{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:2JHIHS2Y6DEOGLRH6HPVYDADQD","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":"d89a0c5d3338a847ea49527b4538ab8fdbba0175dedf35e4fdd704bb9b88557f","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2020-11-13T07:24:13Z","title_canon_sha256":"2f32759c545e84982b82851f9f78ffc06531f9e9c308eb5631ed3d8c77843e88"},"schema_version":"1.0","source":{"id":"2011.06793","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2011.06793","created_at":"2026-07-05T01:51:25Z"},{"alias_kind":"arxiv_version","alias_value":"2011.06793v1","created_at":"2026-07-05T01:51:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2011.06793","created_at":"2026-07-05T01:51:25Z"},{"alias_kind":"pith_short_12","alias_value":"2JHIHS2Y6DEO","created_at":"2026-07-05T01:51:25Z"},{"alias_kind":"pith_short_16","alias_value":"2JHIHS2Y6DEOGLRH","created_at":"2026-07-05T01:51:25Z"},{"alias_kind":"pith_short_8","alias_value":"2JHIHS2Y","created_at":"2026-07-05T01:51:25Z"}],"graph_snapshots":[{"event_id":"sha256:3f2b6de8509013d072c9862240e7e9071b84c273af37c8e1fc201e809d227318","target":"graph","created_at":"2026-07-05T01:51:25Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2011.06793/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The first author has recently classified the Morita equivalence classes of 2-blocks B of finite groups with elementary abelian defect group of order 32. In all but three cases he proved that the Morita equivalence class determines the inertial quotient of B. We finish the remaining cases by utilizing the theory of lower defect groups. As a corollary, we verify Brou\\'e's Abelian Defect Group Conjecture in this situation.","authors_text":"Benjamin Sambale, Cesare G. Ardito","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2020-11-13T07:24:13Z","title":"Brou\\'e's Conjecture for 2-blocks with elementary abelian defect groups of order 32"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.06793","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":"sha256:8cbcdf8fa36c59fb68a9f9170b2d058adecd52d83f38ea58baf909675755bdd9","target":"record","created_at":"2026-07-05T01:51:25Z","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":"d89a0c5d3338a847ea49527b4538ab8fdbba0175dedf35e4fdd704bb9b88557f","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2020-11-13T07:24:13Z","title_canon_sha256":"2f32759c545e84982b82851f9f78ffc06531f9e9c308eb5631ed3d8c77843e88"},"schema_version":"1.0","source":{"id":"2011.06793","kind":"arxiv","version":1}},"canonical_sha256":"d24e83cb58f0c8e32e27f1df5c0c0380c7afd03968de3b8b3f0e8be51919409d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d24e83cb58f0c8e32e27f1df5c0c0380c7afd03968de3b8b3f0e8be51919409d","first_computed_at":"2026-07-05T01:51:25.049503Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:51:25.049503Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"z5zCtFKAV+qCNo6X0SHyCH5rCxOKNX5nfE7fv/XdIL+SfxzgF2T7qZLGJEr1CyiJY8ZiQN7Gy2AJIWyM1gOYAA==","signature_status":"signed_v1","signed_at":"2026-07-05T01:51:25.049836Z","signed_message":"canonical_sha256_bytes"},"source_id":"2011.06793","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8cbcdf8fa36c59fb68a9f9170b2d058adecd52d83f38ea58baf909675755bdd9","sha256:3f2b6de8509013d072c9862240e7e9071b84c273af37c8e1fc201e809d227318"],"state_sha256":"626579dc54b551c54af093a9fcdbecf1a7b9cb15624b9a75255064ce9a2630b1"}