e93e24f7f26fa453f","target":"record","created_at":"2026-05-17T23:53:49Z","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":"15c3f514746aa2ca0117c15a4608c4ce17bbfe2f42e7037ba2c7860a9ea51de8","cross_cats_sorted":["math.AG","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-01-12T19:31:41Z","title_canon_sha256":"08121ac5cf9988286a3f8abe94b10010f8f2272908ac0ec1b208ae10aa465827"},"schema_version":"1.0","source":{"id":"1901.03894","kind":"arxiv","version":2}},"canonical_sha256":"377ce0b14fc7d80af459634d3ea9afc992070df23d243022f07846addb7185ea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"377ce0b14fc7d80af459634d3ea9afc992070df23d243022f07846addb7185ea","first_computed_at":"2026-05-17T23:53:49.643075Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:49.643075Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sRtjMb5dhmHaSiHZKuNkRp9pAWfpkddKWbH4Dr5tudWQOjlq2HnP3MCPPs3yPRJtUoqwgK7J87K1Q7bcOAkPBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:49.643755Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.03894","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4013af8f23a0f579653584388b215258a3f57ded8945012e93e24f7f26fa453f","sha256:aa4e9eaaa0524bd0c0be1233e3b8b21185485068490cf744edebabb1cb50b3c6"],"state_sha256":"13a94724c0e220e722651c6f4832c7547e927396ea909e194692bfa95a641acb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xEOlECbz8rC3EoMywulGgnE3M/sBx8crY5fpWOwxzlGZwV9T8nH3+MdGQ1pyoce13k73kAb9PHjkaqvy4QFwAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T17:12:22.524580Z","bundle_sha256":"98181341f1adccf3d023c89e2780bec6c3978437968baca7c31968d255e9d4d4"}}