{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2003:M4PQRXIISDS7OY4PJAJYRR3BZN","short_pith_number":"pith:M4PQRXII","canonical_record":{"source":{"id":"math/0301084","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.AT","submitted_at":"2003-01-09T15:04:15Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"27256f7de4d010b2f646a005cb55e734a6a1939f6a826d5e8cf303b326fc587c","abstract_canon_sha256":"54415d0b2673e24a7c5c109ca195d85e5a9c6378244d06ec5851ff25da135e55"},"schema_version":"1.0"},"canonical_sha256":"671f08dd0890e5f7638f481388c761cb664247ebf0dec3c6c1b22eff7c264f2a","source":{"kind":"arxiv","id":"math/0301084","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0301084","created_at":"2026-05-18T02:38:00Z"},{"alias_kind":"arxiv_version","alias_value":"math/0301084v2","created_at":"2026-05-18T02:38:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0301084","created_at":"2026-05-18T02:38:00Z"},{"alias_kind":"pith_short_12","alias_value":"M4PQRXIISDS7","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"M4PQRXIISDS7OY4P","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"M4PQRXII","created_at":"2026-05-18T12:25:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2003:M4PQRXIISDS7OY4PJAJYRR3BZN","target":"record","payload":{"canonical_record":{"source":{"id":"math/0301084","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.AT","submitted_at":"2003-01-09T15:04:15Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"27256f7de4d010b2f646a005cb55e734a6a1939f6a826d5e8cf303b326fc587c","abstract_canon_sha256":"54415d0b2673e24a7c5c109ca195d85e5a9c6378244d06ec5851ff25da135e55"},"schema_version":"1.0"},"canonical_sha256":"671f08dd0890e5f7638f481388c761cb664247ebf0dec3c6c1b22eff7c264f2a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:38:00.454430Z","signature_b64":"FZHKMR9hSeQ9sg6blOnKXmKIB8hgZKqPWCfTx2rkOlViWRd7/oGZtlKL4VErkWDC5PTPbuSACR0nprs8IWkFAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"671f08dd0890e5f7638f481388c761cb664247ebf0dec3c6c1b22eff7c264f2a","last_reissued_at":"2026-05-18T02:38:00.453887Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:38:00.453887Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0301084","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":"2026-05-18T02:38:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gOFdczNJa/lSCLF3xwtJQD446k7bLXZiXqLcqHf425NcsBvx2CBjxgEigQO7ebBerq+BzM/jYU+fuq2xIrLJDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T22:15:31.773567Z"},"content_sha256":"dd73e6d8e9701418fbc9a0d5a2fda7051525adafb43e6399d68afd351f497925","schema_version":"1.0","event_id":"sha256:dd73e6d8e9701418fbc9a0d5a2fda7051525adafb43e6399d68afd351f497925"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2003:M4PQRXIISDS7OY4PJAJYRR3BZN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Construction of 2-local finite groups of a type studied by Solomon and Benson","license":"","headline":"","cross_cats":["math.GR"],"primary_cat":"math.AT","authors_text":"Bob Oliver, Ran Levi","submitted_at":"2003-01-09T15:04:15Z","abstract_excerpt":"A p-local finite group is an algebraic structure with a classifying space which has many of the properties of p-completed classifying spaces of finite groups. In this paper, we construct a family of 2-local finite groups, which are exotic in the following sense: they are based on certain fusion systems over the Sylow 2-subgroup of Spin_7(q) (q an odd prime power) shown by Solomon not to occur as the 2-fusion in any actual finite group. Thus, the resulting classifying spaces are not homotopy equivalent to the 2-completed classifying space of any finite group. As predicted by Benson, these class"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0301084","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":"2026-05-18T02:38:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"277cY3Nmsj9P6ZlmNLAedrnqVI/YgG5Mfm8QZ/VSw8kA/inMidp0aHI3z0ll5+nDVrmR57O57V7BGx759lDvBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T22:15:31.774236Z"},"content_sha256":"29ada3fc1fef07428a97f2a5c98e035b1144891934951ffccffd67486fa45bcd","schema_version":"1.0","event_id":"sha256:29ada3fc1fef07428a97f2a5c98e035b1144891934951ffccffd67486fa45bcd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M4PQRXIISDS7OY4PJAJYRR3BZN/bundle.json","state_url":"https://pith.science/pith/M4PQRXIISDS7OY4PJAJYRR3BZN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M4PQRXIISDS7OY4PJAJYRR3BZN/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":"2026-05-24T22:15:31Z","links":{"resolver":"https://pith.science/pith/M4PQRXIISDS7OY4PJAJYRR3BZN","bundle":"https://pith.science/pith/M4PQRXIISDS7OY4PJAJYRR3BZN/bundle.json","state":"https://pith.science/pith/M4PQRXIISDS7OY4PJAJYRR3BZN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M4PQRXIISDS7OY4PJAJYRR3BZN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:M4PQRXIISDS7OY4PJAJYRR3BZN","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":"54415d0b2673e24a7c5c109ca195d85e5a9c6378244d06ec5851ff25da135e55","cross_cats_sorted":["math.GR"],"license":"","primary_cat":"math.AT","submitted_at":"2003-01-09T15:04:15Z","title_canon_sha256":"27256f7de4d010b2f646a005cb55e734a6a1939f6a826d5e8cf303b326fc587c"},"schema_version":"1.0","source":{"id":"math/0301084","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0301084","created_at":"2026-05-18T02:38:00Z"},{"alias_kind":"arxiv_version","alias_value":"math/0301084v2","created_at":"2026-05-18T02:38:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0301084","created_at":"2026-05-18T02:38:00Z"},{"alias_kind":"pith_short_12","alias_value":"M4PQRXIISDS7","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"M4PQRXIISDS7OY4P","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"M4PQRXII","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:29ada3fc1fef07428a97f2a5c98e035b1144891934951ffccffd67486fa45bcd","target":"graph","created_at":"2026-05-18T02:38:00Z","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 p-local finite group is an algebraic structure with a classifying space which has many of the properties of p-completed classifying spaces of finite groups. In this paper, we construct a family of 2-local finite groups, which are exotic in the following sense: they are based on certain fusion systems over the Sylow 2-subgroup of Spin_7(q) (q an odd prime power) shown by Solomon not to occur as the 2-fusion in any actual finite group. Thus, the resulting classifying spaces are not homotopy equivalent to the 2-completed classifying space of any finite group. As predicted by Benson, these class","authors_text":"Bob Oliver, Ran Levi","cross_cats":["math.GR"],"headline":"","license":"","primary_cat":"math.AT","submitted_at":"2003-01-09T15:04:15Z","title":"Construction of 2-local finite groups of a type studied by Solomon and Benson"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0301084","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:dd73e6d8e9701418fbc9a0d5a2fda7051525adafb43e6399d68afd351f497925","target":"record","created_at":"2026-05-18T02:38:00Z","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":"54415d0b2673e24a7c5c109ca195d85e5a9c6378244d06ec5851ff25da135e55","cross_cats_sorted":["math.GR"],"license":"","primary_cat":"math.AT","submitted_at":"2003-01-09T15:04:15Z","title_canon_sha256":"27256f7de4d010b2f646a005cb55e734a6a1939f6a826d5e8cf303b326fc587c"},"schema_version":"1.0","source":{"id":"math/0301084","kind":"arxiv","version":2}},"canonical_sha256":"671f08dd0890e5f7638f481388c761cb664247ebf0dec3c6c1b22eff7c264f2a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"671f08dd0890e5f7638f481388c761cb664247ebf0dec3c6c1b22eff7c264f2a","first_computed_at":"2026-05-18T02:38:00.453887Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:38:00.453887Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FZHKMR9hSeQ9sg6blOnKXmKIB8hgZKqPWCfTx2rkOlViWRd7/oGZtlKL4VErkWDC5PTPbuSACR0nprs8IWkFAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:38:00.454430Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0301084","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dd73e6d8e9701418fbc9a0d5a2fda7051525adafb43e6399d68afd351f497925","sha256:29ada3fc1fef07428a97f2a5c98e035b1144891934951ffccffd67486fa45bcd"],"state_sha256":"b63dbf770cf5bb7687976b6a2c2e98617d23758c486683837c16f472f9c2ad39"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"olYNPDVBgaeAIuRMJSC+f9aAJajA7l3HBQNdX4mf5EQ0nnNAL7uRtq6w8SWeDLPcZ0Fc8W+ZIrZdZ6Di/DoJBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-24T22:15:31.777884Z","bundle_sha256":"e6a0dacf6cd718779ff40c4a6ed439ac28c81ae1e5c717dfd5c5d14874905bdc"}}