{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:YOLL2Z7GSGFVUDLW35ZLICRJUF","short_pith_number":"pith:YOLL2Z7G","canonical_record":{"source":{"id":"1405.7541","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-05-29T13:02:22Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"bde264d55d14622001c8e37410a0983ff1e432a63d8b3cc0871445ba1a743a0d","abstract_canon_sha256":"f688cfdb1ca7dfc3fec6cf7d30110a20c45661a510079e3df6632ad6e6057547"},"schema_version":"1.0"},"canonical_sha256":"c396bd67e6918b5a0d76df72b40a29a1507f1c2f1e178941511a14bd081c04fe","source":{"kind":"arxiv","id":"1405.7541","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.7541","created_at":"2026-05-18T02:50:51Z"},{"alias_kind":"arxiv_version","alias_value":"1405.7541v1","created_at":"2026-05-18T02:50:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.7541","created_at":"2026-05-18T02:50:51Z"},{"alias_kind":"pith_short_12","alias_value":"YOLL2Z7GSGFV","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"YOLL2Z7GSGFVUDLW","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"YOLL2Z7G","created_at":"2026-05-18T12:28:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:YOLL2Z7GSGFVUDLW35ZLICRJUF","target":"record","payload":{"canonical_record":{"source":{"id":"1405.7541","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-05-29T13:02:22Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"bde264d55d14622001c8e37410a0983ff1e432a63d8b3cc0871445ba1a743a0d","abstract_canon_sha256":"f688cfdb1ca7dfc3fec6cf7d30110a20c45661a510079e3df6632ad6e6057547"},"schema_version":"1.0"},"canonical_sha256":"c396bd67e6918b5a0d76df72b40a29a1507f1c2f1e178941511a14bd081c04fe","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:50:51.015180Z","signature_b64":"dqGYjnk3r41N2YqllkIl8WsvAICtcR1vXpibEN90DSgo39ilb/l1g7nKwxXs3gg2EJ6dllv6ZAN23ihSKApQBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c396bd67e6918b5a0d76df72b40a29a1507f1c2f1e178941511a14bd081c04fe","last_reissued_at":"2026-05-18T02:50:51.014530Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:50:51.014530Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.7541","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":"2026-05-18T02:50:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"83haoaGDuHiAL97/isBN7vm1KSSSS2MUUtOBB1pd3XffxHHBGJNgoM6kf/38zMdjVqZCArIqREFB/GDSOb1rAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T08:32:38.568824Z"},"content_sha256":"0689286d8eb7a6b25fd9f605bf5ae1fad0969180dc25f95c82b00078d1caa6fa","schema_version":"1.0","event_id":"sha256:0689286d8eb7a6b25fd9f605bf5ae1fad0969180dc25f95c82b00078d1caa6fa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:YOLL2Z7GSGFVUDLW35ZLICRJUF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Strongly Real Beauville Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.GR","authors_text":"Ben Fairbairn","submitted_at":"2014-05-29T13:02:22Z","abstract_excerpt":"A strongly real Beauville group is a Beauville group that defines a real Beauville surface. Here we discuss efforts to find examples of these groups, emphasising on the one extreme finite simple groups and on the other abelian and nilpotent groups. We will also discuss the case of characteristically simple groups and almost simple groups. \\emph{En route} we shall discuss several questions, open problems and conjectures as well as giving several new examples of infinite families of strongly real Beauville groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.7541","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":"2026-05-18T02:50:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iJBzB/k+9TITlxBZF8HL2VaZb1ctVj5GbakNZpmjV6NZ9D/zifwewVQ0gOWPIO69iFJduNHYBSChqRtmJHQ1DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T08:32:38.569187Z"},"content_sha256":"516909a56453da430aeef671bb686f9a595d599149467464a328da7ea79ff78c","schema_version":"1.0","event_id":"sha256:516909a56453da430aeef671bb686f9a595d599149467464a328da7ea79ff78c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YOLL2Z7GSGFVUDLW35ZLICRJUF/bundle.json","state_url":"https://pith.science/pith/YOLL2Z7GSGFVUDLW35ZLICRJUF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YOLL2Z7GSGFVUDLW35ZLICRJUF/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":"2026-06-04T08:32:38Z","links":{"resolver":"https://pith.science/pith/YOLL2Z7GSGFVUDLW35ZLICRJUF","bundle":"https://pith.science/pith/YOLL2Z7GSGFVUDLW35ZLICRJUF/bundle.json","state":"https://pith.science/pith/YOLL2Z7GSGFVUDLW35ZLICRJUF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YOLL2Z7GSGFVUDLW35ZLICRJUF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:YOLL2Z7GSGFVUDLW35ZLICRJUF","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":"f688cfdb1ca7dfc3fec6cf7d30110a20c45661a510079e3df6632ad6e6057547","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-05-29T13:02:22Z","title_canon_sha256":"bde264d55d14622001c8e37410a0983ff1e432a63d8b3cc0871445ba1a743a0d"},"schema_version":"1.0","source":{"id":"1405.7541","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.7541","created_at":"2026-05-18T02:50:51Z"},{"alias_kind":"arxiv_version","alias_value":"1405.7541v1","created_at":"2026-05-18T02:50:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.7541","created_at":"2026-05-18T02:50:51Z"},{"alias_kind":"pith_short_12","alias_value":"YOLL2Z7GSGFV","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"YOLL2Z7GSGFVUDLW","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"YOLL2Z7G","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:516909a56453da430aeef671bb686f9a595d599149467464a328da7ea79ff78c","target":"graph","created_at":"2026-05-18T02:50:51Z","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":"A strongly real Beauville group is a Beauville group that defines a real Beauville surface. Here we discuss efforts to find examples of these groups, emphasising on the one extreme finite simple groups and on the other abelian and nilpotent groups. We will also discuss the case of characteristically simple groups and almost simple groups. \\emph{En route} we shall discuss several questions, open problems and conjectures as well as giving several new examples of infinite families of strongly real Beauville groups.","authors_text":"Ben Fairbairn","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-05-29T13:02:22Z","title":"Strongly Real Beauville Groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.7541","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":"sha256:0689286d8eb7a6b25fd9f605bf5ae1fad0969180dc25f95c82b00078d1caa6fa","target":"record","created_at":"2026-05-18T02:50:51Z","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":"f688cfdb1ca7dfc3fec6cf7d30110a20c45661a510079e3df6632ad6e6057547","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-05-29T13:02:22Z","title_canon_sha256":"bde264d55d14622001c8e37410a0983ff1e432a63d8b3cc0871445ba1a743a0d"},"schema_version":"1.0","source":{"id":"1405.7541","kind":"arxiv","version":1}},"canonical_sha256":"c396bd67e6918b5a0d76df72b40a29a1507f1c2f1e178941511a14bd081c04fe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c396bd67e6918b5a0d76df72b40a29a1507f1c2f1e178941511a14bd081c04fe","first_computed_at":"2026-05-18T02:50:51.014530Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:50:51.014530Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dqGYjnk3r41N2YqllkIl8WsvAICtcR1vXpibEN90DSgo39ilb/l1g7nKwxXs3gg2EJ6dllv6ZAN23ihSKApQBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:50:51.015180Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.7541","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0689286d8eb7a6b25fd9f605bf5ae1fad0969180dc25f95c82b00078d1caa6fa","sha256:516909a56453da430aeef671bb686f9a595d599149467464a328da7ea79ff78c"],"state_sha256":"112abf459bfe63fa2925bd1e803ad895a2c126b4dcc6ca5a7a0dca4b100d1ef1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eWkIzeBxTTo5S04JWZaK+HqKoSpRj+1lJdMu16AHjqpOAC/dB+U8JAuBbz2myQdC351E/CNB1trvAb2D5zd/Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T08:32:38.571223Z","bundle_sha256":"e789f8c5f3e7baaabc5768b894b9bb43aab294308c57341e8a75b87d04fb8b25"}}