{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:FVFTY2BI55YAGOAM4RWE6S42JY","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":"069693d074d453302e6e7265d0910167fe0495e4e26c5124d872712eda856ae6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-06-02T09:37:48Z","title_canon_sha256":"00efc90de94d659266b33388aa3309d315956de2dcb5eae5e728826cbcf217f5"},"schema_version":"1.0","source":{"id":"1206.0358","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.0358","created_at":"2026-05-18T03:54:25Z"},{"alias_kind":"arxiv_version","alias_value":"1206.0358v1","created_at":"2026-05-18T03:54:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.0358","created_at":"2026-05-18T03:54:25Z"},{"alias_kind":"pith_short_12","alias_value":"FVFTY2BI55YA","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"FVFTY2BI55YAGOAM","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"FVFTY2BI","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:2975afc027cb989eafd77f906cc677ef319c67bafe52e245b538de3bf4d83ef3","target":"graph","created_at":"2026-05-18T03:54:25Z","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"},"paper":{"abstract_excerpt":"In the representation theory of finite groups, there is a well-known and important conjecture, due to Brou\\'e saying that for any prime p, if a p-block A of a finite group G has an abelian defect group P, then A and its Brauer corresponding block B of the normaliser N_G(P) of P in G are derived equivalent. We prove in this paper, that Brou\\'e's abelian defect group conjecture, and even Rickard's splendid equivalence conjecture are true for the faithful 3-block A with an elementary abelian defect group P of order 9 of the double cover 2.HS of the Higman-Sims sporadic simple group. It then turns","authors_text":"Felix Noeske, J\\\"urgen M\\\"uller, Shigeo Koshitani","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-06-02T09:37:48Z","title":"Brou\\'e's abelian defect group conjecture holds for the double cover of the Higman-Sims sporadic simple group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.0358","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":"sha256:96f47e8dcbd6b958184aa06dadacb9a6cc5dc3093474134dcbda4ead7d1390de","target":"record","created_at":"2026-05-18T03:54:25Z","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":"069693d074d453302e6e7265d0910167fe0495e4e26c5124d872712eda856ae6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-06-02T09:37:48Z","title_canon_sha256":"00efc90de94d659266b33388aa3309d315956de2dcb5eae5e728826cbcf217f5"},"schema_version":"1.0","source":{"id":"1206.0358","kind":"arxiv","version":1}},"canonical_sha256":"2d4b3c6828ef7003380ce46c4f4b9a4e079b445ac52399a702596f7df70aa1fd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2d4b3c6828ef7003380ce46c4f4b9a4e079b445ac52399a702596f7df70aa1fd","first_computed_at":"2026-05-18T03:54:25.171725Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:54:25.171725Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"onjdFDckCmWHR9WXY4rrnCGxmbh++SdB/0rbWL0Vli0ZGMFZpcS/2aaitFWKdWiSe+bnz3K8P2tMwsYHbckkCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:54:25.172152Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.0358","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:96f47e8dcbd6b958184aa06dadacb9a6cc5dc3093474134dcbda4ead7d1390de","sha256:2975afc027cb989eafd77f906cc677ef319c67bafe52e245b538de3bf4d83ef3"],"state_sha256":"7d6bd04f7761c2fd457809f8c8d71da3f5db67dfde1cab48d8821a79c0dfc66a"}