{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:PLG5LHS6IYLIILCGH74XQHA5EN","short_pith_number":"pith:PLG5LHS6","canonical_record":{"source":{"id":"1811.05712","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-11-14T10:14:58Z","cross_cats_sorted":["math.AG","math.GR"],"title_canon_sha256":"f6956c612861a517a69ab361e01a2e2680064aa74e2017bd36dd185cf6d67b8e","abstract_canon_sha256":"80c3f12479ae58deebcbcae66666ac540561ed02e9a6140292faf250f5bc2a6e"},"schema_version":"1.0"},"canonical_sha256":"7acdd59e5e4616842c463ff9781c1d2357885473ffb053c13bb151673fdb6c27","source":{"kind":"arxiv","id":"1811.05712","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.05712","created_at":"2026-05-18T00:00:42Z"},{"alias_kind":"arxiv_version","alias_value":"1811.05712v1","created_at":"2026-05-18T00:00:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.05712","created_at":"2026-05-18T00:00:42Z"},{"alias_kind":"pith_short_12","alias_value":"PLG5LHS6IYLI","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"PLG5LHS6IYLIILCG","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"PLG5LHS6","created_at":"2026-05-18T12:32:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:PLG5LHS6IYLIILCGH74XQHA5EN","target":"record","payload":{"canonical_record":{"source":{"id":"1811.05712","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-11-14T10:14:58Z","cross_cats_sorted":["math.AG","math.GR"],"title_canon_sha256":"f6956c612861a517a69ab361e01a2e2680064aa74e2017bd36dd185cf6d67b8e","abstract_canon_sha256":"80c3f12479ae58deebcbcae66666ac540561ed02e9a6140292faf250f5bc2a6e"},"schema_version":"1.0"},"canonical_sha256":"7acdd59e5e4616842c463ff9781c1d2357885473ffb053c13bb151673fdb6c27","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:42.260360Z","signature_b64":"B+EQhvUKeWksLrSMZfxGH9we6CO9sqSwk8daigUc3reMmpGYeeckjkmEidoInarjTgU/6rY2hXJ4yJf9K5CgBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7acdd59e5e4616842c463ff9781c1d2357885473ffb053c13bb151673fdb6c27","last_reissued_at":"2026-05-18T00:00:42.259895Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:42.259895Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1811.05712","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":"2026-05-18T00:00:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L0Sc76i46SEwMf9PpxE3nfxQF2vNH0rUE3v67qtVrcM8ekumeLJnSLhqv0wgeQIVYo3bRM1HgrzMGKocc/qYCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T14:23:34.068866Z"},"content_sha256":"276ea83eca4a8c2d81cf625984d19f5bf49021ea514926272e1a0955987fe0e0","schema_version":"1.0","event_id":"sha256:276ea83eca4a8c2d81cf625984d19f5bf49021ea514926272e1a0955987fe0e0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:PLG5LHS6IYLIILCGH74XQHA5EN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rigid local systems with monodromy group the Conway group Co_2","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":"2018-11-14T10:14:58Z","abstract_excerpt":"We first develop some basic facts about hypergeometric sheaves on the multiplicative group ${\\mathbb G}_m$ in characteristic $p >0$. Certain of their Kummer pullbacks extend to irreducible local systems on the affine line in characteristic $p>0$. One of these, of rank $23$ in characteristic $p=3$, turns out to have the Conway group $\\mathrm{Co}_2$, in its irreducible orthogonal representation of degree $23$, as its arithmetic and geometric monodromy groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.05712","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":"2026-05-18T00:00:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9BbsS0RPDrcmdOoTc9LoflcF5jZnnT3CCRL5+vcYTfSq9e+7/0BkFozZn9/Eh8HGIRNk5HAenBHI5gN0aaR3DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T14:23:34.069214Z"},"content_sha256":"09237a6ad5ae93b30691e843e76467cbf393823c347b148b8cf15f13854f29eb","schema_version":"1.0","event_id":"sha256:09237a6ad5ae93b30691e843e76467cbf393823c347b148b8cf15f13854f29eb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PLG5LHS6IYLIILCGH74XQHA5EN/bundle.json","state_url":"https://pith.science/pith/PLG5LHS6IYLIILCGH74XQHA5EN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PLG5LHS6IYLIILCGH74XQHA5EN/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":"2026-06-22T14:23:34Z","links":{"resolver":"https://pith.science/pith/PLG5LHS6IYLIILCGH74XQHA5EN","bundle":"https://pith.science/pith/PLG5LHS6IYLIILCGH74XQHA5EN/bundle.json","state":"https://pith.science/pith/PLG5LHS6IYLIILCGH74XQHA5EN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PLG5LHS6IYLIILCGH74XQHA5EN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:PLG5LHS6IYLIILCGH74XQHA5EN","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":"80c3f12479ae58deebcbcae66666ac540561ed02e9a6140292faf250f5bc2a6e","cross_cats_sorted":["math.AG","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-11-14T10:14:58Z","title_canon_sha256":"f6956c612861a517a69ab361e01a2e2680064aa74e2017bd36dd185cf6d67b8e"},"schema_version":"1.0","source":{"id":"1811.05712","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.05712","created_at":"2026-05-18T00:00:42Z"},{"alias_kind":"arxiv_version","alias_value":"1811.05712v1","created_at":"2026-05-18T00:00:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.05712","created_at":"2026-05-18T00:00:42Z"},{"alias_kind":"pith_short_12","alias_value":"PLG5LHS6IYLI","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"PLG5LHS6IYLIILCG","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"PLG5LHS6","created_at":"2026-05-18T12:32:46Z"}],"graph_snapshots":[{"event_id":"sha256:09237a6ad5ae93b30691e843e76467cbf393823c347b148b8cf15f13854f29eb","target":"graph","created_at":"2026-05-18T00:00:42Z","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 first develop some basic facts about hypergeometric sheaves on the multiplicative group ${\\mathbb G}_m$ in characteristic $p >0$. Certain of their Kummer pullbacks extend to irreducible local systems on the affine line in characteristic $p>0$. One of these, of rank $23$ in characteristic $p=3$, turns out to have the Conway group $\\mathrm{Co}_2$, in its irreducible orthogonal representation of degree $23$, as its arithmetic and geometric monodromy groups.","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":"2018-11-14T10:14:58Z","title":"Rigid local systems with monodromy group the Conway group Co_2"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.05712","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":"sha256:276ea83eca4a8c2d81cf625984d19f5bf49021ea514926272e1a0955987fe0e0","target":"record","created_at":"2026-05-18T00:00:42Z","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":"80c3f12479ae58deebcbcae66666ac540561ed02e9a6140292faf250f5bc2a6e","cross_cats_sorted":["math.AG","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-11-14T10:14:58Z","title_canon_sha256":"f6956c612861a517a69ab361e01a2e2680064aa74e2017bd36dd185cf6d67b8e"},"schema_version":"1.0","source":{"id":"1811.05712","kind":"arxiv","version":1}},"canonical_sha256":"7acdd59e5e4616842c463ff9781c1d2357885473ffb053c13bb151673fdb6c27","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7acdd59e5e4616842c463ff9781c1d2357885473ffb053c13bb151673fdb6c27","first_computed_at":"2026-05-18T00:00:42.259895Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:00:42.259895Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"B+EQhvUKeWksLrSMZfxGH9we6CO9sqSwk8daigUc3reMmpGYeeckjkmEidoInarjTgU/6rY2hXJ4yJf9K5CgBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:00:42.260360Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.05712","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:276ea83eca4a8c2d81cf625984d19f5bf49021ea514926272e1a0955987fe0e0","sha256:09237a6ad5ae93b30691e843e76467cbf393823c347b148b8cf15f13854f29eb"],"state_sha256":"17b387953c0989fd75600d8df39c90b43889841340d45cf062ccb07ff6ba8ccc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wo79b0hIKQCTCLy8QK5g+nTttFBZKHAO1ATCwr8BTukBMlSxxeRgwWXkPOTQgow5I9ucAYGpkgDblDAXaxe1CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T14:23:34.071167Z","bundle_sha256":"13b45d2ce0ed31fd76b9eb7822fa5ff206b5b280e799b12b8d681b3ff3f6b548"}}